Polymeric micelles are used in a variety of applications, with the micelle's shape often playing an important role. Consequently, a scheme to design micelles of arbitrary shape is desirable. In this paper, we consider micelles formed from a single, linear, multiblock copolymer, and we study how easily the micelle's shape can be controlled by altering the copolymer block lengths. Using a rational design scheme, we identify a few aspects of the multiblock composition that are expected to have a well-behaved, predictable effect on micelle shape. Starting from a reference micelle composition, itself already exhibiting a nonstandard shape having a moderately sized dimple, we alter these aspects of the multiblock composition and observe the regularity of the micelle shape response. The response of the shape is found to be somewhat smooth, but significantly nonlinear and sometimes nonmonotonic, suggesting that sophisticated techniques may be required to aid in micelle design.
We investigate the effect of polymer length dispersity on the properties of self-assembled micelles in solution by self-consistent field calculations. Polydispersity stabilizes micelles by raising the free energy barriers of micelle formation and dissolution. Most importantly, it significantly reduces the size fluctuations of micelles: Block copolymers of moderate polydispersity form more uniform particles than their monodisperse counterparts. We attribute this to the fact that the packing of the solvophobic monomers in the core can be optimized if the constituent polymers have different lengt…
Conventional micelles, composed of simple amphiphiles, exhibit only a few standard morphologies, each characterized by its mean surface curvature set by the amphiphiles. Here we demonstrate a rational design scheme to construct micelles of more general shape from polymeric amphiphiles. We replace the many amphiphiles of a conventional micelle by a single flexible, linear, block copolymer chain containing two incompatible species arranged in multiple alternating segments. With suitable segment lengths, the chain exhibits a condensed spherical configuration in solution, similar to conventional m…
Following up a recent paper on grafted sliding polymer layers (Macromolecules 2005, 38, 1434-1441), we investigated the influence of the sliding degree of freedom on the self-assembly of sliding polymeric surfactants that can be obtained by complexation of polymers with cyclodextrins. In contrast to the micelles of quenched block copolymer surfactants, the free energy of micelles of sliding surfactants can have two minima: the first corresponding to small micelles with symmetric arm lengths, and the second corresponding to large micelles with asymmetric arm lengths. The relative sizes and conc…
We use the Random Phase Approximation (RPA) to compute the structure factor, S(q), of a solution of chains interacting through a soft and short range repulsive potential V. Above a threshold polymer concentration, whose magnitude is essentially controlled by the range of the potential, S(q) exhibits a peak whose position depends on the concentration. We take advantage of the close analogy between polymers and wormlike micelles and apply our model, using a Gaussian function for V, to quantitatively analyze experimental small angle neutron scattering profiles of semi-dilute solutions of hairy wo…
The equilibrium properties of block copolymer micelles confined in polymer thin films are investigated using self-consistent field theory. The theory is based on a model system consisting of AB diblock copolymers and A homopolymers. Two different methods, based on the radius of gyration tensor and the spherical harmonics expansion, are used to characterize the micellar shape. The results reveal that the morphology of micelles in thin films depends on the thickness of the thin films and the selectivity of the confining surfaces. For spherical (cylindrical) micelles, the spherical (cylindrical) …
We use a hybrid method that combines the Multiparticle collision dynamics (MPCD) for solvent particles with the molecular dynamics for equilibrium polymers to simulate the shearing of the equilibrium polymers (or Wormlike micelles) at a mesoscopic length scale. The MPCD method incorporates the hydrodynamic interaction with the polymeric chains. We show successful implementation of the method on the model equilibrium polymers (or Wormlike micelles) and observe that the order of the Iso-Nem transition of the polymeric system is affected by the shear rate. Moreover, the chains of the equilibrium …
The effects of the length of each hydrophobic end block N_{st} and polymer concentration \barϕ_{P} on the transition broadness in amphiphilic ABA symmetric triblock copolymer solutions are studied using the self-consistent field lattice model. When the system is cooled, micelles are observed, i.e.,the homogenous solution (unimer)-micelle transition occurs. When N_{st} is increased, at fixed \barϕ_{P}, micelles occur at higher temperature, and the temperature-dependent range of micellar aggregation and half-width of specific heat peak for unimer-micelle transition increase monotonously. Compare…
If many micelles adsorb onto the same polymer molecule then they are said to form a necklace. A minimal model of such a necklace is proposed and shown to be almost equivalent to a 1-dimensional fluid with nearest-neighbour interactions. The thermodynamic functions of this fluid are obtained and then used to predict the change in the critical micellar concentration of the surfactant in the presence of the polymer. If the amount of polymer is not too large there are two critical micellar concentrations, one for micelles in necklaces and one for free micelles.
We present an extensive computer simulation study of structure formation in amphiphilic block copolymer solutions after a quench from a homogeneous state. By using a mesoscopic field-based simulation method, we are able to access time scales in the range of a second. A phase diagram of final structures is mapped out as a function of the concentration and solvent-philicity of the copolymers. A rich spectrum of structures is observed, ranging from spherical and rodlike micelles and vesicles to toroidal and net-cage micelles. The dynamical pathways leading to these structures are analyzed in deta…
We survey the linear viscoelasticity of a new type of transient network: bridged wormlike micelles, whose structure has been characterized recently [Ramos and Ligoure, (2007)]. This composite material is obtained by adding telechelic copolymers (water-soluble chains with hydrophobic stickers at each extremity) to a solution of entangled wormlike micelles (WM). For comparison, naked WM and WM decorated by amphiphilic copolymers are also investigated. While these latter systems exhibit almost a same single ideal Maxwell behavior, solutions of bridged WM can be described as two Maxwell fluids com…
Amphiphilic block copolymer solutions form various micellar structures including micelles and vesicles. We applied the density functional theory for block copolymers which we have proposed to amphiphilic block copolymer systems. The 3 dimensional simulation for AB diblock copolymer solutions and AB diblock copolymer / A homopolymer blends has been done and it is shown that the spherical micelles, cylindrical micelles and spherical vesicles are formed. It is also shown that the phase diagram for AB diblock copolymer / A homopolymer blends qualitatively agrees with the phase diagram obtained by …
The nanoparticle-Equilibrium polymer (or Wormlike micellar) system shows morphological changes from percolating network-like structures to non-percolating clusters with a change in the minimum approaching distance (EVP-excluded volume parameter) between nanoparticles and the matrix of equilibrium polymers. The shape anisotropy of nanoparticle clusters can be controlled by changing the polymer density. In this paper, the synergistic self-assembly of nanoparticles inside equilibrium polymeric matrix (or Wormlike micellar matrix) is investigated with respect to the change in the strength of attra…
We investigate the effect of the size of nanoparticles on the behaviour of equilibrium polymers (Wormlike micelles) and nanoparticle system. The self-organised structures of nanoparticles in the system show a morphological change from percolating networks to non-percolating clusters with an increase in the minimum approaching distance (EVP-excluded volume parameter) between nanoparticles and the equilibrium polymers. The shape of the nanoparticle clusters (nanorods, nanosheets, etc.) depends on the density of the polymer matrix, irrespective of the size of nanoparticles. We show that with an i…
Homogeneous polymer solutions are well-known to exhibit viscoelastic flow instabilities: purely elastic when inertia is negligible, inertio-elastic otherwise. Recently, shear-banding wormlike micelles solutions were also discovered to follow a similar phenomenology. In the shear-banding regime, inertia is usually negligible so only purely elastic flows have been reported. Here, we investigate a non-shear-banding solution where inertia becomes significant, leading to flow patterns akin to the inertio-elastic regime of dilute polymer solutions. We show that the instability follows a supercritica…
Polymers with both soluble and insoluble blocks typically self-assemble into micelles, aggregates of a finite number of polymers where the soluble blocks shield the insoluble ones from contact with the solvent. Upon increasing concentration, these micelles often form gels that exhibit crystalline order in many systems. In this paper, we present a study of both the dynamics and the equilibrium properties of micellar crystals of triblock polymers using molecular dynamics simulations. Our results show that equilibration of single micelle degrees of freedom and crystal formation occurs by polymer …
Using the self-consistent field lattice model, polymer concentration $\barϕ_{P}$ and chain length $N$ (keeping the length ratio of hydrophobic to hydrophilic blocks constant) the effects on temperature-dependent behavior of micelles are studied, in amphiphilic symmetric ABA triblock copolymer solutions. When chain length is increased, at fixed $\barϕ_{P}$, micelles occur at higher temperature. The variations of average volume fraction of stickers $\barϕ_\textrm{co}^\textrm{s}$ and the lattice site numbers $N_\textrm{co}^\textrm{ls}$ at the micellar cores with temperature are dependent on $N$ a…
PEP-PEO block copolymer micelles offer the possibility to investigate phase behaviour and interactions of star polymers (ultra-soft colloids). A star-like architecture is achieved by an extremely asymmetric block ratio (1:20). Micellar functionality f can be smoothly varied by changing solvent composition (interfacial tension). Structure factors obtained by SANS can be quantitatively described in terms of an effective potential developed for star polymers. The experimental phase diagram reproduces to a high level of accuracy the predicted liquid/solid transition. Whereas for intermediate f a b…
We study theoretically the formation of shear bands in time-dependent flows of polymeric and wormlike micellar surfactant fluids, focussing on the protocols of step shear stress, step shear strain (or in practice a rapid strain ramp), and shear startup, which are commonly studied experimentally. For each protocol we perform a linear stability analysis to provide a fluid-universal criterion for the onset of shear banding, following our recent Letter [Phys. Rev. Lett. 110 (2013) 086001]. In each case this criterion depends only on the shape of the experimentally measured rheological response fun…
Half-integer Topological Defects Paired via String Micelles in Polar Liquids
Southern University of Science and Technology（南方科技大学）；Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology（广东省功能性与智能杂化材料器件重点实验室，华南理工大学）
In this paper we examine the effective interactions introduced between the droplets of an oil in water microemulsion upon progressive addition of hydrophobically modified water soluble poly(ethylene oxide)-PEO using essentially small angle neutron scattering. To discuss the relative importance of decoration and bridging of the droplets we compare analogous samples with addition of a PEO grafted at both extremities with hydrophobic C12H 25 chains (PEO-2m) or addition of a PEO grafted at one extremity only with a C12H 25 chain (PEO-m). PEO-m or PEO-2m adsorb onto the droplets via their hydrophob…
We investigate theoretically shear banding in large amplitude oscillatory shear (LAOS) of polymers and wormlike micelles. In LAOStrain we find banding at low frequencies and sufficiently high strain rate amplitudes in fluids for which the underlying constitutive curve of shear stress as a function of shear rate is non-monotonic. This is the direct analogue of quasi steady state banding seen in slow strain rate sweeps along the flow curve. At higher frequencies and sufficiently high strain amplitudes we report a different but related phenomenon, which we call `elastic' shear banding. This is as…
Double emulsions, due to their compartmental structures, are essential in food, agricultural, and pharmaceutical applications. Traditionally, double emulsifications rely on the presence of both oil-soluble and water-soluble surfactants or external stimuli responsive materials and require sequential droplet formation settings or unique fluidic designs. We report on unusual phenomenon where double emulsions are spontaneously formed as soon an aqueous nanoparticle dispersion is placed in contact with an oleic micellar solution. Nanoscale water droplets nucleate in oil in the form of swollen micel…
We report on the formation of colloidal complexes resulting from the electrostatic self-assembly of polyelectrolyte-neutral block copolymers and oppositely charged surfactants. The copolymers investigated are asymmetric and characterized by a large neutral block. Using light, neutron and x-ray scattering experiments, we have shown that the colloidal complexes exhibit a core-shell microstructure. The core is described as a dense and disordered micro-phase of micelles connected by the polyelectrolyte blocks, whereas the shell is a diffuse brush made from the neutral chains. Colloidal complexes w…
We carry out numerical simulations of vesicle formation based on the density functional theory for block copolymer solutions. It is shown by solving the time evolution equations for concentrations that a polymer vesicle is spontaneously formed from the homogeneous state. The vesicle formation mechanism obtained by our simulation agree with the results of other simulations based on the particle models as well as experiments. By changing parameters such as the volume fraction of polymers or the Flory-Huggins interaction parameter between the hydrophobic subchains and solvents, we can obtain the …
We investigate the nucleation and propagation of cracks in self-assembled viscoelastic fluids, which are made of surfactant micelles reversibly linked by telechelic polymers. The morphology of the micelles can be continuously tuned, from spherical to rod-like to wormlike, thus producing transient double networks when the micelles are sufficiently long and entangled, and transient single networks otherwise. For a single network, we show that cracks nucleate when the sample deformation rate involved is comparable to the relaxation time scale of the network. For a double network, by contrast, sig…
When polyelectrolyte-neutral block copolymers are mixed in solutions to oppositely charged species (e.g. surfactant micelles, macromolecules, proteins etc), there is the formation of stable supermicellar aggregates combining both components. The resulting colloidal complexes exhibit a core-shell structure and the mechanism yielding to their formation is electrostatic self-assembly. In this contribution, we report on the structural properties of supermicellar aggregates made from yttrium-based inorganic nanoparticles (radius 2 nm) and polyelectrolyte-neutral block copolymers in aqueous solution…
A micelle consists of monolayer of lipid molecules containing hydrophilic head and hydrophobic tail. These amphiphilic molecules in aqueous environment aggregate spontaneously into monomolecular layer held together due to hydrophobic effect by weak non-covalent forces. Micelles are flexible surfaces that show variety of shapes of different topology, but remarkably in mechanical equilibrium conditions they are spherical in shape. The shape and size of a micelle are functions of many variables such as lipid concentration, temperature, ionic strength, etc. Addressing the question, why the shape o…
We present a self-consistent field theory (SCFT) study of spherical micelle formation in a blend of poly(styrene-butadiene) diblocks and homopolystyrene. The micelle core radii, corona thicknesses and critical micelle concentrations are calculated as functions of the polymer molecular weights and the composition of the diblocks. Our results are compared with an earlier scaling theory and with X-ray scattering data. The agreement between self-consistent field theory and experiment for the micelle structure is sometimes quantitative and is generally more successful than scaling theory. For copol…
Starting from a microscopic lattice model, we investigate clustering, micellization and micelle ordering in semi-dilute solutions of AB diblock copolymers in a selective solvent. To bridge the gap in length scales, from monomers to ordered micellar structures, we implement a two-step coarse graining strategy, whereby the AB copolymers are mapped onto ``ultrasoft'' dumbells with monomer-averaged effective interactions between the centres of mass of the blocks. Monte Carlo simulations of this coarse-grained model yield clear-cut evidence for self-assembly into micelles with a mean aggregation nu…
A novel type of hybrid colloids is presented, based on the association of several polymeric systems and ferrofluids. On the one hand, we use inorganic nanoparticles made of magnetic iron oxide prepared at the LI2C, which response to a magnetic field of low intensity. On the other hand the organic part is made either of long linear polyacrylamide chains or of mesoscopic structures (vesicles and micelles) self-assembled from amphiphile polybutadiene-b-poly(glutamic acid) di-block copolymers, which conformation is pH-sensitive.
We investigate condensation of a long confined chiral nematic polymer inside a spherical enclosure, mimicking condensation of DNA inside a viral capsid. The Landau-de Gennes nematic free energy {\sl Ansatz} appropriate for nematic polymers allows us to study the condensation process in detail with different boundary conditions at the enclosing wall that simulate repulsive and attractive polymer-surface interactions. Increasing the chirality, we observe a transformation of the toroidal condensate into a closed surface with an increasing genus, akin to the ordered domain formation observed in cr…
Inwardly curved polymer brushes are present in cylindrical and spherical micelles or in membranes tubes and vesicles decorated with anchored polymers, and influence their stability. We consider such polymer brushes in good solvent and show that previous works, based on a self-similar concentric structure of the brush, are physically inconsistent. We use scaling laws to derive very simply the leading term of the free energy in the high curvature limit, where the osmotic pressure is the relevant physical ingredient. We also derive the complete conformation at all curvatures using a self-consiste…
The isothermal, isobaric spontaneous crystallization of a supercooled polymer melt is investigated by MD simulation of an ensemble of fully-flexible linear chains. Frustration is introduced via two incommensurate length scales set by the bond length and the position of the minimum of the non-bonding potential. Marked polymorphism with considerable bond disorder, distortions of both the local packing and the global monomer arrangements is observed. The analyses in terms of: i) orientational order parameters characterizing the global and the local order and ii) the angular distribution of the ne…
We investigate by scattering techniques the structure of water-based soft composite materials comprising a crystal made of Pluronic block-copolymer micelles arranged in a face-centered cubic lattice and a small amount (at most 2% by volume) of silica nanoparticles, of size comparable to that of the micelles. The copolymer is thermosensitive: it is hydrophilic and fully dissolved in water at low temperature (T ~ 0°C), and self-assembles into micelles at room temperature, where the block-copolymer is amphiphilic. We use contrast matching small-angle neuron scattering experiments to probe indepen…
We study the dynamics of a knot in a semiflexible polymer confined to a narrow channel of width comparable to the polymers' persistence length. Using a combination of Brownian dynamics simulations and a coarse-grained stochastic model, we characterize the coupled dynamics of knot size variation and knot diffusion along the polymer, which ultimately leads to spontaneous unknotting. We find that the knot grows to macroscopic size before disappearing. Interestingly, an external force applied to the ends of the confined polymer speeds up spontaneous unknotting.
During the past years we have investigated the complexation between nanocolloids and oppositely charged polymers. The nanocolloids examined were ionic surfactant micelles and inorganic oxide nanoparticles. For the polymers, we used homopolyelectrolytes and block copolymers with linear and comb architectures. In general, the attractive interactions between oppositely charged species are strong and as such, the simple mixing of solutions containing dispersed constituents yield to a precipitation, or to a phase separation. We have developed means to control the electrostatically-driven attraction…
Molecular process of polymer collapse was reproduced by isothermal molecular dynamics simulation. The initial polymer chains were obtained by mean of random walks in continuum space. Two potential models were considered to represent short range interactions between monomers. Various structural properties during the collapse of the polymer were measured and different collapse pathways were observed. For low temperatures, we have obtained a spontaneous collapse to helical states.
We have linked the structural and dynamic properties in aqueous solution of amphiphilic charged diblock copolymers poly(butyl acrylate)-b-poly(acrylic acid), PBA-b-PAA, synthesized by controlled radical polymerization, with the physico-chemical characteristics of the samples. Despite product imperfections, the samples self-assemble in melt and aqueous solutions as predicted by monodisperse microphase separation theory. However, the PBA core are abnormally large; the swelling of PBA cores is not due to AA (the Flory parameter chiPBA/PAA, determined at 0.25, means strong segregation), but to h-P…
We model the environment of eukaryotic nuclei by representing macromolecules by only their entropic properties, with globular molecules represented by spherical colloids and flexible molecules by polymers. We put particular focus on proteins with both globular and intrinsically disordered regions, which we represent with `tadpole' constructed by grafting single polymers and colloids together. In Monte Carlo simulations we find these tadpoles support phase separation via depletion flocculation, and demonstrate several surfactant behaviours, including being found preferentially at interfaces and…
Minimizing the elastic free energy of a thin sheet of nematic polymer network among smooth isometric immersions is the strategy purported by the mainstream theory. In this paper, we broaden the class of admissible spontaneous deformations: we consider ridged isometric immersions, which can cause a sharp ridge in the immersed surfaces. We propose a model to compute the extra energy distributed along such ridges. This energy comes from bending; it is shown under what circumstances it scales quadratically with the sheet's thickness, falling just in between stretching and bending energies. We put …
Inspired by recent experiments on the spatial organization of bacterial chromosomes, we consider a type of "bottle brush" polymer consisting of a flexible backbone chain, to which flexible side loops are connected. We show that such a model with an open linear backbone spontaneously adopts a helical structure with a well-defined pitch when confined to small cylindrical volume. This helicity persists over a range of sizes and aspect-ratios of the cylinder, provided the packing fraction of the chain is suitably large. We analyze this results in terms of the interplay between the effective stiffn…
The complexation between charged-neutral block copolymers and oppositely charged surfactants was investigated by light scattering experiments and by isothermal titration calorimetry (ITC). The copolymer was poly(sodium acrylate)-b-poly(acrylamide) and the surfactant dodecyltrimethylammonium bromide (DTAB). In a previous report, we had shown that the copolymers and the surfactants co-assembled spontaneously into colloidal complexes. Depending of the charge ratio Z = [DTA+]/[COO-], the complexes were either single surfactant micelles decorated by copolymers, or core-shell hierarchical structures…
The structural properties of polymers adsorbed onto a surface have been widely investigated using self-consistent mean-field theories. Recently, analytical mean-field theories have been applied to study polymer adsorption on curved surfaces but all in the context of the ground state dominance approximation in which the polymer chain length (N) is essentially infinite. Using an expression for the free energy by Semenov, we determine leading order (in 1/N) corrections due to the finiteness of the polymer chain length on surface tension, spontaneous curvature, and rigidity constants.
We study the spontaneous out-of-plane bending of a planar untwisted ribbon composed of nematic polymer networks activated by a change in temperature. Our theory accounts for both stretching and bending energies, which compete to establish equilibrium. We show that when equilibrium is attained these energy components obey a \emph{complementarity} relation: one is maximum where the other is minimum. Moreover, we identify a \emph{bleaching} regime: for sufficiently large values of an activation parameter (which measures the mismatch between the degrees of order in polymer organization in the refe…
The stability of copolymer tethers is investigated theoretically. Self-assembly of diblockor triblock copolymers can lead to tubular polymersomes which are known experimentallyto undergo shape instability under thermal, chemical and tension stresses. It leads to aperiodic modulation of the radius which evolves to assembly-line pearls connected by tinytethers. We study the contributions of shear surface viscosity and spontaneous curvatureand their interplay to understand the pearling instability. The performed linear analysisof stability of this cylinder-to-pearls transition shows that such sys…
We report on a computational study of the statics and dynamics of long flexible linear polymers that spontaneously knot and unknot. Specifically, the equilibrium self-entanglement properties, such as the knotting probability, knot length and position, are investigated with extensive Monte Carlo sampling of chains of up to 15,000 beads. Tens of such equilibrated chains of up to 4, 096 beads are next used as starting points for Langevin dynamics simulations. The complex interplay of chain dynamics and self-knotting is addressed by monitoring the time evolution of various metric and entanglement …
A paradigm for internally driven matter is the active nematic liquid crystal, whereby the equations of a conventional nematic are supplemented by a minimal active stress that violates time reversal symmetry. In practice, active fluids may have not only liquid crystalline but also viscoelastic polymer degrees of freedom. Here we explore the resulting interplay by coupling an active nematic to a minimal model of polymer rheology. We find that adding polymer can greatly increase the complexity of spontaneous flow, but can also have calming effects, thereby increasing the net throughput of spontan…
