Self-consistent mode-coupling theory for the viscosity of rod-like polyelectrolyte solutions

A self-consistent mode-coupling theory is presented for the viscosity of solutions of charged rod-like polymers. The static structure factor used in the theory is obtained from polymer integral equation theory; the Debye-H\"{u}ckel approximation is inadequate even at low concentrations. The theory predicts a non-monotonic dependence of the reduced excess viscosity, $\eta_R$, on concentration from the behaviour of the static structure factor in polyelectrolyte solutions. The theory predicts that the peak in $\eta_R$ occurs at concentrations slightly lower than the overlap threshold concentration, $c^\ast$. The peak height increases dramatically with increasing molecular weight and decreases with increased concentrations of added salt. The position of the peak, as a function of concentration divided by $c^\ast$ is independent of salt concentration or molecular weight. The predictions can be tested experimentally.Comment: 9 pages, 9 figures (2 figures added in the revise version

Dielectric relaxation of DNA aqueous solutions

We report on a detailed characterization of complex dielectric response of Na-DNA aqueous solutions by means of low-frequency dielectric spectroscopy (40 Hz - 110 MHz). Results reveal two broad relaxation modes of strength 20<\Delta\epsilon_LF<100 and 5<\Delta\epsilon_HF<20, centered at 0.5 kHz<\nu_LF<70 kHz and 0.1 MHz<\nu_HF<15 MHz. The characteristic length scale of the LF process, 50<L_LF<750nm, scales with DNA concentration as c_DNA^{-0.29\pm0.04} and is independent of the ionic strength in the low added salt regime. Conversely, the measured length scale of the LF process does not vary with DNA concentration but depends on the ionic strength of the added salt as I_s^{-1} in the high added salt regime. On the other hand, the characteristic length scale of the HF process, 3<L_HF<50 nm, varyes with DNA concentration as c_DNA^{-0.5} for intermediate and large DNA concentrations. At low DNA concentrations and in the low added salt limit the characteristic length scale of the HF process scales as c_DNA^{-0.33}. We put these results in perspective regarding the integrity of the double stranded form of DNA at low salt conditions as well as regarding the role of different types of counterions in different regimes of dielectric dispersion. We argue that the free DNA counterions are primarily active in the HF relaxation, while the condensed counterions play a role only in the LF relaxation. We also suggest theoretical interpretations for all these length scales in the whole regime of DNA and salt concentrations and discuss their ramifications and limitations.Comment: 15 pages, 9 figure

Equilibrium Phase Behavior and Mass Transport in Neutral and Oppositely Charged Polymer Assemblies

Polyelectrolyte (PE) complexation (PEC) occurs upon mixing solutions of oppositely charged ‎polyelectrolytes. This electrostatic self-assembly paradigm is also extended to layer-by-layer ‎‎(LbL) assembled polyelectrolyte multilayers (PEM). Despite the broad applications of both PEC ‎and PEM, bulk phase behavior of PEC and mass transport controlling the structure and film ‎growth rate of PEMs and their connection is poorly understood. In this doctoral work, we ‎present a combined experimental and theoretical investigation of PEC and PEM LbL assembly. ‎We first observe that polymer-specific interactions have a profound effect on both PEC and LbL ‎growth rate while salinity has a non-monotonic and a rather universal effect on LbL growth rate ‎of fully ionized polyelectrolytes when normalized by the critical salinity required to suppress ‎PEC. We next develop a free energy model of PEC by incorporating counterion association-‎dissociation, cross-chain ion pairing (IP) and protonation, treating each as a reversible reaction ‎using laws of mass action. The importance of each reaction is controlled by a corresponding ‎chemistry-dependent standard free energy input parameter that could be measured via ‎experimentation or molecular simulations. In monophasic systems, the thermodynamic model can ‎qualitatively explain the shifts in acidity and basicity observed in potentiometric titration of weak ‎PEs in the presence of salt and oppositely charged PEs in accordance with Le Châtelier’s ‎principle. We demonstrate how a competition between counterion condensation and IP can ‎explain the complex coacervation of strongly charged PEs. Binodal diagrams predicted in our ‎model are most sensitive to IP strength both for weak and strong PEs. We compare binodal ‎diagrams predicted by our model against experimental data, and find a plausible parameter set ‎that leads to agreement between them. Finally, we develop a transport modeling framework for ‎LbL assembly by variational minimization of the Rayleighian of a mixture of oppositely charged ‎PEs, simple salt and water with respect to species velocities yielding species flux laws that equate ‎the net mutual friction between components with the diffusional driving force on each species. ‎The latter includes gradients in the conventional mixing chemical potential, electrostatic potential ‎and mechanical stress (only for PEs). We also develop a constitutive equation for mixtures of PEs ‎that accounts for solvent imbibition and IP. The result is a modification of the upper-convected ‎Maxwell model. Our LbL transport model captures PE adsorption and film swelling in the ‎equilibrium limit. A dynamic coupling of elastic stress and diffusion is applied in a different ‎context to an electroneutral system involving drug release from polymer tablets, capturing ‎Fickian, anomalous and case II modes of drug transport that arise naturally from the model. In ‎addition to LbL, the transport framework proposed in this work can be applied to any system of ‎charged and neutral components.‎PHDChemical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143922/1/salehi_1.pd

Inverted critical adsorption of polyelectrolytes in confinement

What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer-surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density $\sigma_c$-defining the adsorption-desorption transition-are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of $\sigma_c$ for the concave interfaces versus the Debye screening length $1/\kappa$ and the extent of confinement $a$ for these three interfaces for small $\kappa a$ values. For large $\kappa a$ the critical adsorption condition approaches the planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness $a$ is of the order of $1/\kappa$. We also rationalize how $\sigma_c(\kappa)$ gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length onto critical adsorption-the effect often hard to tackle theoretically-putting an emphasis on polymers inside attractive spherical cavities.Comment: 12 pages, 10 figures, RevTe

Optical tweezers: wideband microrheology

Microrheology is a branch of rheology having the same principles as conventional bulk rheology, but working on micron length scales and micro-litre volumes. Optical tweezers have been successfully used with Newtonian fluids for rheological purposes such as determining fluid viscosity. Conversely, when optical tweezers are used to measure the viscoelastic properties of complex fluids the results are either limited to the material's high-frequency response, discarding important information related to the low-frequency behavior, or they are supplemented by low-frequency measurements performed with different techniques, often without presenting an overlapping region of clear agreement between the sets of results. We present a simple experimental procedure to perform microrheological measurements over the widest frequency range possible with optical tweezers. A generalised Langevin equation is used to relate the frequency-dependent moduli of the complex fluid to the time-dependent trajectory of a probe particle as it flips between two optical traps that alternately switch on and off.Comment: 13 pages, 6 figures, submitted to Special Issue of the Journal of Optic

On the mesoscopic origins of high viscosities in some polyelectrolyte-surfactant mixtures

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in J. Chem. Phys. 143, 074902 (2015) and may be found at https://doi.org/10.1063/1.4928583.Oppositely charged polyelectrolyte (PE) surfactant mixtures allow the control of rheological parameters of a solution even at fairly low concentrations. For example, addition of 0.3 wt. % of anionic surfactant to a 1 wt. % solution of the polycation JR 400 increases the viscosity by 4 orders of magnitude. Recently, we could show that this increase is related to the formation of mixed, rod-like PE/surfactant aggregates which interconnect several polyelectrolyte chains [Hoffmann et al., Europhys. Lett. 104, 28001 (2013)]. In this paper, we refine our structural model of the aggregates to obtain a more consistent picture of their internal structure for different anionic surfactants. Combining small angle neutron scattering (SANS) and neutron spin-echo (NSE) allows us to determine the size of the aggregates. By comparing different contrasts, the internal structure of the aggregates can be elucidated and it is seen that the PE in the aggregates retains a relatively high freedom of movement. We proceeded to investigate the influence of the surfactant concentration and the surfactant type on structure and dynamics of the mixed aggregates. It is seen that the structural parameters of the aggregates depend very little on the surfactant concentration and headgroup. However, it is crucial to incorporate a sufficient amount of PE in the aggregates to increase the viscosity of the aggregates. By comparing viscous samples at 1 wt. % PE concentration with samples at a PE concentration of 0.3 wt. %, where no significant increase in viscosity is observed, we find that similar aggregates are formed already at this lower PE concentrations. However, the amount of PE incorporated in them is insufficient to interconnect several PE chains and therefore, they do not increase viscosity. So, our detailed investigation combining contrast variation SANS and NSE does not only allow to explain the viscosity behavior but also to deduced detailed information regarding the structures and the dynamics especially of the polyelectrolyte within the complexes.BMBF, 05K13KT1, Probenumgebung und paralle Charakterisierung bei hochpräzisen Neutronen Spin-Echo (NSE) Messungen an komplexen Systemen der weichen Materi