Distribution Of Polymer Segments Research Articles

Electrophoresis of polyelectrolyte-adsorbed soft particle with hydrophobic inner core.

This article deals with the electrophoresis of hydrophobic colloids absorbed by a layer of polymers with an exponential distribution of the polymer segments. The functional groups present in the polymer layer further follow the exponential distribution. We made an extensive mathematical study of the electrophoresis of such core-shell structured soft particles considering the combined impact of heterogeneity in polymer segment distribution, ion steric effect, and hydrodynamic slippage of the inner core. The mathematical model is based on the flat-plate formalism and deduced numerical results for electrophoretic mobility are valid for weak to highly charged particles for which the particle size well exceeds the Debye-layer thickness. In addition, we have derived closed form analytical results for electrophoretic mobility of the particle under several electrohydrodynamic limits. We have further illustrated the results for electrophoretic mobility considering a charged and hydrophobic inner core coated with an uncharged polymer layer or a polymer layer that entraps either positive or negatively charged functional groups. The impact of pertinent parameters on the overall electrophoretic motion is furtherillustrated.

Preparation of Epoxy Resin with Disulfide-Containing Curing Agent and Its Application in Self-Healing Coating.

Intrinsic self-healing polymers via dynamic covalent bonds have been attracting extensive attention because of their repeatable self-healing property. Herein, a novel self-healing epoxy resin was synthesized with disulfide-containing curing agent via the condensation of dimethyl 3,3'-dithiodipropionate (DTPA) and polyether amine (PEA). Therefore, in the structure of cured resin, flexible molecular chains and disulfide bonds were imported into the cross-linked polymer networks for triggering self-healing performance. The self-healing reaction of cracked samples was realized under a mild condition (60 °C for 6 h). The distribution of flexible polymer segments, disulfide bonds and hydrogen bonds in cross-linked networks plays a great role in the self-healing process of prepared resins. The molar ratio of PEA and DTPA strongly affects the mechanical performance and self-healing property. Especially when that molar ratio of PEA to DTPA is 2, the cured self-healing resin sample showed great ultimate elongation (795%) and excellent healing efficiency (98%). The products can be used as an organic coating, in which the crack could self-repair during a limited time. The corrosion resistance of a typical cure coating sample has been testified by an immersion experiment and electrochemistry impedance spectrum (EIS). This work provided a simple and low-cost route to prepare a self-healing coating for prolonging the service life of conventional epoxy coatings.

Spatial Distribution of Hydrophobic Drugs in Model Nanogel-Core Star Polymers

Star polymers with a cross-linked nanogel core are promising carriers of cargo for therapeutic applications due to the synthetic control of amphiphilicity of arms and stability at infinite dilution. Three nanogel-core star polymers were investigated to understand how the arm-block chemical structure controls loading efficiency of a model drug, ibuprofen, and its spatial distribution. The spatial distribution profiles of hydrophobic core, hydrophilic corona, and encapsulated drug were determined by small-angle neutron scattering (SANS). SANS provides the nanometer-scale sensitivity to determine how the arm-block chemistry enhances the sequestering of ibuprofen. Validated molecular dynamics simulations capture the trends in drug profile and polymer segment distribution with further details on drug orientation distribution. This work provides a basis to study structure-function relationships in macromolecular-based carriers of cargo and represents a path toward validated and predictive simulation.

Effect of hydrophobic core on the electrophoresis of a diffuse soft particle

Electrophoresis of a diffuse soft particle with a charged hydrophobic core is considered under the weak field and low charge density assumptions. The hydrophobic surface of the core is coated with a diffuse polyelectrolyte layer (PEL) in which a gradual transition of the polymer segment distribution from the impenetrable core to the surrounding electrolyte medium is considered. A mathematical model is adopted to analyse the impact of the core hydrophobicity on the diffuse soft particle electrophoresis. The mobility based on the present model for the limiting cases such as bare colloids with hydrophobic core and soft particles with no-slip rigid cores are in good agreement with the existing results. The presence of PEL charges produces the impact of the core hydrophobicity on the soft particle mobility different from the corresponding bare colloid with hydrophobic surface in an electrolyte medium. The impact of the core hydrophobicity is subtle when the hydrodynamic screening length of the PEL is low. Reversal in mobility can be achieved by tuning the core hydrophobicity for an oppositely charged core and PEL.

A multi-chain polymer slip-spring model with fluctuating number of entanglements: Density fluctuations, confinement, and phase separation.

Coarse grained simulation approaches provide powerful tools for the prediction of the equilibrium properties of polymeric systems. Recent efforts have sought to develop coarse-graining strategies capable of predicting the non-equilibrium behavior of entangled polymeric materials. Slip-link and slip-spring models, in particular, have been shown to be capable of reproducing several key aspects of the linear response and rheology of polymer melts. In this work, we extend a previously proposed multi-chain slip-spring model in a way that correctly incorporates the effects of the fluctuating environment in which polymer segments are immersed. The model is used to obtain the equation of state associated with the slip-springs, and the results are compared to those of related numerical approaches and an approximate analytical expression. The model is also used to examine a polymer melt confined into a thin film, where an inhomogeneous distribution of polymer segments is observed, and the corresponding inhomogeneities associated with density fluctuations are reflected on the spatial slip-spring distribution.

Microphase Separation and Phase Diagram of Concentrated Diblock Copolyelectrolyte Solutions Studied by Self-Consistent Field Theory Calculations in Two-Dimensional Space

The self-consistent field theory (SCFT) is applied to the microphase separation of concentrated solutions of weakly charged polyelectrolytes. The generalized Poisson–Boltzmann equation describing the electrostatic interactions at the mean-field level is numerically solved by a full multigrid algorithm, which enables one to solve the SCFT equations of polyelectrolyte systems in real space as efficient as neutral polymer systems. To demonstrate the power of the real-space numerical scheme, we consider a diblock copolyelectrolyte consisting of a charged block and a neutral block in two-dimensional space. The phase diagram in the Flory–Huggins interaction parameter—the composition space is constructed by numerical calculations. The density distribution of polymer segments, the counterions, and the net charge of the ordered structures, namely the lamellar phase and the hexagonal phase, are intensively examined. The effects of the interaction parameter and the degree of ionization are examined carefully. The numerical scheme can be easily extended to 3D calculations, various chain architectures, various charge distribution models, and other statistics chain models such as the worm-like chain model without losing any computational efficiency.

The heterogeneity of segmental dynamics of filled EPDM by 1H transverse relaxation NMR

Residual second moment of dipolar interactions M∼2 and correlation time segmental dynamics distributions were measured by Hahn-echo decays in combination with inverse Laplace transform for a series of unfilled and filled EPDM samples as functions of carbon-black N683 filler content. The fillers–polymer chain interactions which dramatically restrict the mobility of bound rubber modify the dynamics of mobile chains. These changes depend on the filler content and can be evaluated from distributions of M∼2. A dipolar filter was applied to eliminate the contribution of bound rubber. In the first approach the Hahn-echo decays were fitted with a theoretical relationship to obtain the average values of the 1H residual second moment 〈M∼2〉 and correlation time 〈τc〉. For the mobile EPDM segments the power-law distribution of correlation function was compared to the exponential correlation function and found inadequate in the long-time regime. In the second approach a log-Gauss distribution for the correlation time was assumed. Furthermore, using an averaged value of the correlation time, the distributions of the residual second moment were determined using an inverse Laplace transform for the entire series of measured samples. The unfilled EPDM sample shows a bimodal distribution of residual second moments, which can be associated to the mobile polymer sub-chains (M∼2≅6.1rad2s-2) and the second one associated to the dangling chains M∼2≅5.4rad2s-2). By restraining the mobility of bound rubber, the carbon-black fillers induce diversity in the segmental dynamics like the apparition of a distinct mobile component and changes in the distribution of mobile and free-end polymer segments.

Potential distribution theorem for the polymer-induced depletion between colloidal particles

The authors investigated the polymer-mediated colloidal interactions in a good solvent wherein the particle size varies from that much smaller than the polymer radius of gyration up to macroscopic and the polymer concentration varies from that corresponding to a dilute solution to that close to a melt. At conditions directly accessible to molecular simulations, the theoretical predictions agree favorably with the simulation results for the distributions of polymer segments and for the polymer-mediated colloidal interactions. The theoretical methods were then exploited to examine the polymer structure and colloidal interactions when the particle/polymer size ratio changes from the "protein" limit to the "colloid" limit at different regimes of the polymer concentration (i.e., dilute, semidilute, and concentrated). The authors found that the surface curvature plays a significant role on the distribution of polymer segments near the particle surface at low polymer concentration, but this effect diminishes as the polymer concentration increases. The Derjaguin approximation works reasonably well at high polymer concentration even in the protein limit, but it may fail qualitatively at low polymer concentration where the polymer-induced colloidal force becomes long range.

Molecular thermodynamics for swelling of a mesoscopic ionomer gel in 1 : 1 salt solutions

For a microphase-separated diblock copolymer ionic gel swollen in salt solution, a molecular-thermodynamic model is based on the self-consistent field theory in the limit of strongly segregated copolymer subchains. The geometry of microdomains is described using the Milner generic wedge construction neglecting the packing frustration. A geometry-dependent generalized analytical solution for the linearized Poisson-Boltzmann equation is obtained. This generalized solution not only reduces to those known previously for planar, cylindrical and spherical geometries, but is also applicable to saddle-like structures. Thermodynamic functions are expressed analytically for gels of lamellar, bicontinuous, cylindrical and spherical morphologies. Molecules are characterized by chain composition, length, rigidity, degree of ionization, and by effective polymer-polymer and polymer-solvent interaction parameters. The model predicts equilibrium solvent uptakes and the equilibrium microdomain spacing for gels swollen in salt solutions. Results are given for details of the gel structure: distribution of mobile ions and polymer segments, and the electric potential across microdomains. Apart from effects obtained by coupling the classical Flory-Rehner theory with Donnan equilibria, viz. increased swelling with polyelectrolyte charge and shrinking of gel upon addition of salt, the model predicts the effects of microphase morphology on swelling.

Distribution kinetics of polymer crystallization and the Avrami equation

Cluster distribution kinetics is adopted to explore the kinetics of polymer crystallization. Population balance equations based on crystal size distribution and concentration of amorphous polymer segments are solved numerically and the related dynamic moment equations are also solved. The model accounts for heterogeneous or homogeneous nucleation and crystal growth. Homogeneous nucleation rates follow the classical surface-energy nucleation theory. Different mass dependences of growth and dissociation rate coefficients are proposed to investigate the fundamental features of nucleation and crystal growth. A comparison of moment solutions with numerical solutions examines the validity of the model. The proposed distribution kinetics model provides a different interpretation of the familiar Avrami equation.

Ionizable polyelectrolyte brushes: brush height and electrosteric interaction

Semi-analytical scaling theory is used to describe quenched and annealed (weakly charged, ionizable, charge-regulating) polyelectrolyte brushes in electrolyte solutions of arbitrary salt concentration. An Alexander-De Gennes box model with homogeneous distribution of polymer segments and the free ends located at the edge of the brush is assumed, as is local electroneutrality in the brush. For annealed polyelectrolyte and in the low-salt regime, the theory predicts that for sufficiently dense brushes, the salt concentration has a small influence on brush height, while the brush expands with increasing grafting density, in agreement with experiment. Expressions are presented for the interaction free energy of compressed ionizable and quenched polyelectrolyte brushes (proportional to the force between particles or curved surfaces). In all cases, the required prefactors are explicitly stated. The theory is compared directly with published experiments on the influence of salt concentration, pH, and grafting density on the thickness and interaction force of polystyrene sulfonate (quenched) and poly(meth)acrylic acid (annealed) brushes. In general, trends are well reproduced but significant deviations remain.

Förster Energy Transfer Studies of Polyelectrolyte Heterostructures Containing Conjugated Polymers: A Means To Estimate Layer Interpenetration

Using a sequential adsorption process, thin film multilayer assemblies of polymers which photophysically interact via the Forster energy transfer mechanism have been fabricated and characterized in order to determine the level of interpenetration between layers. The assemblies consisted of layers of poly(phenylene vinylene) (PPV) which were separated from layers of a sulfonatopropoxy anion derivatized poly(p-phenylene) [(−)PPP] by nonconjugated polyelectrolyte spacer bilayers. The spacer bilayers were composed of poly(allylamine hydrochloride) (PAH) with a polyanion of either poly(acrylic acid) (PAA), poly(methacrylic acid) (PMA), or poly(styrenesulfonate) (PSS). An estimate of the level of interpenetration of the layers was made for each type of spacer bilayer by correlating the relative amount of quenching of the (−)PPP photoluminescence with the measured total thickness of the spacer bilayer(s) utilizing a diffuse layer model which assumed a Gaussian distribution of polymer segments. Using this approac...

Motion of a Colloidal Sphere Covered by a Layer of Adsorbed Polymers Normal to a Plane Surface

A combined analytical–numerical study is presented for the slow motion of a spherical particle coated with a layer of adsorbed polymers perpendicular to an infinite plane, which can be either a solid wall or a free surface. The Reynolds number is assumed to be vanishingly small, and the thickness of the surface polymer layer is assumed to be much smaller than the particle radius and the spacing between the particle and the plane boundary. A method of matched asymptotic expansions in a small parameter λ incorporated with a boundary collocation technique is used to solve the creeping flow equations inside and outside the adsorbed polymer layer, where λ is the ratio of the characteristic thickness of the polymer layer to the particle radius. The results for the hydrodynamic force exerted on the particle in a resistance problem and for the particle velocity in a mobility problem are expressed in terms of the effective hydrodynamic thickness (L) of the polymer layer, which is accurate to O(λ2). The O(λ) term forLnormalized by its value in the absence of the plane boundary is found to be independent of the polymer segment distribution and the volume fraction of the segments. The O(λ2) term forL, however, is a sensitive function of the polymer segment distribution and the volume fraction of the segments. In general, the boundary effects on the motion of a polymer-coated particle can be quite significant.

The structure of block copolymers at the fluid/fluid interface

We have developed a method of measuring the distribution of polymer segments at a liquid/liquid interface using neutron reflection. The method consists of forming a stable (1–4 μm) hexane layer on top of an aqueous sub-phase so that two interfaces contribute to the measured reflectivity. This has been done by condensing vapour onto the surface in an accurately temperature-controlled environment. The neutron reflectivity was measured at four angles of incidence on the SURF reflectometer. The attenuation of the reflectivity from the lowest angle is used to determine the thickness of the hexane layer. A series of poly(ethylene oxide) poly(propylene oxide) ABA block copolymers adsorbed at the hexane/water interface have been investigated. Since the polymers were hydrogenous, measurements were made with D 2O as the aqueous phase and with either null reflecting hexane or 60% D-hexane as the oil phase in order to obtain adequate contrast. The polymer volume fraction profile has been determined by simultaneous fits to the data from these combinations of solvent contrasts. It was found that there was a good correlation between the molar mass of the poly(ethylene oxide) block and the thickness of the polymer layer in the aqueous phase and that the chains were stretched beyond their radii of gyration expected for bulk solution.

Effects of Adsorbed Polymers on the Axisymmetric Motion of Two Colloidal Spheres

The effects of adsorbed polymer on the slow motion of two spherical particles along the line of their centers are examined semianalytically. The particles may have unequal radii, and their surface polymer layers are allowed to differ in characteristics. The surface polymer layer on each particle is assumed to be thin relative to the radius of the particle and to the surface-to-surface distance between the particles. A method of matched asymptotic expansions in small parameters λi(wherei= 1 and 2) combined with a boundary collocation technique is used to find the solution for the creeping flow field within and outside the adsorbed polymer layers, where λiis the ratio of the polymer-layer length scale to the radius of particlei. The results for the hydrodynamic forces exerted on the particles in a resistance problem and for the particle velocities in a mobility problem are expressed in terms of the effective hydrodynamic thicknesses (Li) of the polymer layers, which are accurate toO(λi2). TheO(λi) term forLinormalized by its value in the absence of the other particle is found to be independent of the polymer segment distribution, the hydrodynamic interactions among the segments, and the volume fraction of the segments. TheO(λi2) term forLi, however, is a sensitive function of the polymer segment distribution and the volume fraction of the segments. In general, the effects of particle interactions on the motion of polymer-coated particles can be quite significant, especially when the particles are moving in the opposite directions.

A New Scaling Theory of Semiflexible Polymer Phases Near Attracting Surfaces

The finite chain backbone stiffness in polymers gives rise to a number of novel behaviors described on short length scales. We analyze the semiflexible polymer phases near surfaces using a new scaling theory, incorporating the surface attraction in terms of its range and depth. It is found that the phase diagram includes five different phases: desorbed, weakly- adsorbed with both isotropic and nematic-type distribution of polymer segments inside the potential well, strongly-adsorbed states with the isotropic and nematic-type distribution. We draw conclusions on the orders of the transitions between the phases. The stiffness of polymer chain backbone means the presence of an orientation memory be- tween segments along the chain. A rigid rod is the very stiff polymer, for which the persistence length is much larger than the total contour length. This polymer can not be crumpled without breakage. On the other hand a very flexible chain can be crumpled practically on any length scales. It can be crumpled as a whole (as in so-called globule-to-coil transition iii and in the ideal limit it can be crumpled on smaller and smaller length scales (down to the microscopic scales of chain diameter order), carrying a self-similar or fractal structure. For the intermediate cases of semiflexible chain, which are probably the most interesting for applications including biophysical problems, the persistence length is much smaller than the total polymer contour length, so it can be crumpled as a whole in a similar way as a flexible chain. In general, we can treat a semiflexible polymer chain as a flexible one, when we are interested in the universal macroscopic polymer properties measured over the scales of whole macromolecule dimensions. But on the scales smaller than the persistence length the semiflexible structure can be con- sidered as an array of rigid rods interconnected at a fixed angle. (Naturally, the semiflexible wormlike chain can be viewed as the continuous limit of the discrete model iii.) Therefore, on these scales already, semiflexible polymer can not be crumpled without breakage and its properties are essentially different from those of flexible polymer. A wide class of synthetic and

Effect of adsorbed polymers on the slow motion of an assemblage of spherical particles relative to a fluid

The effects of adsorbed polymers on the sedimentation of a homogeneous distribution of colloidal spheres and on the fluid flow through a bed of particles are investigated theoretically. The Reynolds number is assumed to be small, and the surface polymer layers are assumed to be thin with respect to the radius of particles and to the surface-to-surface spacing between neighboring particles. The effects of interaction of the individual particles are taken into explicit account by employing a fundamental cell-model representation which is known to provide good predictions for the motion of a swarm of spheres within a fluid in the absence of adsorbed polymers. To solve the Stokes flow equations within and outside the polymer layer a method of matched asymptotic expansions in a small parameter λ is used, where λ is the ratio of the length scale of the polymer layer to the particle radius. The results for the sedimentation rate and the pressure drop are expressed in terms of an effective hydrodynamic thickness (L) of the polymer layer, which are accurate to O(λ2). When the concentration of particles in a suspension or a bed is increased, L becomes larger, meaning the settling velocity decreases or the pressure drop increases. The O(λ) term for L normalized by its value in the limit λ → 0 is found to be independent of the polymer segment distribution, the hydrodynamic interactions among the segments, and the volume fraction of the segments. The O(λ2) term for L, however, is a sensitive function of the polymer segment distribution and the volume fraction of the segments. In general, the particle-interaction effects on the motion of polymer-coated particles relative to a fluid can be quite significant.

Many-body depletion interactions among protein spheres in a semidilute polymer solution

The polymer segment distribution is shown to obey the Laplace equation for a suspension of small protein spheres and semidilute polymer. The depletion interaction is computed at all protein concentrations by introducing void distributions. Within a linear response Ansatz for the solution to the Laplace equation, the average depletion energy depends on two- and three-point void (-surface) correlation functions. It is concluded that depletion correlations of long range do not appear at high protein concentrations.

Self-consistent-field modelling of adsorbed casein Interaction between two protein-coated surfaces

E. Dickinson, V. J. Pinfield, D. S. Horne and F. A. M. Leermakers, J. Chem. Soc., Faraday Trans., 1997, 93, 1785 DOI: 10.1039/A608417F

Motion of a Colloidal Particle Coated with a Layer of Adsorbed Polymers in a Spherical Cavity

An analytical study is presented for the quasisteady translation and steady rotation of a spherical particle covered by a layer of adsorbed polymers located at the center of a spherical cavity that may also have an adsorbed polymer layer on its inside wall. The Reynolds number is assumed to be small, and the surface polymer layers are assumed to be thin with respect to the particle radius and the spacing between solid surfaces. To solve the Stokes flow equations within and outside the polymer layers a method of matched asymptotic expansions in small parameters λ1and λ2is used, where λ1and λ2are the ratios of the polymer-layer length scale to the radius of curvature at the particle surface and at the cavity wall, respectively. The results for the hydrodynamic force and torque exerted on the particle are expressed as an effective hydrodynamic thickness (L) of the adsorbed polymer layer surrounding the particle, which are accurate toO(λ21). TheO(λ1) term forLnormalized by its value in the absence of the cavity is found to be independent of the polymer segment distribution, the hydrodynamic interactions among the segments, and the volume fraction of the segments. TheO(λ21) term forL, however, is a sensitive function of the polymer segment distribution and the volume fraction of the segments. In general, the boundary effects on the motion of a polymer-coated particle can be quite significant in appropriate situations.