Interaction between brushes

Two brushes repel each other as they are brought into contact. This repulsion, which is a result of the osmotic interaction between the polymer segments, is the basis for colloidal stabilization. It has also been utilized to probe the brush structure. Most of these studies have been on 

25 Free end distribution for brushes with A, = 20 and pa = Q.. The brush contains an equal number of long and short chains. (o)A( = 40, distribution for short chains (D) = 40, distribution for long chains (A) monodisperse brush (o)JV = 60, distribution for short chains (V)- / = 60, distribution for long chains. (From Ref. 309.) 

Simulations of the interaction between two parallel brushes in a good solvent have been carried out using and methods. 

The MD study of Murat and Grest concentrated on the interpenetration of two symmetric brushes as well as on the force between them as a function of their separation. The force profile was compared to experimental results 

As two brushes are brought into contact, two processes are found to occur concurrently interpenetration and compression. When the distance D between the brushes equals twice the maximum extent hext of each, the parabolic profiles of both brushes begin to overlap and the density increases everywhere between the two grafting surfaces. At small separations the density becomes almost uniform in the gap between the grafting surfaces. However, for low to moderate compressions, the density profile of each brush remains roughly parabolic. This behavior is observed in all the simulations mentioned here, as well as in the numerical SCF calculations of Muthukumar and Ho. The amount of interpenetration at a given separation decreases as the N increases. One can quantify the amount of interpenetration in several ways. The quantity I D), where 

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The present model is based on several assumptions (i) the possible configurations of the grafted chain are described by a random walk (ii) their free energy densities are expressed as functions of the local monomer volume fraction alone (iii) the configurations of minimum energy dominate the partition function of the system (iv) only the configurations with monomers distributed between the surface and the position of the last monomer of the chain, assumed to be the farthest one, are taken into account. The latter assumption basically implies that the probability that the most distant monomer from the surface reaches the distance z is equal to the probability that the last monomer of the chain reaches this distance this approximation clearly fails when z is in the vicinity of the surface. However, in swollen brushes the behavior of the monomers in the vicinity of the surface is less important than the behavior of the distant monomers, which are primarily responsible for the brush thickness and for the interactions between brushes. 

Let us now analyze how the interactions between brushes occur in the present model. Our system is described by the statistical average of all possible configurations of chains that start from opposite surfaces and end up at the distances z and z2, respectively. For each possible path that is not reflected by the opposite wall, it is assumed that the monomers of the chains grafted on surfaces 1 and 2 are distributed between 0 and z and between z2 and 2d, respectively. The paths that are reflected by the opposite walls have the monomers distributed everywhere between 0 and 2d. Only the configurations that minimize the Flory—Huggins free energy are taken into account. Since a complete evaluation of all possible combinations is quite tedious, we will focus... 

It is of interest to note that below (but in the vicinity of) the temperature, the minimum confinement distance for which the overlap reduces the free energy might exceed the maximum length of the chains, 2d , , > 2Na. Because for 2d > 2Na there are no interactions between brushes, since the chains cannot overlap, the interactions occur in this case for 2d < 2Na < 2dmm and hence are repulsive. Therefore, the brushes repel each other at all separations, as if they would have been immersed in a good solvent. This might explain the repulsion (and no attraction) between brushes observed recently in near- solvents.26... 

Russano, D., Carrillo, J.-M.Y., Dobrynin, A.V. Interaction between brush layers of bottlebrush polyelectrolytes molecular dynamics simulations. Langmuir 27, 11044—11051 (2011). doi 10.1021/la2018067... 

The brush-type (Pirkle-type) CSPs have been used predominantly under normal phase conditions in LC. The chiral selector typically incorporates tt-acidic and/or n-basic functionality, and the chiral interactions between the analyte and the CSP include dipole-dipole interactions, n-n interactions, hydrogen bonding, and steric hindrance. The concept of reciprocity has been used to facilitate the rational design of chiral selectors having the desired selectivity [45]. 

The importance of polydispersity is an interesting clue that it may be possible to tailor the weak interactions between polymer brushes by controlled polydispersity, that is, designed mixtures of molecular weight. A mixture of two chain lengths in a flat tethered layer can be analyzed via the Alexander model since the extra chain length in the longer chains, like free chains, will not penetrate the denser, shorter brush. This is one aspect of the vertical segregation phenomenon discussed in the next section. 

PEG is a widely used molecule as a component in pharmaceutical formulations. PEG is particularly useful thanks to its low cost and various simple synthetic methods (26). PEG-lipid has been developed as a means of stabilizing conventional liposomes. A lipid moiety has been linked to the large PEGylated head in order to anchor the molecule to the particles. Instead of shielding a direct layer of polymer PEG around the particle, which would be less stable, the idea is to favor hydrophobic interactions between the PEG-lipid and the particle bilayer lipids. This anchor had led to two conformations of the PEG on the particle surface commonly called mushroom and brush regimes (27), representing a more condensed or extended conformations... 

An additional electrostatic component to the polymer interaction term is typically unimportant since the counterions strongly screen any Coulomb interactions [92]. Finally, an electrostatic interaction between polymers and counterions Tint occurs if the PE brush is not locally electro-neutral throughout the system, an example is depicted in Fig. 10a. This energy is given by... 

Another attractive application of polymer brushes is directed toward a biointerface to tune the interaction of solid surfaces with biologically important materials such as proteins and biological cells. For example, it is important to prevent surface adsorption of proteins through nonspecific interactions, because the adsorbed protein often triggers a bio-fouling, e.g., the deposition of biological cells, bacteria and so on. In an effort to understand the process of protein adsorption, the interaction between proteins and brush surfaces has been modeled like the interaction with particles, the interaction with proteins is simplified into three generic modes. One is the primary adsorption. 

Calculations from SCF theory of the mixed layer structure, and of the interaction potential for a pair of mixed layers as a function of interlayer separation, suggest that the mixed layer has a heterogeneous morphology perpendicular to die interface (Parkinson et al., 2005). This localized segregation arises from the excluded volume interaction between spaced-out casein chains and the dense brush-like layer that was invoked in the simple SCF model to represent the p-lactoglobulin adsorbed monolayer. 

Melander, B. 1998b. Interactions between soil cultivation in darkness, flaming and brush weeding when used for in-row weed control in vegetables. Biological Agriculture and Horticulture 16(1) 1-14. 

As with normal hydrocarbon-based surfactants, polymeric micelles have a core-shell structure in aqueous systems (Jones and Leroux, 1999). The shell is responsible for micelle stabilization and interactions with plasma proteins and cell membranes. It usually consists of chains of hydrophilic nonbiodegradable, biocompatible polymers such as PEO. The biodistribution of the carrier is mainly dictated by the nature of the hydrophilic shell (Yokoyama, 1998). PEO forms a dense brush around the micelle core preventing interaction between the micelle and proteins, for example, opsonins, which promote rapid circulatory clearance by the mononuclear phagocyte system (MPS) (Papisov, 1995). Other polymers such as pdty(sopropylacrylamide) (PNIPA) (Cammas etal., 1997 Chung etal., 1999) and poly(alkylacrylicacid) (Chen etal., 1995 Kwon and Kataoka, 1995 Kohorietal., 1998) can impart additional temperature or pH-sensitivity to the micelles, and may eventually be used to confer bioadhesive properties (Inoue et al., 1998). 

From the measured core radii the grafting distance b can be calculated. Its variation as a function of added salt concentration is shown in Fig. 6 a. In the osmotic brush regime at low added salt concentrations the grafting distances are practically constant. At concentrations above c s 0.05 mol/1 ( salted brush ) the grafting distances decrease with increasing salt due to screening of the repulsive interactions between the corona chains [49]. 

E. Ruckenstein, B. Li Steric interactions between two grafted polymer brushes, JOURNAL OF CHEMICAL PHYSICS 107 3 (1997) 932-942. 

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