Interpenetration Zone Research Articles

Interpenetration and Friction of Brush-Coated Surfaces under External Load: Analytical Theory and SCF Calculations

We studied the compression and interpenetration properties of two opposing monodisperse polymer brushes under external load by analytical theory and by a numerical self-consistent field (SCF) approach. Analytical expressions are proposed for the brush density profiles in the interpenetration zone and verified by numerical SCF calculations. We quantify the interpenetration of two opposing brushes by the characteristic penetration length and by two integral parameters: the overlap integral, Γ, representing the number of interbush contacts, and the number of brush monomer units in the foreign half-space, Σ. The interpenetration parameters are studied in two conjugate ensembles as functions of the brush separation and of the external pressure. We propose a theoretical description of the solvent-mediated friction force in the low shearing rate regime on the basis of the Brinkman equation for two compressed brushes sliding against each other. We demonstrate that the total friction force which also includes direct brush–brush friction is expressed in terms of Γ and Σ. The SCF data for the interpenetration parameters Γ and Σ and hence for the total sliding friction force in the pressure ensemble collapse onto universal master curves when rescaled by the factor (N/σ)1/3 as suggested by the theory, where N is the chain length and σ is the surface grafting density. Finally, we define the kinetic friction coefficient as a function of the external pressure and analyze its universal rescaled behavior in the two limits of nondraining and free-draining brushes.

Local Structure of Polymer-Grafted Nanoparticle Melts.

Polymer-grafted nanoparticle (GNP) membranes show unexpected gas transport enhancements relative to the neat polymer, with a maximum as a function of graft molecular weight (MWg ≈ 100 kDa) for sufficiently high grafting densities. The structural origins of this behavior are unclear. Simulations suggest that polymer segments are stretched near the nanoparticle (NP) surface and form a dry layer, while more distal chain fragments are in their undeformed Gaussian states and interpenetrate with segments from neighboring NPs. This theoretical basis is derived by considering the behavior of two adjacent NPs; how this behavior is modified by multi-NP effects relevant to gas separation membranes is unexplored. Here, we measure and interpret SAXS data for poly(methyl acrylate)-grafted silica NPs and find that for very low MWgs, contact between GNPs obeys the two-NP theory─namely that the NPs act like hard spheres, with radii that are linear combinations of the NP core sizes and the dry zone dimensions; thus, the interpenetration zones relax into the interstitial spaces. For chains with MWg > 100 kDa, the interpenetration zones are in the contact regions between two NPs. These results suggest that for MWgs below the transition, gas primarily moves through a series of dry zones with favorable transport, with the interpenetration zone with less favorable transport properties in parallel. For higher MWgs, the dry and interpenetration zones are in series, resulting in a decrease in transport enhancement. The MWg at the transport maximum then corresponds to the chain length with the largest, unfavorable stretching free energy.

Effect of chain architecture on properties of self-assembled dendron brushes

We present self-consistent field theory targeted to describe the equilibrium structure of self-assembled solvent-free planar brushes formed by regularly branched polymeric ’surfactants' that adsorb ’head’-on from a polymer melt. By using numerical and analytical approaches we examine how the width of a melt-brush interpenetration zone depends on the surfactant architecture. We demonstrate that the macrocyclization of the surfactant molecules leads to the smallest brush-melt interpenetration compared to linear and starlike variants. Theoretical predictions are compared to results of computer simulations and experiments.

Virtual crack closure technique for an interface crack between two transversely isotropic materials

The virtual crack closure technique makes use of the forces ahead of the crack tip and the displacement jumps on the crack faces directly behind the crack tip to obtain the energy release rates $${{\mathcal {G}}}_I$$ and $${\mathcal {G}}_{II}$$ . The method was initially developed for cracks in linear elastic, homogeneous and isotropic material and for four noded elements. The method was extended to eight noded and quarter-point elements, as well as bimaterial cracks. For bimaterial cracks, it was shown that $${\mathcal {G}}_I$$ and $${\mathcal {G}}_{II}$$ depend upon the virtual crack extension $$\varDelta a$$ . Recently, equations were redeveloped for a crack along an interface between two dissimilar linear elastic, homogeneous and isotropic materials. The stress intensity factors were shown to be independent of $$\varDelta a$$ . For a better approximation of the Irwin crack closure integral, use of many small elements as part of the virtual crack extension was suggested. In this investigation, the equations for an interface crack between two dissimilar linear elastic, homogeneous and transversely isotropic materials are derived. Auxiliary parameters are used to prescribe an optimal number of elements to be included in the virtual crack extension. In addition, in previous papers, use of elements smaller than the interpenetration zone were rejected. In this study, it is shown that these elements may, indeed, be used.

Excluded volume effects in compressed polymer brushes: A density functional theory.

A classical density functional theory (DFT) is applied to investigate the behavior of compressed polymer brushes composed of hard-sphere chains. The excluded volume interactions among the chain segments are explicitly treated. Two compression systems are used to study the behavior of brush-wall and brush-brush interactions. For the brush-brush systems, an obvious interpenetration zone has been observed. The extent of the interpenetration depends strongly on the grafting density. Furthermore, the repulsive force between the brush and wall or between the two brushes has been obtained as a function of the compression distance. Compared to the prediction of the analytic self-consistent field theory, such force increases more rapidly in the brush-wall compression with high polymer grafting densities or at higher compressions. In the brush-brush compression system, the interpenetration between the two compressed brushes creates a "softer" interaction. The influence of hard-sphere solvents on the behavior of compressed brushes is also discussed.

Macromolecular anchoring layers for polymer grafting: comparative study

Comparative study of efficiency of macromolecular anchoring layers in the grafting of end-functionalized polymers to a surface was conducted. Poly(glycidyl methacrylate) (PGMA) and epoxydized polybutadienes (EPB) were utilized as the primary anchoring films. Amount of the epoxy moieties introduced to the surface was varied via thickness of the modifying polymer layer or amount of epoxy groups in the polymer backbone. Comparison between the grafting of polystyrene and poly(ethylene glycol) to the various macromolecular anchoring layers indicated that grafting ability of a layer was mostly governed by thickness of the interpenetration zone between the two polymers (anchoring and being grafted). In case of low level of the interpenetration, only functional groups at the periphery of the primary polymer layer were available for the grafting. Then, amount of grafted polymer did not increase with total number of epoxy groups in the anchoring film. However, as the thickness of the interpenetration zone increased, higher amount of the functional groups become available for the grafting.

Shear in Surface Gel of Associative Polymer

The normal and shear forces between adsorbed layers of telechelic associative polymer poly(ethylene oxide) end-terminated with octadecyl groups have been studied using a surface force balance. The normal forces profiles measured for polymer monolayers and surface gels were similar to those reported for the same polymer in earlier studies. The shear forces between the polymer-covered surfaces were very weak up to compression of ca. 0.27 of the original thickness of the polymer layers, corresponding to the effective friction coefficient μ < 0.04. Weak frictional forces were attributed to osmotic repulsion between poly(ethylene oxide) chains and shear thinning of the gelled polymer. At higher polymer compression the shear forces gradually increased due to compression-forced increase in interpenetration and entanglement of the macromolecules adhering to the two opposite surfaces and interactions between the octadecyl groups. Shear thinning was also observed for long-time shear and for shear velocity v s exceeding 600 nm/s. For strongly compressed polymer and v s < 600 nm/s the dependence of frictional forces on the shear velocity was weak, caused by a thinning of the interpenetration zone between the sheared polymer layers and/or a transition of the slip plane to the polymer-substrate interface.

Sliding friction with polymer brushes.

Using high-resolution shear force measurements, we examine in detail the frictional drag between rubbing surfaces bearing end-tethered polymeric surfactants (brushes). The drag attains a maximum on initial motion, attributed to elastic stretching of the chains, which falls by a cascade of relaxations to a value characteristic of kinetic friction. This has a very weak velocity dependence, attributed to chain moieties dragging within a self-regulating, mutual interpenetration zone. When sliding stops, the shear stress across the polymer layers decays logarithmically with time, consistent with the relaxation of a network of dangling ends.

On the tribology and rheology of polymer brushes in good solvent conditions: a molecular dynamics study

Tribological and rheological properties of two polymer brushes in relative sliding motion and good solvent conditions are investigated by means of molecular dynamics (MD) simulations. The lateral forces between the brushes are found to decrease logarithmically with increasing relative sliding velocity v 0 over a range of more than one decade in v 0. We also observe an almost logarithmic relaxation of the end-to-end distance vector that occurs after sliding is stopped. The coincidence of these logarithmic dependencies support the picture that friction between polymer brushes is small due to the retraction of the polymers from the interpenetration zone. The shear stress relaxes almost instantly in our simulations after sliding is stopped, unless poor solvent conditions are considered.

Shear deformation of two interpenetrating polymer brushes: Stochastic dynamics simulation

The interaction between two polymer brushes (layers of polymer chains grafted at one end onto an impermeable surface) brought into a close contact and moving with respect to each other in the lateral direction is studied by the method of stochastic dynamics simulation. The structural properties of the brushes such as the monomer density profile, the distribution of the free ends of the chains, as well as the disjoining pressure have been studied as functions of the separation between grafting planes (the degree of static overlapping of brushes) and of the lateral displacement rate. We have found that at zero shear rate the extension of grafted chains perpendicular to the grafting planes monotonically decreases with decreasing distance between the planes, but not as rapidly so that significant overlapping and interpenetration of brushes occurs. At strong compression the free ends of the chains are distributed all over the gap between grafting planes. An increase in the shear rate is accompanied by inclination and extension of chains in the direction of shear and by a simultaneous decrease in the chain dimensions in the direction perpendicular to the grafting planes: the free ends are localized near the middle plane and progressive decoupling of brushes occurs. At large shear rate the width of the interpenetration zone almost vanishes. The inclination of chains at given shear rate increases with decreasing grafting density and decreasing width of the gap between the grafting planes. The disjoining pressure exhibits a weak maximum as a function of the shear rate that is in qualitative agreement with the predictions of scaling theories.

The Political Regulation of Technological Risks

This paper addresses the debate on the political regulation of technological risks currently taking place in the fields of policy analysis, research on neo-corporatism and sociological theory, and then goes on to interrelate these areas of research and discourse. It starts with the assumption that political regulation takes place in the interpenetration zone between the different functional subsystems of social action; subsystems which operate according to their own laws analytically, but merge in concrete social action empirically. Political regulation is an arena in which we can study the interchange between these functional subsystems and the reciprocal transformation of communication media. The paper discusses four ideal-typical models of interchange: synthesis, competition, statism and compromise. These models have specific effects on the formulation of political regulation in terms of its effectiveness and flexibility. The dynamics of political regulation are characterized by processes of upswing, downswing, inflation, deflation and recession. The theory of generalized communication media provides the analytical tools for investigating these dynamic processes. Due to limited space, the paper concentrates on the interchange between the political system and the societal community and the reciprocal transformation and dynamic processing of political power and influence.

The Structure and Conformation ofn-Hydrocarbon Chains in Bilayer Systems in the “Fluid” Phase

Abstract A realistic computer model of a bilayer of hexadecyl groups at a surface area per chain corresponding to that present in systems of biological interest has been obtained using the Monte Carlo technique. Properties evaluated from the model are in good agreement with results of deuterium magnetic resonance (d.m.r.) and X-ray and neutron diffraction experiments, showing that the distribution of matter and the degree of order in the model are not too far from those in real bilayer systems. The structure of the model bilayer consists of two “single layer” regions, closely related to the plateau of the d.m.r. order parameters, separated by a large interpenetra-tion zone. The conformation of the alkyl chains, though extended along the normal to the layers, is not perturbed to a great extent with respect to the unperturbed model. A uniform filling of the space is obtained in the model in the absence of long range orientational correlations such as the collective tilt postulated in the literature.

The kinetics and mechanism of formation of polymers, constructed of pairs of macromolecules (as exemplified by the interaction of poly-1,1,2-trichlorobutadiene-1,3 with polystyrene

Abstract Theoretical and experimental analysis of the interaction of two types of different macromolecules in solution resulting in the formation of paired polymers, has been carried out. By analysing the structure and properties of these products by refractometry, viscometry, sedimentation, statistical analysis etc. it was shown that the paired polymers represent a “coil in coil” type system, the coils being interconnected in the interpenetration zone.