Polyelectrolyte solutions: Intrachain and interchain correlations observed by SANS

Structure and phase behavior of poly(acrylic acid)-ferric ion complex aqueous solutions

In this study, we investigate the conformational evolution and phase behavior of poly(acrylic acid) (PAA) solution upon the introduction of ferric ions through a combination of small angle X-ray scattering (SAXS), turbidity, zeta-potential and pH measurements. Salt-free PAA aqueous solution is a weak polyelectrolyte solution. The introduced ferric ion can coordinate with the carboxylic acid groups, yielding H+ ions to lower the pH value. We find two transitions with increasing concentration of the ferric ions: a polyelectrolyte to apparent good solution transition characterized by the disappearance of the polyelectrolyte peak in the X-ray scattering, and a phase separation characterized by a sharp increase of the turbidity. Detailed analyses of pH and zeta-potential reveal the molecular details of the three regions. Namely, (1) the polyelectrolyte region locates at log[H+] (= -pH) ≫ log(3[Fe3+]), where the H+ ions are mainly contributed from the dissociation of carboxylic acid, and the polymer chains are negatively charged, (2) the good solution region locates at log[H+] ∼ log(3[Fe3+]), where the H+ ions are mainly yielded from coordination between COO- and Fe3+, and polymer chains are nearly neutralized, and (3) the phase separation locates at log[H+] ≪ log(3[Fe3+]), where the Fe3+ ions are not fully coordinated, and charge inversion occurs. The phase separation occurs when the chains are densely and tightly coordinated with Fe3+ ions.

Percus–Yevick structure factors made simple

Measuring the structure factor,S(q), of a dispersion of particles by small-angle X-ray scattering provides a unique method to investigate the spatial arrangement of colloidal particles. However, it is impossible to find the exact location of the particles fromS(q) because some information is inherently lacking in the measured signal. The two standard ways to analyse an experimentalS(q) are then to compare it either with structure factors computed from simulated systems or with analytical ones calculated from approximated systems. However, such approaches may prove inadequate for dispersions of variously polydisperse particles. While Vrij, Bloom and Stell established a mean-field approach that could yield fairly accurate approximations for experimentalS(q), this solution has remained underused because of its mathematical complexity. In the present work, the complete Percus–Yevick solution for general polydisperse hard-sphere systems is derived in a concise form that is straightforward to use. The form of the solution has been simplified enough to provide experimentalists with ready solutions of several commonly encountered particle-radius distributions in real systems (Schulz, truncated normal and inverse Gaussian). The approach is also illustrated with a case study of the exponential radius distribution. Finally, the application of the proposed solution to the power-law radius distribution is discussed in detail by comparing the calculations with experimentally measuredS(q) for an Apollonian packing of spherical droplets recently reported in high-internal-phase-ratio emulsions.

Disappearance of the polyelectrolyte peak in salt-free solutions

We investigate the nature of the polyelectrolyte peak in salt-free solutions by molecular dynamics simulations using a minimal model of polyelectrolyte solutions that includes an explicit solvent and counterions and small angle scattering experiments. It is found that the polyelectrolyte peak progressively disappears as the strength of solvation for the charged species is increased and the scattering profiles start to resemble those of neutral polymer solutions. The disappearance of the polyelectrolyte peak coincides with the emergence of attractive interchain interactions over a wide range of length scales. These findings provide insights into the microscopic origin of the polyelectrolyte peak.

Polyelectrolyte character of rigid rod peptide bundlemer chains constructed via hierarchical self-assembly

Short α-helical peptides were computationally designed to self-assemble into robust coiled coils that are antiparallel, homotetrameric bundles. These peptide bundle units, or 'bundlemers', have been utilized as anisotropic building blocks to construct bundlemer-based polymers via a hierarchical, hybrid physical-covalent assembly pathway. The bundlemer chains were constructed using short linker connections via 'click' chemistry reactions between the N-termini of bundlemer constituent peptides. The resulting bundlemer chains appear as extremely rigid, cylindrical rods in transmission electron microscopy (TEM) images. Small angle neutron scattering (SANS) shows that these bundlemer chains exist as individual rods in solution with a cross-section that is equal to that of a single coiled coil bundlemer building block of ≈20 Å. SANS further confirms that the interparticle solution structure of the rigid rod bundlemer chains is heterogeneous and responsive to solution conditions, such as ionic-strength and pH. Due to their peptidic constitution, the bundlemer assemblies behave like polyelectrolytes that carry an average charge density of approximately 3 charges per bundlemer as determined from SANS structure factor data fitting, which describes the repulsion between charged rods in solution. This repulsion manifests as a correlation hole in the scattering profile that is suppressed by dilution or addition of salt. Presence of rod cluster aggregates with a mass fractal dimension of ≈2.5 is also confirmed across all samples. The formation of such dense, fractal-like cluster aggregates in a solution of net repulsive rods is a unique example of the subtle balance between short-range attraction and long-rage repulsion interactions in proteins and other biomaterials. With computational control of constituent peptide sequences, it is further possible to deconvolute the underlying sequence driven structure-property relationships in the modular bundlemer chains.

Conformational Transitions of Polymer Chains in Solutions Characterized by Fluorescence Resonance Energy Transfer

The critical overlap concentration C* is an important concept in polymer solutions and is defined as the boundary between dilute and semidilute regimes. In this study, the chain conformational changes of polystyrene (PS) with both high (M_n = 200,000 Da) and low (M_n = 13,000 Da) molecular weights in cis-decalin were compared by intrachain fluorescence resonance energy transfer (FRET). The random labeling of donor and acceptor chromophores strategy was employed for long PS chains, whereas chain-end labeling was used for short PS chains. By monitoring the spectroscopic intensity ratio between acceptor and donor, the concentration dependence on chain conformation from dilute to semidilute solutions was determined. Both long and short chains exhibit a conformational transition concentration, above which the polymer chains begin to collapse with concentration significantly. Interestingly, for randomly labeled polymer long chains, such concentration is consistent with C* determined from the viscosity result, below which only slight conformational change of polymer chain takes place. However, for the chain-end labeled short chain, the conformational transition concentration takes place earlier than C*, below which no significant polymer conformation change is observed.

Morphology-Induced Defects Enhance Lipid Transfer Rates

Molecular transfer between nanoparticles has been considered to have important implications regarding nanoparticle stability. Recently, the interparticle spontaneous lipid transfer rate constant for discoidal bicelles was found to be very different from spherical, unilamellar vesicles (ULVs). Here, we investigate the mechanism responsible for this discrepancy. Analysis of the data indicates that lipid transfer is entropically favorable, but enthalpically unfavorable with an activation energy that is independent of bicelle size and long- to short-chain lipid molar ratio. Moreover, molecular dynamics simulations reveal a lower lipid dissociation energy cost in the vicinity of interfaces ("defects") induced by the segregation of the long- and short-chain lipids in bicelles; these defects are not present in ULVs. Taken together, these results suggest that the enhanced lipid transfer observed in bicelles arises from interfacial defects as a result of the hydrophobic mismatch between the long- and short-chain lipid species. Finally, the observed lipid transfer rate is found to be independent of nanoparticle stability.

Fluorescence correlation spectroscopy studies of diffusion of a weak polyelectrolyte in aqueous solutions

We apply fluorescent correlation spectroscopy (FCS) to investigate solution dynamics of a synthetic polyelectrolyte, i.e., a weak polycarboxylic acid in aqueous solutions. The technique brings single molecule sensitivity and molecular specificity to dynamic measurements of polyelectrolyte solutions. Translational diffusion of Alexa-labeled poly(methacrylic acid), PMAA*, chains was studied in very dilute, 10(-4) mg/ml, solutions as a function of solution pH and ionic strength. The observed changes in diffusion coefficients were consistent with about twofold expansion of PMAA* coils when pH was changed from 5 to 8, and with chain contraction for alkaline metal ion concentrations from 0.01 to 0.1 M. The dependence of the hydrodynamic size of PMAA* chains on the counterion type followed the sequence: Li(+)>Na(+) approximately equal to Cs(+)>K(+). The dependence of translational diffusion on polyacid concentration was weak at the low concentration limit, but chain motions were significantly slower at higher polymer concentrations when PMAA chains overlapped. Finally, measurements of dynamics of PMAA* chains in "salt-free" solutions showed that self-diffusion of PMAA* chains significantly slowed down when PMAA concentration was increased, probably reflecting the sensitivity of PMAA* translational motions to the onset of interchain domain formation. These results illustrate the utility of the FCS technique for studying hydrodynamic sizes of polyelectrolyte coils in response to variation in solution pH or concentration of salt and polyelectrolytes. They also suggest that FCS will be a promising technique for selective observation of the dynamics of polyelectrolyte components in complex polymer mixtures.

Charge Stoichiometry Inside Polyelectrolyte−Protein Complexes: A Direct SANS Measurement for the PSSNa−Lysozyme System

We study by small angle neutron scattering and UV titration how the ratio of negative to positive charges, [-]/[+](intro), acts on the structure of complexes formed by short negatively charged polyelectrolyte chains (PSS) and globular positively charged proteins (lysozyme). The range of [-]/[+](intro) lies between 0.65 and 3.33. In all ratios, dense primary complexes are formed with radii around 10 nm. The species composition and the water content of the primary complexes are precisely obtained by the systematic use of the contrast matching of (deuterated) polymer or protein in SANS, yielding the compactness and the inner charge ratio [-]/[+](inner). The primary complexes have (i) an inner charge ratio [-]/[+](inner) close to 1 whatever [-]/[+](intro), (ii) a high total volume fraction (0.25-0.4), (iii) a constant radius (75 A) for [-]/[+](intro) <or= 1 that increases up to 150 A for [-]/[+](introduced) > 1, and (iv) a shell of PSS chains when [-]/[+](intro) > 1. Moreover, UV titration shows that there are free proteins if [-]/[+](introduced) < 1 and free PSS chains if [-]/[+](intro) is largely superior to 1. Hence, we observe that the primary complexes reach a finite size, controlled by electrostatic repulsion, and then aggregate at a higher scale with a fractal dimension of 2.1 characteristic of reaction-limited colloidal aggregation.

The triple isotopic substitution method in small angle neutron scattering. Application to the study of the ternary complex EF-Tu.GTP.aminoacyl-tRNA

The TIS (triple isotopic substitution) method in small angle neutron scattering was applied to determine the radius of gyration of polypeptide elongation factor Tu (EF-Tu) from E. coli associated with GDP and within the ternary complex EF-Tu.GTP.aminoacyl-tRNA. The results showed that, within errors of about 1 A, there is no change in the radius of gyration of the EF-Tu moiety upon ternary complex formation. Experiments were performed in H2O buffer, in which complex formation could be followed on an absolute scale because of the relatively large contrast of both protein and tRNA. The TIS method is based on the analysis of a scattering curve that is the difference between the scattering of two solutions containing appropriately deuterium labelled particles. A necessary condition for the application of the method is that the two solutions are identical in all respects except for the extent of deuterium label. The main properties of TIS that make it very useful for the study of complex particles in solution were confirmed by this study. These are the elimination of interparticle effects in the difference curve, the 'invisibility' of unlabelled parts of the particles and the independence of the difference scattering curve on the buffer 2H2O-H2O content. The last property is of particular interest for the study of interactions that may be influenced by 2H2O, since, contrary to classical contrast variation methods, TIS experiments can be performed in H2O buffer alone.