Polymer Depletion Research Articles

Stochastic interactions of two Brownian hard spheres in the presence of depletants.

A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near the trapped positions. The investigation focuses on the long-time correlated Brownian motion. The mobility tensor altered by the polymer depletion effect is computed by the boundary integral method, and the corresponding random displacement is determined by the fluctuation-dissipation theorem. From our computations it follows that the presence of depletion layers around the hard spheres has a significant effect on the hydrodynamic interactions and particle dynamics as compared to pure solvent and uniform polymer solution cases. The probability distribution functions of random walks of the two interacting hard spheres that are trapped clearly shift due to the polymer depletion effect. The results show that the reduction of the viscosity in the depletion layers around the spheres and the entropic force due to the overlapping of depletion zones have a significant influence on the correlated Brownian interactions.

Stress-gradient induced migration of polymers in corrugated channels

We study the flow of a dilute polymer solution in a wavy channel under steady-state flow conditions by employing the nonequilibrium thermodynamics two-fluid model [Mavrantzas and Beris, Phys. Rev. Lett. 69, 273–276 (1992)], allowing for the coupling between polymer concentration and polymer stresses. The resulting highly complex system of partial differential equations describing inhomogeneous transport phenomena in the fluid are solved with an efficient implementation of the mixed finite-element method. We present numerical results for polymer concentration, stress, velocity, and fluxes of polymer as a function of the nondimensional parameters of the problem (the Deborah number De, the Peclet number Pe, the Reynolds number Re, the ratio of the solvent viscosity to the total fluid viscosity β, and the constriction ratio of the channel width cr). We find that the constricted part of the wall is depleted of polymer, when the polymer diffusion length scale, expressed by the ratio of De/Pe, increases. The migration is more pronounced for macromolecules characterized by longer relaxation times and takes place toward the expanding part of the channel or toward the centerplane. Migration is also enhanced by the width variability of the channel: The more corrugated the channel, the stronger the transfer of polymer to the centerplane. This increases the spatial extent of polymer depletion near the wall or induces a zone of sharp variation in polymer stress and concentration, which moves away from the channel wall, especially in lower polymer concentration. The development of a polymer-depleted layer smooths out the boundary layer which is known to arise with Boger fluids at the walls of such corrugated channels or tubes and gives rise to an “apparent” slip in the constricted section of the wall and to a very low value of the drag force on the wall. When and where boundary layers arise, they scale as (1/De) for the stresses and as (De/Pe)1/3 for the concentration.

Characterization of Polymer Adsorption onto Drug Nanoparticles Using Depletion Measurements and Small-Angle Neutron Scattering

Production of polymer and/or surfactant-coated crystalline nanoparticles of water-insoluble drugs (nanosuspensions) using wet bead milling is an important formulation approach to improve the bioavailability of said compounds. Despite the fact that there are a number of nanosuspensions on the market, there is still a deficiency in the characterization of these nanoparticles where further understanding may lead to the rational selection of polymer/surfactant. To this end small-angle neutron scattering (SANS) measurements were performed on drug nanoparticles milled in the presence of a range of polymers of varying molecular weight. Isotopic substitution of the aqueous solvent to match the scattering length density of the drug nanoparticles (i.e., the technique of contrast matching) meant that neutron scattering resulted only from the adsorbed polymer layer. The layer thickness and amount of hydroxypropylcellulose adsorbed on nabumetone nanoparticles derived from fitting the SANS data to both model-independent and model dependent volume fraction profiles were insensitive to polymer molecular weight over the range Mv = 47-112 kg/mol, indicating that the adsorbed layer is relatively flat but with tails extending up to approximately 23 nm. The constancy of the absorbed amount is in agreement with the adsorption isotherm determined by measuring polymer depletion from solution in the presence of the nanoparticles. Insensitivity to polymer molecular weight was similarly determined using SANS measurements of nabumetone or halofantrine nanoparticles stabilized with hydroxypropylmethylcellulose or poly(vinylpyrrolidone). Additionally SANS studies revealed the amount adsorbed, and the thickness of the polymer layer was dependent on both the nature of the polymer and drug particle surface. The insensitivity of the adsorbed polymer layer to polymer molecular weight has important implications for the production of nanoparticles, suggesting that lower molecular weight polymers should be used when preparing nanoparticles by wet bead milling since nanoparticle formation is more rapid but with no likely consequence on the resultant physical stability of the nanoparticles.

Complex formation and stability of colloidal wood resin pitch suspensions with hemicellulose polymers

This paper explores the impact of the wood polymers released by Pinus radiata on the stability of wood resin colloids under varying ionic strength conditions with the addition of calcium chloride. A photometric dispersion analyser was used to study the kinetics of aggregation under shear conditions. Addition of the wood polymers to an aqueous dispersion of wood resins was found to cause destabilisation of the wood extractive colloids in two stages, separated by an apparent stabilisation region. The behaviour observed is typical of aggregation due to polymer bridging at low polymer addition, followed by steric stabilisation of the colloids at medium polymer concentration and depletion flocculation at higher polymer additions and then finally depletion stabilisation. At 10mM calcium ion concentration, destabilisation of the colloids occurred at low wood polymer addition, while at wood polymer concentrations above 50mg/L restabilisation of the colloids occurred at this level of calcium. The wood polymers were found to be unable to stabilise the colloids at high calcium levels of 50mM. At high calcium levels the wood polymers themselves were found to undergo aggregation. The stabilisation of the colloids was found to be affected by the way in which the colloids and wood polymer complexes are formed and allowed to reorganise with time.Adsorption isotherms for the adsorption of the wood polymers onto wood resin coated surfaces were determined. A low affinity Langmuir isotherm was obtained in the absence of electrolyte indicating that interaction between the wood polymers and the wood resin arises due to hydrogen bonding between the carboxylic acid groups despite the negative charge on both. The higher than expected loading capacity showed that the wood polymers adsorb as aggregates which extend from the surface and act to screen the negative charge of the wood resin colloids. In the presence of 10mM CaCl2 the isotherm was found to be modelled by a Freundlich isotherm with a greater amount of wood polymer being adsorbed due to folding of the wood polymer and reduction in its volume.

Organization of Strongly Interacting Directed Polymer Liquids in the Presence of Stringent Constraints

The impact of impenetrable obstacles on the energetics and equilibrium structure of strongly repulsive directed polymers is investigated. As a result of the strong interactions, regions of severe polymer depletion and excess are found in the vicinity of the obstacle, and the associated free-energy cost is found to scale quadratically with the average polymer density. The polymer-polymer interactions are accounted for via a sequence of transformations: from the 3D line liquid to a 2D fluid of Bose particles to a 2D composite fermion fluid and, finally, to a 2D one-component plasma. The results presented here are applicable to a range of systems consisting of noncrossing directed lines.

Effect of Linear Nonionic Polymer Additives on the Kinetic Stability of Dispersions of Poly(diallyldimethylammonium chloride)/Sodium Dodecylsulfate Nanoparticles

In this article, the impact of different neutral polymers on the kinetic stability of charge-stabilized poly(diallyldimethylammonium chloride) (PDADMAC)/sodium dodecylsulfate (SDS) colloidal dispersions is analyzed using dynamic light scattering, electrophoretic mobility, turbidity, and coagulation kinetics measurements. Poly(ethyleneoxide) (PEO), poly(vinylpyrrolidone) (PVP), and dextran of comparable molecular masses as well as a higher-molecular-weight dextran sample were tested as nonionic additives. The light scattering and mobility data indicate that the PEO and PVP molecules may adsorb on the surface of the PDADMAC/SDS nanoparticles formed in the presence of excess surfactant. The primary effect of these additives is manifested in enhanced coagulation of the PDADMAC/SDS nanoparticles due to bridging at lower polymer concentrations and depletion flocculation at higher polymer concentrations. These findings are in sharp contrast to the earlier published effect of the same nonionic polymers on the poly(ethyleneimine) (PEI)/SDS colloidal dispersions, which can be sterically stabilized at appropriate PEO or PVP concentrations. However, the adsorption of the investigated dextran samples is negligible on the PDADMAC/SDS nanoparticles. Therefore, dextran molecules may cause only depletion flocculation in the PDADMAC/SDS system in the vicinity of the critical overlap concentration.

Effect of confinement on polymer-induced depletion interactions between nanoparticles

Using a numerical implementation of polymer mean-field theory, we probe the effects of a structureless wall on the insertion free energies and the depletion interactions between nanoparticles in polymer solutions. Our results indicate that the insertion free energies and the polymer-induced interactions become mitigated in the presence of a wall. The range of influence of the walls is shown to correspond to the correlation length of the polymer solution. Surprisingly, our results demonstrate that even for particle sizes comparable to the correlation length of the polymer solution, the polymer depletion density profiles near the wall (in the absence of particles) can be used as a means to quantitatively predict the influence of the wall on both the insertion free energies and the depletion interactions.

Rheology of polymer solutions using colloidal-probe atomic force microscopy

We use colloidal-probe atomic force microscope (AFM) to study the rheological behavior of polymer solutions confined between two surfaces: the surface of a sphere and a flat surface on which the fluid is deposited. Measurements of the hydrodynamic force exerted on the sphere by the flowing liquid allowed retrieving the viscosity of the solution for different distances between the sphere and the flat surface. This method has been experimentally tested for Newtonian fluids for which the viscosity does not vary versus the gap dimensions. On the other hand, for non-Newtonian fluids, such as the large molecular weight polymer solutions used here, the measured viscosity depends on the gap height D between the flat surface and the sphere. The decrease of the viscosity versus gap height is similar to previously observed variations in colloidal suspensions. Depletion of polymers in the gap region due to the high shear rates involved is a possible cause for such a variation.

Instability of flat disks with respect to the formation of twisted ribbons in smectic-A*monolayers

Smectic-A* monolayers self-assembled from aqueous solutions of chiral fd viruses and a polymer depletant can assume a variety of shapes such as flat disks and twisted ribbons. A first order phase transition from a flat disk to a ribbon occurs upon lowering the concentration of polymer depletant or the temperature. A theoretical model based on the de Gennes model for the smectic-A phase, the Helfrich model of membrane elasticity, and a simple edge energy has been previously used to calculate the disk-ribbon phase diagram. In this paper we apply this model to the nucleation process of ribbons. First, we study the "rippled disks" that have been observed as precursors of ribbons. Using a model shape proposed by Meyer which includes rippling in both the in-plane and out-of-plane directions, we study the energetics of the disks as functions of the edge energy modulus (a measure of the polymer concentration) and the mean curvature modulus k. We find that as the edge energy modulus is reduced the radial size of the ripples grows rapidly in agreement with experimental observations. For small enough k we find that the out-of-plane size of the ripples grows but its value saturates at a fraction of the twist penetration depth, too small to be experimentally observable. For large k the membrane remains flat though rippled in the radial direction. Such membranes do not have negative Gaussian curvature and thus will not likely spawn twisted ribbons. We also study the creation of twisted ribbons produced by stretching the edge of a flat membrane in a localized region. In experiments using a pair of optical traps it has been observed that once the membrane has been sufficiently stretched a ribbon forms on the stretched edge. We study this process theoretically using a free energy consisting of the Helfrich and edge energies alone. We add a small ribbonlike perturbation to the protrusion produced by stretching and determine whether it is energetically favorable as a function of the size of the protrusion. In qualitative agreement with experiment we find a nonzero value for the critical size of the protrusion needed to make a ribbon energetically favorable, though the value we find is an order of magnitude lower than the experimental value possibly due to our neglect of the director field. As in the case of the rippled disks we find that the mean curvature energy acts as a barrier between the disk and twisted ribbon structures.

Theory of self-assembled smectic-Acrenellated disks: Membranes with cusped edges

Smectic-A monolayers self-assembled in aqueous solutions of chiral fd viruses and a polymer depletant have been shown to exhibit a variety of structures including large, flat disks and twisted ribbons. The virus particles twist near the edge of the structure in a direction determined by the chirality of the viruses. When fd viruses and their mutants of opposite chirality are mixed together in nearly equal amounts unusual structures referred to as "crenellated disks" can appear. These disks are achiral overall but the twist at the edge alternates between left- and right-handedness. To minimize the mismatch where the two regions of opposing twist meet, the "crenellated" structure exhibits cusps rising out of the plane of the monolayer. We use a phenomenological elastic theory previously applied to flat disks and twisted ribbons to analyze an analytic model proposed to describe the "crenellated" structure . When compared with flat, circular disks, we find that the model "crenellated disks" are stable or at least metastable in a wide region of the phase diagram spanned by the Gaussian curvature modulus and the edge energy modulus, with a large energy barrier separating the two structures. The director pattern and geometric parameters of the "crenellated disks" are found to be in qualitative agreement with experimental observations.

The apparent hydrodynamic slip of polymer solutions and its implications in electrokinetics

The apparent hydrodynamic slip of polymer solutions is a result of polymer depletion at channel walls, and its fluid dynamic effects are well known. This work reviews the evidences of apparent slip in electrokinetics, and discusses practical consequences in the following fields: (i) electrokinetic transport of polymer solutions in microchannels, which is of interest for the design and operation of microfluidic chips, particularly for electrophoresis; (ii) electroosmotic pumping, where it has been observed that the employment of polymer solutions greatly enhances the output pressure; and (iii) electrokinetic energy conversion, where the apparent slip also contributes to improve the conversion efficiency. In all cases, critical discussions are taken from basic physical concepts.

ADP-ribose polymer depletion leads to nuclear Ctcf re-localization and chromatin rearrangement

Ctcf (CCCTC-binding factor) directly induces Parp [poly(ADP-ribose) polymerase] 1 activity and its PARylation [poly(ADPribosyl)ation] in the absence of DNA damage. Ctcf, in turn, is a substrate for this post-synthetic modification and as such it is covalently and non-covalently modified by PARs (ADP-ribose polymers). Moreover, PARylation is able to protect certain DNA regions bound by Ctcf from DNA methylation. We recently reported that de novo methylation of Ctcf target sequences due to overexpression of Parg [poly(ADP-ribose)glycohydrolase] induces loss of Ctcf binding. Considering this, we investigate to what extent PARP activity is able to affect nuclear distribution of Ctcf in the present study. Notably, Ctcf lost its diffuse nuclear localization following PAR (ADP-ribose polymer) depletion and accumulated at the periphery of the nucleus where it was linked with nuclear pore complex proteins remaining external to the perinuclear Lamin B1 ring. We demonstrated that PAR depletion-dependent perinuclear localization of Ctcf was due to its blockage from entering the nucleus. Besides Ctcf nuclear delocalization, the outcome of PAR depletion led to changes in chromatin architecture. Immunofluorescence analyses indicated DNA redistribution, a generalized genomic hypermethylation and an increase of inactive compared with active chromatin marks in Parg-overexpressing or Ctcf-silenced cells. Together these results underline the importance of the cross-talk between Parp1 and Ctcf in the maintenance of nuclear organization.

Temperature as an external field for colloid–polymer mixtures: ‘quenching’ by heating and ‘melting’ by cooling

We investigate the response to temperature of a well-known colloid–polymer mixture. At room temperature the gas–liquid critical value of the second virial coefficient of the effective pairwise colloid–colloid interaction for the Asakura–Oosawa model predicts the onset of gelation observed experimentally with remarkable accuracy. Upon cooling the system the effective attraction between colloids induced by polymer depletion is reduced, because the polymer radius of gyration decreases as the θ-temperature is approached. Paradoxically this raises the effective temperature, leading to ‘melting’ of colloidal gels. We find that the Asakura–Oosawa model of effective colloid interactions, together with a simple description of the polymer temperature response, provides a quantitative description of the observed location of the fluid–gel transition in the colloid volume fraction polymer reservoir number density plane. Further, we present evidence for enhancement of crystallization rates in the vicinity of the metastable critical point.

Liposome and protein–water partitioning of polybrominated diphenyl ethers (PBDEs)

Bioaccumulation of polybrominated diphenyl ethers (PBDEs) in marine and terrestrial organisms is of great environmental concern. Understanding the partitioning of PBDEs to biological phases is crucial for elucidating their bioaccumulation behavior. In this study, partitioning coefficients of PBDEs from water to phospholipid liposomes (Klipw) and to bovine serum albumin (BSA) (KBSAw) were measured using a polymer depletion method. Klipw values measured in two laboratories are in an excellent agreement (within 0.14 log units), indicating a high method repeatability. The values of log Klipw and log KBSAw are in the range of 6.3–8.2 and 5.1–7.0, respectively, representing the highest of these partition coefficients measured to date. Log Klipw values for PBDEs are similar to the log of the octanol–water partition coefficients (Kow) (log Klipw−log Kow=−0.06±0.23; mean±SD of 7 congeners), consistent with the data of chlorobenzenes and polychlorinated biphenyls (PCBs) reported in the literature. No hydrophobicity cutoff was observed for partitioning to the liposome membrane. Log KBSAw values for PBDEs increase linearly with log Kow and do not follow the non-linear trend observed for polycyclic aromatic hydrocarbons (PAHs). This difference between PBDEs and PAHs suggests specific binding mechanisms to serum albumin even for hydrophobic compounds.

How flow changes polymer depletion in a slit

A theoretical model is developed for predicting dynamic polymer depletion under the influence of fluid flow. The results are established by combining the two-fluid model and the self-consistent field theory. We consider a uniform fluid flow across a slit containing a solution with polymer chains. The two parallel and infinitely long walls are permeable to solvent only and the polymers do not adsorb to these walls. For a weak flow and a narrow slit, an analytic expression is derived to describe the steady-state polymer concentration profiles in a Θ-solvent. In both Θ- and good-solvents, we compute the time evolution of the concentration profiles for various flow rates characterized by the Peclet number. The model reveals the interplay of depletion, solvent condition, slit width, and the relative strength of the fluid flow.

Combined depletion and electrostatic forces in polymer-induced membrane adhesion: A theoretical model

We develop a semi-quantitative analytical theory to describe adhesion between two identical planar charged surfaces embedded in a polymer-containing electrolyte solution. Polymer chains are uncharged and differ from the solvent by their lower dielectric permittivity. The solution mimics physiological fluids: It contains 0.1 M of monovalent ions and a small number of divalent cations that form tight bonds with the headgroups of charged lipids. The components have heterogeneous spatial distributions. The model was derived self-consistently by combining: (a) a Poisson-Boltzmann like equation for the charge densities, (b) a continuum mean-field theory for the polymer profile, (c) a solvation energy forcing the ions toward the polymer-poor regions, and (d) surface interactions of polymers and electrolytes. We validated the theory via extensive coarse-grained Molecular Dynamics (MD) simulations. The results confirm our analytical model and reveal interesting details not detected by the theory. At high surface charges, polymer chains are mainly excluded from the gap region, while the concentration of ions increases. The model shows a strong coupling between osmotic forces, surface potential and salting-out effects of the slightly polar polymer chains. It highlights some of the key differences in the behaviour of monomeric and polymeric mixed solvents and their responses to Coulomb interactions. Our main findings are: (a) the onset of long-ranged ion-induced polymer depletion force that increases with surface charge density and (b) a polymer-modified repulsive Coulomb force that increases with surface charge density. Overall, the system exhibits homeostatic behaviour, resulting in robustness against variations in the amount of charges. Applications and extensions of the model are briefly discussed.

Effects of attraction strength on microchannel flow of colloid–polymer depletion mixtures

We investigated the effect of the strength of the interparticle attraction on the flow properties and microstructure of colloid–polymer depletion mixtures during microchannel flow. When the strength of the interparticle attraction is increased, the additional elasticity imparted by the formation of interparticle bonds does not modify the magnitude of the flow velocities downstream, but instead leads to changes in the flow profiles near the edges of the microchannel that reflect yielding at the weak bonds between clusters. As a result, increasing the strength of attraction increases the resistance of the suspension to densification and to shear-induced migration.

Transient cage formation around hot gold colloids dispersed in polymer solutions

Gold colloids dispersed in dilute to concentrated polymer solutions can efficiently be heated by laser irradiation and act as almost pointlike heat sources. In systems with positive Soret coefficients S(T) of the polymer, such as solutions of polystyrene in toluene, the polymer can almost entirely be removed from the particle surface. The colloid attracts the solvent and a transient cage of low viscosity and dramatically enhanced mobility is formed, which follows the motion of the particle with a certain retardation. Based on a complete parameterization of S(T)(M, c, T), we analyze in detail the stationary temperature, concentration, and viscosity profiles. Depending on the polymer molar mass and concentration on the distance to the glass transition temperature, the negative or positive feedback-loops are established that lead to either attenuation or self-amplification of the polymer depletion.

Direct Measurement of Double-Layer, van der Waals, and Polymer Depletion Attraction Forces between Supported Cationic Bilayers

The interactions of supported cationic surfactant bilayers and the effects of nonadsorbing cationic polyelectrolytes on these interactions were studied using the surface forces apparatus (SFA) technique. Bilayers of the cationic surfactant di(tallow ethyl ester) dimethyl ammonium chloride (DEEDMAC) were deposited on mica surfaces using the Langmuir-Blodgett technique, and the interactions between the bilayers were measured in various salt, nonionic polymer (PEG), and cationic polyelectrolyte solutions at different polymer molecular weights and concentrations. The forces between the bilayers in CaCl(2) solution are purely repulsive and follow the DLVO theory quantitatively down to bilayer separations of ∼2 nm. Addition of nonadsorbing polymer or polyelectrolyte has a number of effects on the interactions including the induction of a depletion-attraction between the bilayers and screening of the double-layer repulsion due to the added ions in the solution from the polyelectrolyte. The experimental results are shown to agree well with standard theories of depletion attraction and double-layer screening associated with dissolved polyelectrolyte. We also observed significant time and rate effects on measuring the equilibrium bilayer-bilayer interactions possibly due to the unexpectedly long times (>1 min) associated with the charge regulation of the bilayer surfaces. Implications for the interactions and stability of vesicle dispersions, i.e., of free rather than supported bilayers, in polymer solutions are discussed.

Attenuation of Vibrio fischeri Quorum Sensing Using Rationally Designed Polymers

A first attempt to attenuate the quorum sensing (QS) of a marine heterotroph microorganism, Vibrio fischeri , using signal molecule-sequestering polymers (SSPs) is presented. A set of rationally designed polymers with affinity toward a signal molecule of V. fischeri , N-(beta-ketocaproyl)-l-homoserine lactone (3-oxo-C6-AHL) was produced. It is reported that computationally designed polymers could sequester a signal molecule of V. fischeri and prevent QS-controlled phenotypes (in this case, bioluminescence) from being up-regulated. It was proven that the attenuation of bioluminescence of V. fischeri was due to sequestration of the signal molecule by specific polymers and not due to the toxicity of polymer or nonspecific depletion of nutrients. The ability to disrupt the bacterial communication using easy to synthesize and chemically inert polymers could provide a new concept for the development of pharmaceuticals and susceptible device coatings such as catheters.