Necklace Globule and Counterion Condensation

Dilute polyelectrolyte solutions: recent progress and open questions

Polyelectrolytes are a class of polymers possessing ionic groups on their repeating units. Since counterions can dissociate from the polymer backbone, polyelectrolyte chains are strongly influenced by electrostatic interactions. As a result, the physical properties of polyelectrolyte solutions are significantly different from those of electrically neutral polymers. The aim of this article is to highlight key results and some outstanding questions in the polyelectrolyte research from recent literature. We focus on the influence of electrostatics on conformational and hydrodynamic properties of polyelectrolyte chains. A compilation of experimental results from the literature reveals significant disparities with theoretical predictions. We also discuss a new class of polyelectrolytes called poly(ionic liquid)s that exhibit unique physical properties in comparison to ordinary polyelectrolytes. We conclude this review by listing some key research challenges in order to fully understand the conformation and dynamics of polyelectrolytes in solutions.

The conformational phase diagram of neutral polymers in the presence of attractive crowders

Extensive coarse-grained molecular dynamics simulations are performed to investigate the conformational phase diagram of a neutral polymer in the presence of attractive crowders. We show that, for low crowder densities, the polymer predominantly shows three phases as a function of both intra-polymer and polymer-crowder interactions: (1) weak intra-polymer and weak polymer-crowder attractive interactions induce extended or coil polymer conformations (phase E), (2) strong intra-polymer and relatively weak polymer-crowder attractive interactions induce collapsed or globular conformations (phase CI), and (3) strong polymer-crowder attractive interactions, regardless of intra-polymer interactions, induce a second collapsed or globular conformation that encloses bridging crowders (phase CB). The detailed phase diagram is obtained by determining the phase boundaries delineating the different phases based on an analysis of the radius of gyration as well as bridging crowders. The dependence of the phase diagram on strength of crowder-crowder attractive interactions and crowder density is clarified. We also show that when the crowder density is increased, a third collapsed phase of the polymer emerges for weak intra-polymer attractive interactions. This crowder density-induced compaction is shown to be enhanced by stronger crowder-crowder attraction and is different from the depletion-induced collapse mechanism, which is primarily driven by repulsive interactions. We also provide a unified explanation of the observed re-entrant swollen/extended conformations of the earlier simulations of weak and strongly self-interacting polymers in terms of crowder-crowder attractive interactions.

Structure of swollen hollow polyelectrolyte nanogels with inhomogeneous cross-link distribution

HYPOTHESIS

Recently, it has become possible to synthesize hollow polyelectrolyte nano- and microgels. The shell permeability can be controlled by external stimuli, while the cavity can serve as a storage place for guest molecules. However, there is a lack of a detailed understanding at the molecular level regarding the role of the network topology, inhomogeneities of the distribution of cross-links, and the impact of the electrostatics on the structural response of hollow microgel to external stimuli. To bridge these gaps, molecular dynamics (MD) of computer simulations are used.

EXPERIMENTS

Here, we propose a fresh methodology to create realistic hollow microgel particles in silico. The technique involves a gradual change in the average local length of subchains depending on the distance to the center of mass of the microgel particles resulting in the microgels with a non-uniform distribution of cross-linking species. In particular, a series of microgels with (i) a highly cross-linked inner part of the shell and gradually decreased cross-linker concentration towards the periphery, (ii) microgels with loosely cross-linked inner and outer parts, as well as (iii) microgels with a more-or-less homogeneous structure, have been created and validated. Counterions and salt ions are taken into account explicitly, and electrostatic interactions are described by the Coulomb potential.

FINDINGS

Our studies reveal a strong dependence of the microgel swelling response on the network topology. Simple redistribution of cross-links plays a significant role in the structure of the microgels, including cavity size, microgel size, fuzziness, and extension of the inner and outer parts of the microgels. Our results indicate the possibilities of qualitative justification of the structure of the hollow microgels in the experiments by measuring the relative change in the size of the sacrificial core to the size of the cavity and by estimation of a power law function, [Formula: see text] , of the hydrodynamic radius of the hollow microgels as a function of added salt concentration.

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.

The effect of explicit polarity on the conformational behavior of a single polyelectrolyte chain

In this work using dissipative particle dynamics simulations with explicit treatment of polar species we demonstrate that the molecular nature of dielectric media has a significant impact on swelling and collapse of a polyelectrolyte chain in a dilute solution. We show that the small-scale effects related to the presence of polar species lead to the intensification of the electrostatic interactions when the charges are close to each other and/or their density is high enough. As a result, the electrostatic strength , usually regarded as the main parameter governing the polyelectrolyte chain collapse, does not have a universal meaning: the value of λ at which the coil-to-globule transition occurs is found to be dependent on the specific fixed value of the solvent bulk permittivity ε while varying the monomer unit charge Q and vice versa. This effect is observed even when the backbone and the counterions have the same polarity as the solvent beads, i.e. no dielectric mismatch is present. The reason for such behavior is rationalized in terms of the "effective" dielectric permittivity ε^eff which depends on the volume fraction φ of charged units inside the polymer chain volume; using ε^eff instead of ε collapses all data onto one master curve describing the chain shrinking with λ. Furthermore, it is shown that a polar chain adopts less swollen conformations in the polyelectrolyte regime and collapses more easily compared to a non-polar chain.

Kinetics of charged polymer collapse in poor solvents

Extensive molecular dynamics simulations, using simple charged polymer models, have been employed to probe the collapse kinetics of a single flexible polyelectrolyte (PE) chain under implicit poor solvent conditions. We investigate the role of the charged nature of PE chain (A), valency of counterions (Z) on the kinetics of such PE collapse. Our study shows that the collapse kinetics of charged polymers are significantly different from those of the neutral polymer and that the finite-size scaling behavior of PE collapse times does not follow the Rouse scaling as observed in the case of neutral polymers. The critical exponent for charged PE chains is found to be less than that of neutral polymers and also exhibits dependence on counterion valency. The coarsening of clusters along the PE chain suggests a multi-stage collapse and exhibits opposite behavior of exponents compared to neutral polymers: faster in the early stages and slower in the later stages of collapse.

Nano-Assembly of Quisinostat and Biodegradable Macromolecular Carrier Results in Supramolecular Complexes with Slow-Release Capabilities

Self-assembly of ionically charged small molecule drugs with water-soluble biodegradable polyelectrolytes into nano-scale complexes can potentially offer a novel and attractive approach to improving drug solubility and prolonging its half-life. Nanoassemblies of quisinostat with water-soluble PEGylated anionic polyphosphazene were prepared by gradient-driven escape of solvent resulting in the reduction of solvent quality for a small molecule drug. A study of binding, analysis of composition, stability, and release profiles was conducted using asymmetric flow field flow fractionation (AF4) and dynamic light scattering (DLS) spectroscopy. Potency assays were performed with WM115 human melanoma and A549 human lung cancer cell lines. The resulting nano-complexes contained up to 100 drug molecules per macromolecular chain and displayed excellent water-solubility and improved hemocompatibility when compared to co-solvent-based drug formulations. Quisinostat release time (complex dissociation) at near physiological conditions in vitro varied from 5 to 14 days depending on initial drug loading. Multimeric complexes displayed dose-dependent potency in cell-based assays and the results were analyzed as a function of complex concentration, as well as total content of drug in the system. The proposed self-assembly process may present a simple alternative to more sophisticated delivery modalities, namely chemically conjugated prodrug systems and nanoencapsulation-based formulations.

Conformational behavior of a semiflexible dipolar chain with a variable relative size of charged groups via molecular dynamics simulations

The conformational behavior of an isolated semiflexible dipolar chain has been studied by molecular dynamics simulations. The dipolar chain was modeled as a backbone chain of charged beads, each containing an oppositely charged unit connected to it by a rigid spring. The main focus was on the effect of the backbone chain rigidity and the size of the charged groups on the morphology of the collapsed states of the chain formed in low-polar media where the electrostatic interactions are essential. It has been found that the stable globular conformations of the long chain of N = 256 backbone beads are a toroid and an elliptical globule. The macroscopic parameters (such as the radius of gyration and shape factors) as well as the local characteristics of these conformations (radial density distributions of ions, orientational correlations of chain segments, dipoles etc.) are studied depending on the chain stiffness. The regions of stability of a torus and an elliptical globule are found for the dipolar chains with variable dipole length and stiffness, which depend on the strength of electrostatic interactions. It has been shown that a size asymmetry of oppositely charged beads destabilizes globular states favoring elongated chain conformations. A coexistence of various metastable states was demonstrated for shorter chains of N = 128, 64, and 32.

Tuning the collapse transition of weakly charged polymers by ion-specific screening and adsorption

The experimentally observed swelling and collapse response of weakly charged polymers to the addition of specific salts displays quite convoluted behavior that is not easy to categorize. Here we use a minimalistic implicit-solvent/explicit-salt simulation model with a focus on ion-specific interactions between ions and a single weakly charged polyelectrolyte to qualitatively explain the observed effects. In particular, we demonstrate ion-specific screening and bridging effects cause collapse at low salt concentrations whereas the same strong ion-specific direct interactions drive re-entrant swelling at high concentrations. Consistently with experiments, a distinct salt concentration at which the salting-out power of anions inverts from the reverse to direct Hofmeister series is observed. At this so called isospheric point, the ion-specific effects vanish. Furthermore, with additional simplifying assumptions, an ion-specific mean-field model is developed for the collapse transition which quantitatively agrees with the simulations. Our work demonstrates the sensitivity of the structural behavior of charged polymers to the addition of specific salt beyond simple screening and shall be useful for further guidance of experiments.

Effect of counterion excluded volume on the conformational behavior of polyelectrolyte chains

Conformational behavior of a single strongly charged polyelectrolyte chain in a dilute solution is studied by molecular dynamics simulations. The novel feature of the model is variation of the excluded volume of counterions for investigating its effect on the chain conformation, especially in low-polar media. It has been confirmed that the chain with conventional counterions collapses into a dense globule with increasing electrostatic interactions. However, if the counterions are bulky enough, they prevent the chain collapse even in media with strong electrostatic interactions. They stay bound in the vicinity of the backbone of the chain that adopts a swollen conformation. In this conformation, the scaling relation for the polymer dimensions with the chain length is the same as for neutral macromolecules in a good solvent, however the polyelectrolyte chain complexed with bulky counterions has a larger gyration radius than its uncharged analogue due to the excluded volume of the counterions contributing to the chain rigidity. Study of the counterion mobility has shown that, similar to the conventional counterions, the bulky counterions do not form stable ion pairs with ions on the polymer chain even in media with strong electrostatic interactions, but rather freely move along the chain backbone. In solutions containing mixtures of counterions with a bimodal size distribution, the conformations of linear polyelectrolytes depend considerably on the fraction of bulky counterions. Furthermore, a kind of intramolecular microphase separation can take place within a polyelectrolyte globule with the formation of a core-shell particle: the smaller counterions concentrate within the globular core while the bulkier counterions form a shell on the globule surface. The stability of the core-shell globule depends on the relative size of the counterions as well as their fractions in the solution. Thus, fine tuning of the balance between the counterion excluded volume and the electrostatic interactions opens new ways for controlling the conformational behavior of polyelectrolytes.

Continuous, size and shape-control synthesis of hollow silica nanoparticles enabled by a microreactor-assisted rapid mixing process

Hollow silica nanoparticles (HSNPs) were synthesized using a microreactor-assisted system with a hydrodynamic focusing micromixer. Due to the fast mixing of each precursor in the system, the poly(acrylic acid) (PAA) thermodynamic-locked (TML) conformations were protected from their random aggregations by the immediately initiated growth of silica shells. When altering the mixing time through varying flow rates and flow rate ratios, the different degrees of the aggregation of PAA TML conformations were observed. The globular and necklace-like TML conformations were successfully captured by modifying the PAA concentration at the optimized mixing condition. Uniform HSNPs with an average diameter ∼30 nm were produced from this system. COMSOL numerical models was established to investigate the flow and concentration profiles, and their effects on the formation of PAA templates. Finally, the quality and utility of these uniform HSNPs were demonstrated by the fabrication of antireflective thin films on monocrystalline photovoltaic cells which showed a 3.8% increase in power conversion efficiency.

Complexation of Polyelectrolytes with Hydrophobic Drug Molecules in Salt-Free Solution: Theory and Simulations

The delivery and dissolution of poorly soluble drugs is challenging in the pharmaceutical industry. One way to significantly improve the delivery efficiency is to incorporate these hydrophobic small molecules into a colloidal polyelectrolyes(PE)-drug complex in their ionized states. Despite its huge application value, the general mechanism of PE collapse and complex formation in this system has not been well understood. In this work, by combining a mean-field theory with extensive molecular simulations, we unveil the phase behaviors of the system under dilute and salt-free conditions. We find that the complexation is a first-order-like phase transition triggered by the hydrophobic attraction between the drug molecules. Importantly, the valence ratio between the drug molecule and PE monomer plays a crucial role in determining the stability and morphology of the complex. Moreover, the sign of the zeta potential and the net charge of the complex are found to be inverted as the hydrophobicity of the drug molecules increases. Both theory and simulation indicate that the complexation point and complex morphology and the electrostatic properties of the complex have a weak dependence on chain length. Finally, the dynamics aspect of PE-drug complexation is also explored, and it is found that the complex can be trapped into a nonequilibrium glasslike state when the hydropobicity of the drug molecule is too strong. Our work gives a clear physical picture behind the PE-drug complexation phenomenon and provides guidelines to fabricate the colloidal PE-drug complex with the desired physical characteristics.

Adsorption of polyelectrolytes to like-charged substrates induced by multivalent counterions as exemplified by poly(styrene sulfonate) and silica

The present study demonstrates that multivalent counterions trigger adsorption of polyelectrolytes on a like-charged substrate. In particular, adsorption of polystyrene sulfonate on silica is studied experimentally in NaCl, MgCl2, and LaCl3 solutions by optical reflectivity. While adsorption is negligible in the presence of Na(+), the polyelectrolyte adsorbs in the presence of Mg(2+) and La(3+). The adsorbed amount of the polyelectrolyte goes through a maximum as a function of the salt concentration. This maximum increases with increasing valence and shifts to lower salt concentrations. At low salt concentration, the adsorption is negligible. At intermediate salt level, ripening and multilayer formation leads to continuous growth of the adsorbed layer. At higher salt level, blocking and formation of a monolayer lead to saturation. These results are tentatively interpreted in terms of a charge reversal of the polyelectrolyte-metal complex. The molecular mass of the polyelectrolyte has an important effect on the adsorption behavior, whereby the tendency towards ripening becomes more pronounced at large molecular mass.

Confined polyelectrolytes: The complexity of a simple system

The interaction between polyelectrolytes and counterions in confined situations and the mutual relationship between chain conformation and ion condensation is an important issue in several areas. In the biological field, it assumes particular relevance in the understanding of the packaging of nucleic acids, which is crucial in the design of gene delivery systems. In this work, a simple coarse-grained model is used to assess the cooperativity between conformational change and ion condensation in spherically confined backbones, with capsides permeable to the counterions. It is seen that the variation on the degree of condensation depends on counterion valence. For monovalent counterions, the degree of condensation passes through a minimum before increasing as the confining space diminishes. In contrast, for trivalent ions, the overall tendency is to decrease the degree of condensation as the confinement space also decreases. Most of the particles reside close to the spherical wall, even for systems in which the density is higher closer to the cavity center. This effect is more pronounced, when monovalent counterions are present. Additionally, there are clear variations in the charge along the concentric layers that cannot be totally ascribed to polyelectrolyte behavior, as shown by decoupling the chain into monomers. If both chain and counterions are confined, the formation of a counterion rich region immediately before the wall is observed. Spool and doughnut-like structures are formed for stiff chains, within a nontrivial evolution with increasing confinement.

Coassembly of aromatic dipeptides into biomolecular necklaces

This paper describes the formation of complex peptide-based structures by the coassembly of two simple peptides, the diphenylalanine peptide and its tert-butyl dicarbonate (Boc) protected analogue. Each of these peptides can self-assemble into a distinct architecture: the diphenylalanine peptide into tubular structures and its analogue into spheres. Integrated together, these peptides coassemble into a construction of beaded strings, where spherical assemblies are connected by elongated elements. Electron and scanning force microscopy demonstrated the morphology of these structures, which we termed "biomolecular necklaces". Additional experiments indicated the reversibility of the coassembly process and the stability of the structures. Furthermore, we suggest a possible mechanism of formation for the biomolecular necklaces. Our suggestion is based on the necklace model for polyelectrolyte chains, which proposes that a necklace structure appears as a result of counterion condensation on the backbone of a polyelectrolyte. Overall, the approach of coassembly, demonstrated using aromatic peptides, can be adapted to any peptides and may lead to the development and discovery of new self-assembled architectures formed by peptides and other biomolecules.

Experimental and theoretical approach to nonequivalent adsorption of novel dicephalic ammonium surfactants at the air/solution interface

The interfacial behavior of novel dicephalic cationic surfactants, N,N-bis[3,3'-(trimethylammonio)propyl]alkylamide dibromides and N,N-bis[3,3'-(trimethylammonio)propyl]alkylamide dimethylsulfates, was analyzed both experimentally and theoretically in comparison to their linear standards, 3-[(trimethylammonio)propyl]dodecanamide bromide and 3-[(trimethylammonio)propyl]dodecanamide methylsulfate. Adsorption of the studied double head-single tail surfactants depends strongly upon their structure, making them less surface active in comparison to the single head-single tail structures having the same alkyl chain length. Surface tension isotherms of aqueous solutions of the studied dicephalic derivatives were measured using the pendant drop shape analysis method and interpreted with the so-called surface quasi-two-dimensional electrolyte (STDE) model of ionic surfactant adsorption. The model is based on the assumption that the surfactant ions and counterions (bromide and methylsulfate ions in the studied case) undergo nonequivalent adsorption within the Stern layer, and it allows for accounting for the formation of surfactant ion-counterion associates in the case of multivalent surfactant headgroup ions. As a result, good agreement between theory and experiment was obtained. Additionally, the presence of surfactant-counterion complexes was successfully confirmed by both measurements of the concentration of free bromide ions in solution and molecular modeling simulations. The results of the present study may prove useful in the potential application of the investigated dicephalic cationic surfactants.

Coarse-grained molecular dynamics simulations of DNA condensation by block copolymer and formation of core-corona structures

Coarse-grained molecular dynamics simulations are used to study the condensation of single polyanion chains with block copolymers composed of cationic and neutral blocks. The simulations are an effort to model complexes formed with DNA and cationic copolymers such as polyethylenimine-g-polyethylene glycol which have been used in gene delivery. The simulations reveal that increases in the cationic block length of the copolymer result in greater condensation of the polyanion. The ability of the complexes to form core-corona structures, with the neutral blocks of the copolymers forming a corona around a dense core formed from the charged beads, is investigated. The core-corona structure is shown to be dependent on both condensation of the polyanion chain and the length of the neutral block of the copolymer. Increasing the length of the cationic and neutral blocks of the copolymer both result in improvement in the core-corona structure. The internal structure of the complex core is shown to be a function of the architecture of the copolymer. Complexes formed from linear diblock copolymers have homogeneous cores with similarly arranged cationic and anionic beads; however, complexes formed with star-shaped copolymers have a layered core structure, with anionic beads found in the center of the cores.

Effective charge and coil-globule transition of a polyelectrolyte chain

Considering the adsorption of counterions on an isolated polyelectrolyte (PE) chain and using a variational theory, phase boundaries and the critical point for the first-order coil-globule transition are calculated. The transition is induced cooperatively by counterion adsorption and chain conformations and the calculation is done self-consistently. The size of the PE chain is a single-valued function of charge. The discontinuous transition of the coil size is accompanied by a discontinuous transition of the charge. Phase boundaries for the coil-globule transitions induced by both Coulomb strength (inverse temperature or dielectric constant) and ionic strength (salt) show that the PE chain collapses at a substantially lower Coulomb strength in the presence of salt. In the expanded state of the coil, an analytical formula is derived for the effective charge of the chain for conditions where the coupling between chain conformations and counterion adsorption is weak. In general, the dielectric heterogeneity of the solvent close to the polymer backbone is found to play a crucial role in the charge regularization and the chain collapse.

Morphologies of planar polyelectrolyte brushes in a poor solvent: molecular dynamics simulations and scaling analysis

Using molecular dynamics simulations and scaling analysis, we study the effect of the solvent quality for the polymer backbone, the strength of the electrostatic interactions, the chain degree of polymerization, and the brush grafting density on conformations of the planar polyelectrolyte brushes in salt-free solutions. Polyelectrolyte brush forms: (1) vertically oriented cylindrical aggregates (bundles of chains), (2) maze-like aggregate structures, or (3) thin polymeric layer covering a substrate. These different brush morphologies appear as a result of the fine interplay between electrostatic and short-range monomer-monomer interactions. The brush thickness shows nonmonotonic dependence on the value of the Bjerrum length. It first increases with the increasing value of the Bjerrum length, and then it begins to decrease. This behavior is a result of counterion condensation within a brush volume.

Charge correlation effects on ionization of weak polyelectrolytes

Ionization curves of weak polyelectrolytes were obtained as a function of the charge coupling strength from Monte Carlo simulations. In contrast to many earlier studies, the present work treats counterions explicitly, thus allowing the investigation of charge correlation effects at strong couplings. For conditions representing typical weak polyelectrolytes in water near room temperature, ionization is suppressed because of interactions between nearby dissociated groups, as also seen in prior work. A novel finding here is that, for stronger couplings, relevant for non-aqueous environments in the absence of added salt, the opposite behavior is observed-ionization is enhanced relative to the behavior of the isolated groups due to ion-counterion correlation effects. The fraction of dissociated groups as a function of position along the chain also behaves non-monotonically. Dissociation is highest near the ends of the chains for aqueous polyelectrolytes and highest at the chain middle segments for non-aqueous environments. At intermediate coupling strengths, dissociable groups appear to behave in a nearly ideal fashion, even though chain dimensions still show strong expansion effects due to ionization. These findings provide physical insights on the impact of competition between acid/base chemical equilibrium and electrostatic attractions in ionizable systems.

Single molecular pair interactions between hydrophobically modified hydroxyethyl cellulose and amylose determined by dynamic force spectroscopy

Interactions among HMHEC (hydrophobically modified hydroxyethyl cellulose) and between HMHEC and amylose were investigated by means of dynamic force spectroscopy of single molecular pairs. The technique was realized using a scanning probe based platform, and the molecular pair interactions were investigated in aqueous solutions over a range of force loading rates. Both hydrophobic interactions among hydrophobe C(16) alkyl side chains in HMHEC and association between these hydrophobes in HMHEC and amylose showed a stretching type peak. The distribution analysis of rupture force based on Bell-Evans's model revealed that the peaks had a most probable rupture force ranging from 27 pN at a force loading rate r(f) = 0.43 nN/s to 125 pN at r(f) = 170 nN/s for HMHEC-HMHEC, and from 13 pN at r(f) = 0.20 nN/s to 34 pN at r(f) = 33.7 nN/s for HMHEC-amylose interactions. The distance of the energy barrier relative to the minimum, x(beta), and the apparent lifetime in the absence of external force, tau, were found to depend on the force loading rate, and the average values are estimated to be 0.99 nm and 0.89s for HMHEC-HMHEC and 0.31 nm and 0.075s for HMHEC-amylose interactions. The obtained data for these pairwise molecular interactions are underpinning the associative behavior of the macroscopic properties of aqueous solutions of these polysaccharides.

Dielectric properties of differently flexible polyions: a scaling approach

The dielectric relaxations associated with counterion polarization along some typical polyion lengths have been measured in an extended frequency range (from 10 kHz to 2 GHz) for four different polyelectrolyte solutions, differing for the polyion molecular weight and the backbone stiffness. Here, we deal with the so-called intermediate dielectric relaxation, falling between the polarization process concerning the whole polyion chain and the polarization process associated with the field-induced re-orientation of the water molecule dipoles. These observed intermediate relaxations have been characterized by means of two parameters, i.e., the dielectric strength Deltaepsilon and the relaxation frequency nu0, and their dependence on the polyion concentration has been described according to the scaling model of a polyelectrolyte solution. These dependencies follow the expected exponents of the scaling laws, both for the dilute and semidilute (unentangled and entangled) regimes. The different concentration regimes evidenced from dielectric relaxation measurements are in very good agreement with the ones determined by means of the zero-shear viscosity measurements. Our results confirm that the intermediate dielectric relaxation in polyelectrolyte solutions should be attributed to counterion fluctuations along some segments (e.g. the subunits of the Mandel model) of the polyion chain, independently of its overall stiffness. This counterion polarization effect is rather confined to the local structure of the polyion chain instead of the whole chain and it is largely independent of the polyion conformation.

Counterion condensation of differently flexible polyelectrolytes in aqueous solutions in the dilute and semidilute regime

The low-frequency limit of the electrical conductivity (dc conductivity) of differently flexible polyions in aqueous solutions has been measured over an extended polyion concentration range, covering both the dilute and semidilute (entangled and unentangled) regime, up to the concentrated regime. The data have been analyzed taking into account the different flexibility of the polymer chains according to the scaling theory of polyion solutions, in the case of flexible polyions, and according to the Manning model, in the case of rigid polyions. In both cases, the fraction f of free counterions, released into the aqueous phase from the ionizable polyion groups, has been evaluated and its dependence on the polyion concentration determined. Our results show that the counterion condensation follows at least three different regimes in dependence on the polyion concentration. The fraction f of free counterions remains constant only in the semidilute regime (a region that we have named the Manning regime), while there is a marked dependence on the polyion concentration both in the dilute and in the concentrated regime. These results are briefly discussed in the light of the scaling theory of polyelectrolyte aqueous solutions.

Folding transition of a single semiflexible polyelectrolyte chain through toroidal bundling of loop structures

We consider how the DNA coil-globule transition progresses via the formation of a toroidal ring structure. We formulate a theoretical model of this transition as a phenomenon in which an unstable single loop generated as a result of thermal fluctuation is stabilized through association with other loops along a polyelectrolyte chain. An essential property of the chain under consideration is that it follows a wormlike chain model. A toroidal bundle of loop structures is characterized by a radius and a winding number. The statistical properties of such a chain are discussed in terms of the free energy as a function of the fraction of unfolded segments. We also present an actual experimental observation of the coil-globule transition of single giant DNA molecules, T4 DNA (165.5 kbp), with spermidine (3+), where intrachain phase segregation appears at a NaCl concentration of more than 10 mM. Both the theory and experiments lead to two important points. First, the transition from a partially folded state to a completely folded state has the characteristics of a continuous transition, while the transition from an unfolded state to a folded state has the characteristics of a first-order phase transition. Second, the appearance of a partially folded structure requires a folded structure to be less densely packed than in the fully folded compact state.