Electrokinetic measurement of hydrodynamic properties of grafted polymer layers on liposome surfaces

Non-monotonic variation of flow strength in nanochannels grafted with end-charged polyelectrolyte layers

The electrokinetic transport of fluids, also called the electroosmotic flow (EOF), in micro/nanoscale devices occurs in promising applications such as electrokinetic energy conversion (EKEC) systems. Recently, EKEC systems grafted with end-charged polyelectrolyte (PE) layers (PELs) have been reported to exhibit higher efficiencies than those of intrinsic systems. Understanding the interplay between the end-charged PELs and electrical double layers (EDLs) on the EOF is crucial for designing highly efficient EKEC systems. The interplay between the end-charged PELs and EDLs on the strength of the EOF (V₀) is studied by explicitly modeling the EOF through nanochannels grafted with end-charged PELs using atomic simulations. The variation of V₀ is examined for nanochannels grafted with PELs at various separations (d = 3.5–0.4 nm) to cover various conformations of PEs, inlcuding mushroom, semi-dilute brushes, and concentrated brushes. We find that V₀ follows a non-monotonic variation as d decreases and this is correlated with the conformation of the PEs. Specifically, as d decreases, V₀ decreases first in the mushroom regime (d = 3.5–2.0 nm), and then V₀ increases in the concentrated brush regime (d = 0.75–0.4 nm). Navigated by the continuum Navier–Stokes–Brinkman model, the above observations are rationalized by the competition between the driving effect from the spatial shift of ions in EDLs and the drag effect from PELs. The insights obtained in this work are important to guide the design of highly efficient EKEC systems by grafting end-charged PELs onto channel surfaces.

A non-monotonic variation of the strength of electroosmotic flow (V₀) is reported for the electroosmotic flow through nanochannels grafted with end-charged polyelectrolytes at various separation using atomic simulations.

Rapid characterization of neutral polymer brush with a conventional zetameter and a variable pinch of salt

The fundamental and practical importance of particle stabilization has motivated various characterization methods for studying polymer brushes on particle surfaces. In this work, we show how one can perform sensitive measurements of neutral polymer coating on colloidal particles using a commercial zetameter and salt solutions. By systematically varying the Debye length, we study the mobility of the polymer-coated particles in an applied electric field and show that the electrophoretic mobility of polymer-coated particles normalized by the mobility of non-coated particles is entirely controlled by the polymer brush and independent of the native surface charge, here controlled with pH, or the surface-ion interaction. Our result is rationalized with a simple hydrodynamic model, allowing for the estimation of characteristics of the polymer coating: the brush length L, and the Brinkman length ξ, determined by its resistance to flows. We demonstrate that the Debye layer provides a convenient and faithful probe to the characterization of polymer coatings on particles. Because the method simply relies on a conventional zetameter, it is widely accessible and offers a practical tool to rapidly probe neutral polymer brushes, an asset in the development and utilization of polymer-coated colloidal particles.

Hydrodynamic Properties of Polymers Screening the Electrokinetic Flow: Insights from a Computational Study

Understanding the hydrodynamic properties of polymeric coatings is crucial for the rational design of molecular transport involving polymeric surfaces and is relevant to drug delivery, sieving, molecular separations, etc. It has been found that the hydrodynamic radius of a polymer segment is an order of magnitude smaller than its physical size, but the origin of this effect does not seem to be well understood. Herein, we study the hydrodynamic properties of polymeric coatings by using molecular dynamics simulations, navigated by the continuous Navier-Stokes-Brinkman model. We confirm that the averaged hydrodynamic radius of a polymer bead is about one order of magnitude smaller than its physical radius, and, in addition, we show that it exhibits a strong dependence on the degree of polymerization. We relate this variation of the hydrodynamic radius to the structural properties and hydrodynamic shielding by surrounding polymer beads. This is done by separating the effects originating from near and far beads. For the near beads, shielding is mainly due to the two nearest beads (of the same polymer) and leads to about a 5-fold reduction in the hydrodynamic radius. Assuming the additivity of the hydrodynamic shielding by far beads, we suggest a simple model, which captures correctly the qualitative behaviour of the hydrodynamic radius with the degree of polymerization. The revealed shielding effects provide important insights relevant to the advanced modelling of hydrodynamic properties of polymeric coatings.

Use of Capillary Electrophoresis for Polysaccharide Studies and Applications

CE applications to charged polysaccharides are briefly reported. A simple procedure is presented to determine the esterification degree of a hyaluronan derivative. In this case the degree of substitution was as low as 14 %.The molecular weight distribution of mannuronic oligosaccharides mixture produced by hydrolysis of native polymannuronic is readily calculated from peak area of the species resolved by CE on the basis of a specific degree of polymerization.The influence of the applied electric field strength on the free solution mobility of hyaluronan samples is briefly addressed for molar masses of the order of 10(5) and 10(6) g/mol. The data are compared with the results obtained for a 50 % galactose substituted HA.Mobility data obtained as a function of buffer pH for a native HA sample as well as for two galactose-amide HA derivatives, having slightly different degrees of substitution, are presented and discussed in terms of the polymer charge density parameters ξ.In most cases, more questions than answers arise from the application of CE to charged polysaccharides. However, perspectives are disclosed for a further understanding of the reliability of CE applied for the structural elucidation of such macromolecules.

Recent Progress and Perspectives in the Electrokinetic Characterization of Polyelectrolyte Films

The analysis of the charge, structure and molecular interactions of/within polymeric substrates defines an important analytical challenge in materials science. Accordingly, advanced electrokinetic methods and theories have been developed to investigate the charging mechanisms and structure of soft material coatings. In particular, there has been significant progress in the quantitative interpretation of streaming current and surface conductivity data of polymeric films from the application of recent theories developed for the electrohydrodynamics of diffuse soft planar interfaces. Here, we review the theory and experimental strategies to analyze the interrelations of the charge and structure of polyelectrolyte layers supported by planar carriers under electrokinetic conditions. To illustrate the options arising from these developments, we discuss experimental and simulation data for plasma-immobilized poly(acrylic acid) films and for a polyelectrolyte bilayer consisting of poly(ethylene imine) and poly(acrylic acid). Finally, we briefly outline potential future developments in the field of the electrokinetics of polyelectrolyte layers.

Effective Condensation of Multivalent Anions into Polyion Complex Micelles Prepared from TiO₂ Nanoparticles and Polyallylamine Bearing Poly(ethylene glycol) Grafts

Physicochemical properties were evaluated for polyion complex micelles (PIC), which were prepared from TiO2 nanoparticles and polyallylamine bearing poly(ethylene glycol) grafts (PAA-g-PEG). The zeta potentials of PIC micelles prepared using PAA-g-PEG with different molecular weights of PEG grafts were measured in different aqueous media (i.e., water, phosphate buffer, and Tris/HCl buffer). The PIC micelles in phosphate buffer and Tris/HCl buffer exhibited quite different zeta potentials despite the same salt concentration (10 mM) of the buffer solutions. More specifically, the zeta potential of the PIC micelles in phosphate buffer was effectively neutralized owing to counteranion condensation effects. The onset of counterion condensation into the PIC micelles was dependent on the valence of the anionic molecules and the ability of the PIC micelles to entrap multivalent anionic molecules. Furthermore, as confirmed by laser confocal microscopy observation, multivalent anionic molecules could be delivered to cultured cells through entrapment in the PIC micelles based on multivalent anion condensation effects.

Electrophoretic mobility of sarcoplasmic reticulum vesicles - analytical model includes amino acid residues of A+P+N domain of Ca(2+)-ATPase and charged lipids

This work is an experimental and theoretical study of electrostatic and hydrodynamic properties of the surface of sarcoplasmic reticulum (SR) membrane using particle electrophoresis. The essential structural components of SR membrane include a lipid matrix and a dense layer of Ca(2+)-ATPases embedded in the matrix. The Ca(2+)-ATPase layer both drives and impedes vesicle mobility. To analyze the experimental mobility data, obtained at pH4.0, 4.7, 5.0, 6.0, 7.5, and 9.0 in 0.1M monovalent (1:1) electrolyte, an analytical solution for the vesicle mobility and electroosmotic flow velocity distribution was obtained by solving the Poisson-Boltzmann and the Navier-Stokes-Brinkman equations. The electrophoretic mobility model includes two sets of charges that represent: (a) charged lipids of the lipid matrix of the vesicle core, and (b) charged amino acid residues of APN domains of Ca(2+)-ATPases. APN domains are assumed to form a charged plane displaced from the surface of lipid matrix. The charged plane is embedded in a frictional layer that represents the surface layer of calcium pumps. Electrophoretic mobility is driven by the charged APN domain and by lipid matrix while the surface layer provides hydrodynamic friction. The charge of APN domain is determined by ionized amino acid residues obtained from the amino acid composition of SERCA1a Ca(2+)-ATPase. Agreement between the measured and the predicted mobility is evaluated by the weighted sum of mobility deviation squared. This model reproduces the experimental dependence of mobility on pH and predicts that APN domains are located in the upper half of the SR vesicle surface layer.

Study of PEGylated lipid layers as a model for PEGylated liposome surfaces: molecular dynamics simulation and Langmuir monolayer studies

We have combined Langmuir monolayer film experiments and all-atom molecular dynamics (MD) simulation of a bilayer to study the surface structure of a PEGylated liposome and its interaction with the ionic environment present under physiological conditions. Lipids that form both gel and liquid-crystalline membranes have been used in our study. By varying the salt concentration in the Langmuir film experiment and including salt at the physiological level in the simulation, we have studied the effect of salt ions present in the blood plasma on the structure of the poly(ethylene glycol) (PEG) layer. We have also studied the interaction between the PEG layer and the lipid bilayer in both the liquid-crystalline and gel states. The MD simulation shows two clear results: (a) The Na(+) ions form close interactions with the PEG oxygens, with the PEG chains forming loops around them and (b) PEG penetrates the lipid core of the membrane for the case of a liquid-crystalline membrane but is excluded from the tighter structure of the gel membrane. The Langmuir monolayer results indicate that the salt concentration affects the PEGylated lipid system, and these results can be interpreted in a fashion that is in agreement with the results of our MD simulation. We conclude that the currently accepted picture of the PEG surface layer acting as a generic neutral hydrophilic polymer entirely outside the membrane, with its effect explained through steric interactions, is not sufficient. The phenomena we have observed may affect both the interaction between the liposome and bloodstream proteins and the liquid-crystalline-gel transition and is thus relevant to nanotechnological drug delivery device design.

On the applicability of the Brinkman equation in soft surface electrokinetics

The Stokes equation is commonly used within the field of electrokinetics of hard impermeable surfaces while the Brinkman equation is adopted for tackling hydrodynamics in the framework of soft (permeable) surface electrokinetics (SSE). The latter was initially proposed for modeling the hydrodynamics in so-called hybrid systems that consist of a porous medium and an adjacent fluid phase basically because the conventional Darcy law or Debye and Bueche model initially proposed for that purpose failed to provide the required velocity and shear stress-continuity conditions at the porous media-fluid interface. However, even though the physical background of the Brinkman equation and its boundary conditions have been discussed when applied to the hydrodynamics of hybrid systems, controversy still remains with respect to their applicability in the field of SSE. Indeed, recent experiments pointed out better agreement between shear flow into a regular array of rods oriented across the flow and the solution of the Brinkman equation for hybrid systems providing a stress-jump boundary condition is taken into account (M.F. Tachie et al., J. Fluid. Mech. 493 (2003) 319). As there is identity in the Brinkman model for hybrid systems and for SSE, the question arises whether the above discontinuity of viscous stress must be incorporated or not into SSE modeling. Recent determination of hydrodynamic penetration length lambda(o)(-1) of swollen and collapsed thermo-responsive films (J.F.L. Duval, R. Zimmermann, A.L. Cordeiro, N. Rein, C. Werner, Langmuir 25 (2009) 10691) suggests that there is no need for a cardinal revision of the Brinkman model, although further experimental investigations are required to support such a conclusion. With regard to these experiments, almost complete agreement between independent determination of lambda(o)(-1) by swelling experiments and its derivation according to Brinkman model was obtained.

Electrokinetics of diffuse soft interfaces. IV. Analysis of streaming current measurements at thermoresponsive thin films

Streaming current measurements were performed on poly(N-isopropylacrylamide)-co-N-(1-phenylethyl) acrylamide [P(NIPAAm-co-PEAAm)] thermoresponsive thin films above and below the transition temperature of the polymer (i.e., at 22 and 4 degrees C, respectively). Electrokinetic measurements (ionic strength 0.01-10 mM KCl, pH 2.5-9.5 in 1 mM KCl) revealed that the charging of the polymer/aqueous solution interface is determined by unsymmetrical adsorption of hydroxide and hydronium ions onto the Teflon AF substrate that supports the hydrogel film. The magnitude of the streaming current significantly decreased with decreasing temperature, that is, when the hydrogel was swelling. The pH- and ionic strength-dependent data for unswollen and swollen films were interpreted on the basis of the here-reported general theory for the electrokinetics of diffuse soft gel layers. The formalism based on the Debye-Brinkman equation for hydrodynamics and the nonlinear Poisson-Boltzmann equation for electrostatics extends previous theoretical studies by considering the most general situation of a charged gel layer supported by a charged rigid surface. Full analytical expression is provided for the streaming current in the limit of homogeneous distribution of segments under low potential conditions. Numerical analysis of the governing transport and electrostatic equations allows for the computation of streaming current for cases where analytical developments are not possible. The theory successfully reproduces the electrokinetic data for the P(NIPAAm-co-PEAAm) copolymer film at 22 and 4 degrees C over the whole range of pH and ionic strength examined. It is found that the 3-fold increase of the hydrogel film thickness with decreasing temperature from 22 to 4 degrees C (i.e., from 23 to 70 nm as measured by ellipsometry), is in line with homogeneous swelling and an increase of the hydrodynamic penetration length (1/lambdao) by a factor of approximately 1.6. Additionally, the hydrodynamic thicknesses (deltaH) of the swollen and unswollen hydrogels are evaluated in terms of their respective hydrodynamic penetration length and electrosurface characteristics of the supporting Teflon AF surface.

The EOF of polymer solutions

The EOF of polymer solutions is analysed in the framework of continuum fluid mechanics and the standard electrokinetic model. Two key aspects are taken into consideration: the non-Newtonian character of the fluid and the polymer concentration near the interface, which greatly modify the fluid viscosity in the region where electroosmosis takes place. A satisfactory mathematical model is derived for the electroosmotic mobility of solutions that present polymer depletion at the wall. The case of solutions containing polymers that adsorb onto the wall is briefly reviewed, and a preliminary approach is discussed for the limit of strong polymer adsorption. In order to illustrate the theoretical discussions, experimental data obtained from aqueous solutions of carboxymethyl cellulose in fused-silica capillaries are presented. Relevant results are observed, which are appropriately captured by the modelling proposed. The fundamental phenomena discussed in this work are of interest in microfluidics and electrophoresis.

Use of capillary electrophoresis for polysaccharide studies and applications

Capillary electrophoresis (CE) applications to charged polysaccharides are briefly reported. A simple procedure is presented to determine the esterification degree of a hyaluronan derivative. In this case, the degree of substitution was as low as 14%. The molecular weight distribution of mannuronic oligosaccharides mixture produced by hydrolysis of native polymannuronic is readily calculated from peak area of the species resolved by CE on the basis of a specific degree of polymerization. The influence of the applied electric field strength on the free solution mobility of hyaluronan samples is briefly addressed for molar masses of the order of 10(5) and 10(6) g/mol. The data are compared with the results obtained for a 50% galactose-substituted hyaluronic acid (HA). Mobility data obtained as a function of buffer pH for a native HA sample as well as for two galactose-amide HA derivatives, having slightly different degrees of substitution, are presented and discussed in terms of the polymer charge density parameters xi. In most cases, more questions than answers arise from the application of CE to charged polysaccharides. However, perspectives are disclosed for a further understanding of the reliability of CE applied for the structural elucidation of such macromolecules.

Adsorption equilibria between liposome membrane formed of phosphatidylcholine and aqueous sodium chloride solution as a function of pH

The effect has been studied of the adsorption of ions (H(+), Na(+), OH(-), Cl(-)) which are present in solution upon the electric charge of the liposome membrane formed of phosphatidylcholine (PC). The surface charge density of the membrane was determined as a function of pH and electrolyte concentration from electrophoretic mobility measurements. The measurements were carried out by the laser-Doppler microelectrophoresis method. A four-equilibria model has been proposed to describe the phenomena occurring on the membrane surface. The equilibria in which the adsorption of other ions on the liposome membrane surface was involved were assumed to exist beside the equilibria in which the H(+) and OH(-) ions were engaged. The idea was confirmed by mathematical calculations. Association constants of the liposome membrane surface with ions of solution (K(AH), K(ANa), K(BOH), K(BCl)) were determined. The proposed model has been proved to be correct by comparing the resulting theoretic charge variation curves of the lecithin membrane with the experimental data.

Hydrodynamics and electrokinetics of spherical liposomes with coatings of terminally anchored poly(ethylene glycol): numerically exact electrokinetics with self-consistent mean-field polymer

A detailed theoretical model is presented to interpret electrokinetic experiments performed on colloids with uncharged polymer layers. The methodology removes many of the degrees of freedom that otherwise have to be accounted for by adopting multiple empirical fitting parameters. Furthermore, the level of detail provides a firm basis for future studies examining liposome surface chemistry and charge, surface-charge mobility, and the dynamics of adsorbed polymer on fluidlike membranes. The model predictions are compared with experimental measurements of the electrophoretic mobility of stealth liposomes with molecular weights of terminally anchored poly(ethylene glycol) (PEG) in the range 0.35-10 kg mol(-1) [J.A. Cohen and V.A. Khorosheva, Colloids Surf. A 195, 113 (2001)]. The experimental data are interpreted by drawing upon self-consistent mean-field calculations of the polymer segment density distributions and numerically exact solutions of the governing transport equations [R.J. Hill, D.A. Saville, and W.B. Russel, J. Colloid Interface Sci. 258, 56 (2003)]. The approach leads to excellent agreement between theory and experiment with one adjustable parameter--the hydrodynamic size (Stokes radius) a(s) approximately equal to 0.175 A of the statistical PEG segments with (Kuhn) length l=7.1 A . The remarkably small Stokes radius is demonstrated to be consistent with other applications of the well-known Debye-Brinkman model and, consequently, this work reveals important limitations of the mean-field hydrodynamic model. Despite such limitations, the "full" electrokinetic model is robust in its predictive capacity. The molecular weights of the terminally anchored PEG span the range where the coatings undergo a transition from mushroomlike to brushlike conformations, and the hydrodynamic size and electrophoretic mobility of the liposomes are demonstrated to be sensitive to the PEG chain length and the effects of double-layer polarization.

Polarizability and complex conductivity of dilute suspensions of spherical colloidal particles with uncharged (neutral) polymer coatings

The polarizability of polymer-coated colloidal particles, as measured via dielectric relaxation spectroscopy, reflects on the degree to which convection, diffusion, and electromigration deform the equilibrium double layer. With a polymer coating, convection and electro-osmosis are resisted by hydrodynamic drag on the polymer segments. The electro-osmotic flow near the underlying bare surface is therefore diminished. Characteristics of the particles and the adsorbed polymer can, in principle, be inferred by measuring the frequency-dependent polarizability. In this work, "exact" numerical solutions of the electrokinetic equations are used to examine how adsorbed polymer changes the particle polarizability and, hence, the conductivity and dielectric constant increments of dilute suspensions. For neutral polymer coatings, the conductivity and dielectric constant increments are found to be very similar to those of the underlying bare particles, so the response depends mostly on the underlying bare particles. These observations suggest that dielectric spectroscopy is best used to determine the underlying surface charge, with characteristics of the coating inferred from the electrophoretic or dynamic mobility, together with the hydrodynamic radius obtained from sedimentation or dynamic light scattering. Addressed briefly are the effects of added counterions and nonspecific adsorption. The electrokinetic model explored in this work can be used to guide experiments (frequency and ionic strength, for example) to either minimize or maximize the sensitivity of the complex conductivity to the coating thickness or permeability.

Hydrogel characteristics of electron-beam-immobilized poly(vinylpyrrolidone) films on poly(ethylene terephthalate) supports

A novel strategy for the preparation of thin hydrogel coatings on top of polymer bulk materials was elaborated for the example of poly(ethylene terephthalate) (PET) surfaces layered with poly(vinylpyrrolidone) (PVP). PVP layers were deposited on PET foils or SiO2 surfaces (silicon wafer or glass coverslips) precoated with PET and subsequently cross-linked by electron beam treatment. The obtained films were characterized by ellipsometry, X-ray photoelectron spectroscopy, infrared spectroscopy in attenuated total reflection, atomic force microscopy (AFM), and electrokinetic measurements. Ellipsometric experiments and AFM force-distance measurements showed that the cross-linked layers swell in aqueous solutions by a factor of about 7. Electrokinetic experiments indicated a strong hydrodynamic shielding of the charge of the underlying PET layer by the hydrogel coatings and further proved that the swollen films were stable against shear stress and variation of pH. In conclusion, electron beam cross-linking ofpreadsorbed hydrophilic polymers permits a durable fixation of swellable polymer networks on polymer supports which can be adapted to materials in a wide variety of shapes.