Theory of Liquid-crystalline Ordering in Polymer Brushes

Summary: We present a review of the works devoted to investigation of LC ordering in polymer brushes. This series has been carried out by the group of T. M. Birshtein and covers the following aspects of the problem: thermotropic LC phase transition in LCP brushes, microphase segregation, homeotropic and planar LC phases, LC polymer in LC solvent, lyotropic LCP brushes, LC transitions under normal or lateral force (shear flow). Analytical theory is developed for simplified model of polymer brush with accounting for thermotropic attraction in Mayer-Saupe approximation and lyotropic repulsion in DiMarzio formalism; numerical calculations are fulfilled in self-consistent field approximation (method of Scheutjens and Fleer). Brownian dynamics simulations are applied for modeling polymer brush in a shear flow.     

Normal and Lateral Deformation of Lyotropically Ordered Polymer Brush

Summary: Planar polymer brush formed by semirigid chains of freely jointed rigid segments and immersed into a solvent is considered. Brush collapse induced by deterioration of the solvent quality and its deformation by external normal or lateral force is studied. It is demonstrated that these three different situations can be described in the framework of the common approach. It is shown that the collapse is accompanied by liquid‐crystalline (LC) ordering within the brush. The LC transition can be jump‐like (the first order) or continuous, depending on the segment's aspect ratio and grafting density. Transition point is investigated in detail, the corresponding phase diagrams are calculated. It is shown that the phase diagrams of a normally deformed brush have different structures, with a narrow ‘leg’ in the good solvent region for sparsely grafted brush, with two coexistence regions and a triple point, in addition, for shorter segment length or without these features if the chains are densely grafted. For the laterally deformed brush, phase diagrams have similar structures with a critical point in the good solvent regime.

Polymer brush subjected to deformation by normal (top) and lateral (bottom) external force.     

Compression of Polymer Brushes Under a Lateral Force

Summary: The influence of a lateral force (or lateral shear) acting on chains in a polymer brush is investigated theoretically. Brushes consisting of chains with temperature dependent anisotropic interactions between monomers (main‐chain mesogenic groups) are considered. It is shown that a lateral force applied to polymer brush induces its compression. In contrast to a conventional brush, the compression of brush, capable of forming a liquid crystalline (LC) state, can be caused by comparatively small shear forces. Moreover, such shear forces can induce a phase transition of a brush into the tilted LC state with a several‐fold decrease in brush thickness. These results allow us to predict a possibility to observe a decrease in brush thickness in a real experiment with reasonably values of shear rate.

Model of a chain in a polymer brush under an influence of lateral force p.     

Dynamic ordering transitions of liquid crystals driven by interfacial complexes formed between polyanions and amphiphilic polyamines

We report the design of an amphiphilic polyamine (polymer 1) based on poly(2-alkenyl azlactone) that strongly couples the formation of polyelectrolyte complexes at aqueous/liquid crystal (LC) interfaces to ordering transitions in the LC. We demonstrate that the addition of a strong anionic polyelectrolyte to aqueous solutions in contact with polymer 1-laden LC interfaces (prepared by Langmuir-Schaefer transfer of monolayers of polymer 1 onto micrometer-thick films of nematic LC) triggers ordering transitions in the LCs. We further demonstrate that changes in the ordering of the LCs (i) are driven by electrostatic interactions between the polyelectrolytes, (ii) involve multivalent interactions between the polyelectrolytes, and (iii) are triggered by reorganization of the hydrophobic side chains of amphiphilic polymer 1 upon formation of the interfacial complexes. The results presented in this paper lead us to conclude that ordering transitions in LCs can be used to provide insights into the structure and dynamics of interfacial complexes formed between polyelectrolytes.     

Phase transitions in polymer brushes

Liquid crystalline ordering in planar polymer brushes is investigated theoretically by numerical calculations within a self-consistent field approximation. The brushes are formed by macromolecules with mesogenic groups in main chain and immersed in a solvent. Existence of a microphase segregated brush (MSB) regime with a collapsed orientationally ordered intrinsic sublayer and a swollen external sublayer is shown. At small grafting density, the transition from a conventional brush state to the microphase segregated state is a jump-wise first order phase transition for a finite chain length (N). The magnitudes of the jumps in the average characteristics of the brush tend to zero in the limit N → ∞ since this transition occurs only in a vanishingly small part (∝ N^−1/2) of the brush. High compressibility of MSB brush is demonstrated. The origin of phase transition in planar brushes is discussed.     

Phase and orientational ordering of low molecular weight rod molecules in a quenched liquid crystalline polymer matrix with mobile side chains

We study the phase diagram and orientational ordering of guest liquid crystalline (LC) rods immersed in a quenched host made of a liquid crystalline polymer (LCP) matrix with mobile side chains. The LCP matrix lies below the glass transition of the polymer backbone. The side chains are mobile and can align to the guest rod molecules in a plane normal to the local LCP chain contour. A field theoretic formulation for this system is proposed and the effects of the LCP matrix on LC ordering are determined numerically. We obtain simple analytical equations for the nematic/isotropic phase diagram boundaries. Our calculation show a nematic-nematic (N/N) first order transition from a guest stabilized to a guest-host stabilized region and the possibility of a reentrant transition from a guest stabilized nematic region to a host only stabilized regime separated by an isotropic phase. A detailed study of thermodynamic variables and interactions on orientational ordering and phases is carried out and the relevance of our predictions to experiments and computer simulations is presented.     

Liquid crystal transitions induced by spherical particles in anisotropic polymer brushes: Molecular dynamics simulation

A change in the structure of a polymer brush formed by chains composed of anisotropic monomers brought about by filling the volume of the system with free spherical particles was studied by means of molecular dynamics simulation. Microphase separation takes place at a certain concentration of spherical particles inside the brush. A microphase that contains a small amount of isotropic particles and is characterized by a high density and high ordering of the monomers is formed near the wall. A disordered microphase with a low monomer density and a high concentration of spherical particles is located at the periphery of the brush. The microphases are separated from one another by a distinct boundary. As the concentration of isotropic particles further increases, the ordered microphase expands until the entire volume of the brush becomes occupied. It was also found that the brush in the ordered state forms different LC structures, namely, smectic or nematic entities at relatively low concentrations or at higher concentrations of spheres, respectively.     

Microphase coexistence in polymeric brushes

A collapse of polymeric brushes in a solvent can be induced by a change in external conditions, for example, solvent quality or its temperature. The systems with following specific interactions are considered in this paper, namely, polyelectrolyte brushes, amphiphilic brushes in a mixture of incompatible solvents, and brushes with possibility of liquid-crystalline ordering of polymer segments. For all the systems it is shown that the brush collapse can be observed under certain conditions, and it occurs through a microphase segregation. There are two microphases of different densities that coexist in the brush. The effect is caused by general properties of the swollen phase of polymeric brush and hence appears at all types of the interactions that can induce a phase transition of the brush into collapsed state.     

Computer simulation of the liquid crystal formation in a semi-flexible polymer system

Molecular dynamic simulations are reported for system of semi-flexible linear rod-like molecules. The molecules are composed of N_c tangent soft spheres, connected by elastic springs. Rigidity is introduced by additional springs between all pairs of spheres along the molecule. The formation of only a nematic LC phase is shown for all systems with N_c = 8 and different flexibility. The effect of flexibility on the order parameter and the volume fraction at the LC phase transition is compared with theoretical predictions by Khokhlov-Semenov and with available simulation data. The dependence of the anisotropy of diffusion on chain flexibility in LC phase was studied. The polymer brushes consisting of flexible and semi-flexible (composed of linear rod-like segments) chains were simulated at different grafting densities. Height of brush, order parameter, distribution of density and chain ends in brush were obtained in both cases and compared with theoretical predictions.     

Self‐Consistent Brownian Dynamics Simulation of an Anisotropic Brush Under Shear Flow

Summary: The behavior of an anisotropic polymer brush under a lateral shear flow is considered in the framework of a hybrid method combining a self‐consistent field approach and Brownian dynamics simulation. It is shown that such a flow can induce the compression of an anisotropic brush at shear rates much smaller than those which induce the compression of a conventional isotropic brush. Moreover, a lateral flow can initiate a thermotropic collapse which occurs as an LC phase transition. This collapse takes place at higher temperatures than in the absence of the flow. This can help to find brush compression experimentally. The variation of the internal structure of a brush (density, order parameter, and director orientation profiles, distribution of terminal groups) is also investigated. An anomalous effect of brush densification and ordering near the outer surface is observed. At large shear rates the distribution of chains over their deformation has a bimodal character: one fraction of chains is strongly stretched and another fraction remains unperturbed by the flow. Average characteristics of a brush were compared with predictions of the lattice theory for the box model where the lateral force is applied to chain ends. Satisfactory agreement was observed.

Polymer brush under an influence of lateral flow.     

Homeotropic and planar structures in liquid-crystalline polymer brushes

The ordering in polymer brushes formed by macromolecules with mesogenic groups in the main chain is investigated. The numerical method of self-consistent field approximation was used. The existence of two different liquid crystalline nematic states is shown: homeotropic (HLC) and planar (PLC) states. The free energy of the HLC state is always less than that of the PLC state. However, with the increase of energy of anisotropic interactions, (with decrease in temperature) our numerical procedure leads us to either one or another state depending on the grafting density. The results obtained show that both brush surfaces, play an essential role in establishing the concrete LC state structure. The grafting surface and the external surface force the planar order.     

Ordering transitions triggered by specific binding of vesicles to protein-decorated interfaces of thermotropic liquid crystals

We report that specific binding of ligand-functionalized (biotinylated) phospholipid vesicles (diameter = 120 ± 19 nm) to a monolayer of proteins (streptavidin or anti-biotin antibody) adsorbed at an interface between an aqueous phase and an immiscible film of a thermotropic liquid crystal (LC) [nematic 4'-pentyl-4-cyanobiphenyl (5CB)] triggers a continuous orientational ordering transition (continuous change in the tilt) in the LC. Results presented in this paper indicate that, following the capture of the vesicles at the LC interface via the specific binding interaction, phospholipids are transferred from the vesicles onto the LC interface to form a monolayer, reorganizing and partially displacing proteins from the LC interface. The dynamics of this process are accelerated substantially by the specific binding event relative to a protein-decorated interface of a LC that does not bind the ligands presented by the vesicles. The observation of the continuous change in the ordering of the LC, when combined with other results presented in this paper, is significant, as it is consistent with the presence of suboptical domains of proteins and phospholipids on the LC interface. An additional significant hypothesis that emerges from the work reported in this paper is that the ordering transition of the LC is strongly influenced by the bound state of the protein adsorbed on the LC interface, as evidenced by the influence on the LC of (i) "crowding" of the protein within a monolayer formed at the LC interface and (ii) aging of the proteins on the LC interface. Overall, these results demonstrate that ordering transitions in LCs can be used to provide fundamental insights into the competitive adsorption of proteins and lipids at oil-water interfaces and that LC ordering transitions have the potential to be useful for reporting specific binding events involving vesicles and proteins.     

Absorption and engulfing transitions in nanoparticle infiltration into a polymer brush: A monte carlo simulation

We study the structure of an infiltrating hard spherical nanoparticle into a polymer brush using extensive off‐lattice Monte Carlo simulations of a basic theoretical model. We show that as long as the spherical particle is coated with a surface layer that interacts attractively with brush monomers, it can penetrate deeply into a dense polymer brush near the grafting surface. The infiltration process contains two stages: diffusing nanoparticle absorbing onto the surface of the polymer brush and engulfing of the nanoparticle by polymer chains. After the nanoparticle fully immerses in the dense polymer brush region, the buoyant forces levels off because of symmetric repulsions that endows increasing nanoparticle mobility and encourages the second transition. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Nanostructure and transition of a strong polyelectrolyte brush at the air/water interface

The strong polyelectrolyte layer in the monolayer of ionic amphiphilic diblock copolymers at the air/water interface consists of carpet and brush layers when the brush density is satisfactorily high like that of the weak acid polymer. Also, a drastic structural change was induced by the addition of salt to the brush layer. In this study, the critical brush density for the transition between "carpet-only" and "carpet + brush" structures for the strongly ionic amphiphilic diblock copolymer, poly(hydrogenated isoprepene)-b-poly(styrene sulfonic acid) sodium salt, monolayer was measured by an in situ X-ray reflectivity technique. The critical brush density was found to be about 0.12 nm-2, which is lower than that observed for a weak acid polymer and, unlike the weak acid polymer, is independent of the hydrophilic chain length. This difference might be attributed to the strong ionic nature of the brush chain. In addition, the reversibility of the transition was confirmed. The effect of salt addition to the nanostructure of the carpet layer was examined in detail. No structural change was found, indicating that most of the ionic groups in the carpet layer do not show an ionic nature because of counterion condensation.     

Polymer nanostructure development of fluorinated and aliphatic monoacrylates in smectic liquid crystals via photopolymerization

To develop viable polymer stabilized liquid crystal systems, it is crucial to understand the factors that affect polymer nanostructure evolution. This work examines the influence of the photopolymerization of aliphatic and fluorinated monoacrylate monomer within a room temperature smectic liquid crystal (LC). Additionally, the effect of LC order on polymerization kinetics, monomer and polymer organization, and the effect of the polymer on LC properties have been examined. Through this work, insight has been gained regarding the impact that the introduction of a fluorinated monoacrylate monomer has on polymerization kinetics, LC organization, and monomer/polymer segregation and organization within a polymer/LC system. Fluorinated moieties lower the surface energy of the monomer to enhance segregation between the smectic layers of the LC as compared with an analogous aliphatic monomer. Additionally, the enhanced segregation significantly increases the polymerization rate in the smectic phase and drives the continued segregation of the fluorinated polymer during and after polymerization. Fluorination also leads to the formation of an ordered polymer nanostructure if polymerized in ordered LC phases. This ordering is particularly evident when the fluorinated monomer is polymerized in the smectic phase in which the monomer is organized between the smectic layers of the LC. In addition, the ordered polymer structure found with the fluorinated monomer in the smectic phase leads to continued birefringence above the clearing point of the LC due to surface interactions between the LC and the ordered fluorinated polymer. The continued birefringence offers an exceptional opportunity to examine how factors such as polymer molecular mass and UV light intensity affect the overall polymer morphology of these polymer/LC systems. As the initiator concentration and UV light intensity are decreased, longer polymer chains form lattice-type morphologies; whereas, shorter polymer chains form smoother morphologies that more closely mirror the texture of the LC smectic phase.     

Polymer nanostructure development of fluorinated and aliphatic monoacrylates in smectic liquid crystals via photopolymerization

To develop viable polymer stabilized liquid crystal systems, it is crucial to understand the factors that affect polymer nanostructure evolution. This work examines the influence of the photopolymerization of aliphatic and fluorinated monoacrylate monomer within a room temperature smectic liquid crystal (LC). Additionally, the effect of LC order on polymerization kinetics, monomer and polymer organization, and the effect of the polymer on LC properties have been examined. Through this work, insight has been gained regarding the impact that the introduction of a fluorinated monoacrylate monomer has on polymerization kinetics, LC organization, and monomer/polymer segregation and organization within a polymer/LC system. Fluorinated moieties lower the surface energy of the monomer to enhance segregation between the smectic layers of the LC as compared with an analogous aliphatic monomer. Additionally, the enhanced segregation significantly increases the polymerization rate in the smectic phase and drives the continued segregation of the fluorinated polymer during and after polymerization. Fluorination also leads to the formation of an ordered polymer nanostructure if polymerized in ordered LC phases. This ordering is particularly evident when the fluorinated monomer is polymerized in the smectic phase in which the monomer is organized between the smectic layers of the LC. In addition, the ordered polymer structure found with the fluorinated monomer in the smectic phase leads to continued birefringence above the clearing point of the LC due to surface interactions between the LC and the ordered fluorinated polymer. The continued birefringence offers an exceptional opportunity to examine how factors such as polymer molecular mass and UV light intensity affect the overall polymer morphology of these polymer/LC systems. As the initiator concentration and UV light intensity are decreased, longer polymer chains form lattice-type morphologies; whereas, shorter polymer chains form smoother morphologies that more closely mirror the texture of the LC smectic phase.     

Detection of creatinine using surface-driven ordering transitions of liquid crystals

Determining creatinine levels in blood is of great importance in the detection of high risk for renal failure. Here, we report a simple methodology for real-time monitoring of creatinine employing surface-driven ordering transitions in liquid crystals (LCs) by changing pH in presence of creatinine deiminase enzyme. It is found that when 5CB (4-Cyano-4?-pentylbiphenyl) LC doped with 4?-hexyl-biphenyl-4-carboxylic acid, a bright optical appearance was observed (at aqueous–LC interface) which is not disturbed in presence of creatinine, consistent with a planar/tilted orientation of the LC molecules at those interface. Interestingly, in presence of creatinine deiminase, an ordering transition was observed resulting from enzymatic reactions (giving rise to NH₄⁺ ions) that can change the local pH values and lead to dark optical appearance of the LC. Presence of different amounts of creatinine would lead varied ordering transition that can be monitored in real time in presence of creatinine deiminase. Our approach could detect the creatinine levels as low as that of the healthy adult (~50 µM) and can be successfully applied to measure higher concentration of creatinine in real time using dynamic optical response of the LC.     

Phase transition of a single star polymer: a Wang-Landau sampling study

Star polymers, as an important class of nonlinear macromolecules, process special thermodynamic properties for the existence of a common connecting point. The thermodynamic transitions of a single star polymer are systematically studied with the bond fluctuation model using Wang-Landau sampling techniques. A new analysis method employing the shape factor is proposed to locate the coil-globule (CG) and liquid-crystal (LC) transitions, which shows a higher efficiency and accuracy than the canonical specific heat function. The LC transition temperature is found to obey the identical scaling law as the linear polymers. However, the CG transition temperature shifts towards the LC transition with the increasing of the arm number. The reason is that for the star polymer a lower temperature is needed for the attractive force to overcome the excluded volume effect of the polymer chain because of its high arm density. This work clearly proves the structural distinction of the linear and star polymers can only affect the CG transition while has no influence on the LC transition.     

Connecting the wetting and rheological behaviors of poly(dimethylsiloxane)-grafted silica spheres in poly(dimethylsiloxane) melts

Using dynamic light scattering, mechanical rheometry, and visual observation, the static wetting behavior of PDMS-grafted silica spheres (PDMS-g-silica) in PDMS melts is related to their rheology. A phase diagram is mapped out for a constant grafted chain length as a function of grafting density and free polymer chain length. The transition between stable and aggregated regions is determined optically and with dynamic light scattering. It is associated with a first-order wetting transition. In the stable region Newtonian behavior is observed for semidilute suspensions. The hydrodynamic brush thicknesses, deduced from viscosity measurements, correspond closely to values obtained from self-consistent field calculations for the various parameter values. At the transition, the brush collapses suddenly and shear-thinning and thixotropy appear. The rheology indicates a degree of aggregation that increases with increasing length of the free polymer, as suggested by the theory.