Diblock Copolymers In Selective Solvent Research Articles

Modeling the Phase Equilibria of Associating Polymers in Porous Media with Respect to Chromatographic Applications.

Associating copolymers self-assemble during their passage through a liquid chromatography (LC) column, and the elution differs from that of common non-associating polymers. This computational study aims at elucidating the mechanism of their unique and intricate chromatographic behavior. We focused on amphiphilic diblock copolymers in selective solvents, performed the Monte Carlo (MC) simulations of their partitioning between a bulk solvent (mobile phase) and a cylindrical pore (stationary phase), and investigated the concentration dependences of the partition coefficient and of other functions describing the phase behavior. The observed abruptly changing concentration dependences of the effective partition coefficient demonstrate the significant impact of the association of copolymers with their partitioning between the two phases. The performed simulations reveal the intricate interplay of the entropy-driven and the enthalpy-driven processes, elucidate at the molecular level how the self-assembly affects the chromatographic behavior, and provide useful hints for the analysis of experimental elution curves of associating polymers.

Self-assembly of linear diblock copolymers in selective solvents: from single micelles to particles with tri-continuous inner structures.

Large-scale dissipative particle dynamics (DPD) simulations have been performed to investigate the self-assembly of over 20 000 linear diblock copolymer chains in a selective solvent. Specifically, we found that the transition from spherical to cylindrical vesicles and in turn to disk-like and onion-like vesicles, and finally to tri-continuous spherical particles is mainly due to the increase in the aggregation number. In addition, the structures with large aggregation numbers are formed through the fusion of smaller aggregates and the length of the corona block of the block copolymer plays a critical role in the resulting morphology. Furthermore, our simulations indicate that the very larger amount of polymer in our simulation is the key to the observation of a state of dynamic equilibrium between free chains and aggregates in solution, as well as the formation of more complex structures from linear diblock copolymers in selective solvents. Overall, this study paves the way for future coordinated experimental/computational studies on the formation of nanoparticles with complex morphologies from diblock copolymers, an area of great scientific and industrial interest.

Rheological characterization of BCC and FCC structures in aqueous diblock copolymer liquid crystals

Low molecular weight, amphiphilic diblock copolymers in selective solvent exhibit complex phase behavior and macroscopic properties that affect the processing and application of these materials. The mechanical properties of the crystalline phases seen in concentrated solutions are dependent on nanoscale structure and sample history. The goal of this study is to characterize macroscopic properties and thermal history effects of lyotropic liquid crystals in aqueous diblock copolymer solutions. Rheological temperature ramps are used to characterize three aqueous concentrations of diblock copolymer [Brij-58®, C16H33(CH2CH2O)20OH]. Between these three samples the order-disorder transitions (ODTs) for BCC and FCC are accessible in addition to the order-order transition (OOT) between BCC and FCC. These transitions are distinguished using rheology. Frequency sweeps are performed across a range of temperatures and parameterized with a loglinear fit to the phase angle data to extract the crossover frequency. We find that a single frequency sweep does not distinguish BCC and FCC structures. By normalizing the temperature with respect to the ODT, we are able to use a series of frequency sweeps to distinguish characteristic trends in the response of BCC and FCC structures to thermal history.

The directed self-assembly of amphiphilic diblock copolymers in selective solvents

ABSTRACTThe directed self-assembly of diblock copolymers in solvents is studied systematically using a simulated annealing method. Effects of the shape, scale, and adsorption capacity of the induced surface on the morphology of the aggregates are examined. A variety of morphologies are predicted. By increasing the scale of induced surface, the micellar shape transforms from cylinder to sheet with a tail and finally to thin sheet without tail. The shape of induced surface determines the sheet’s shape, such as rounded and square. Configurations of hydrophobic blocks and interfacial energies are investigated by calculating the mean square end-to-end distances and the contact numbers between hydrophobic monomer and other species, respectively.

Physical deposition behavior of charged amphiphilic diblock copolymers: Effect of charge distribution and electric field

Coarse-grained molecular dynamics simulations are used to investigate physical deposition behavior of charged amphiphlic diblock copolymers. The effects of solvent selectivity, charge distribution in amphiphlic diblock copolymers, and electric field strength on deposition conformations are studied qualitatively. Flat amphiphilic bilayers, which consist of hydrophilic monolayer and hydrophobic brush, are formed by physical deposition of charged amphiphlic diblock copolymers in nonselective solvents. For physically deposited amphiphlic diblock copolymers in selective solvents, amphiphilic bilayers consist of disc-shaped hydrophilic monolayers and hydrophobic nanospheres are found. This study sheds light on the formation of various amphiphlic diblock copolymer deposition conformations in different solvents and interaction mechanism of different components. Furthermore, the evolution of physical deposition process of charged amphiphlic diblock copolymers layer offers new insight to the controlling of amphiphilic bilayer thickness, hydrophobic nanosphere size, and interface property of depositional amphiphlic diblock copolymers.

Aggregation behavior of cyclic rod-coil diblock copolymers in selective solvents

The aggregation behavior of cyclic rod-coil (RC) diblock copolymers in dilute solutions is investigated through dissipative particle dynamics simulation. By varying the rod length and coil length, cyclic RC copolymers in selective solvents exhibit various morphologies, including spherical micelle, vesicle, bilayer disc, and ribbon bundle structure. Compared with the equivalent linear RC copolymer, only spherical micelle and barrel bundle phase are observed. Rod length is the major factor that controls the liquid-crystalline behavior of RC copolymer systems, while the coil length has a secondary effect on the aggregate morphology. The size of rod bundle varies with the coil length, especially for the end-toend ribbon bundle and side-by-side barrel bundle, which are assembled by cyclic and linear RC copolymer solutions. This finding indicates that the ribbon bundle or nanofiber-like structure in cyclic RC copolymers can be obtained by controlling the rod length and coil length, and thus the optical and electrical properties of RC copolymer would be further controlled and optimized. Results illustrate that cyclization of a linear RC copolymer induces remarkable differences in the rod arrangement and aggregation behavior, thereby indicating the competition between interfacial energy, rod orientational entropy, coil stretching entropy, and packing constraints.

Trivial and Non-Trivial Supramolecular Assemblies Based on Nafion

We demonstrate that Nafion, a perfluorosulfonic acid ionomer, undergoes synergistic mixing with non-ionic diblock copolymers in selective solvents. A range of experimental techniques (Quartz Crystal Microbalance, Dynamic Light Scattering, optical microscopy, TEM and SEM) was employed to gain insights on the evolution of ionomer–copolymer supramolecular assemblies. Depending on the copolymer architecture and the type of the suspension medium, spherical nanoparticles, micron-long tubular conformations or vesicular structures are formed. Those morphologies are dictated by localized interactions arising from Nafion's amphiphilicity. The effect has implications on the preparation of the technologically important ion conducting membranes.

Critical Micelle Concentration of Micelles with Different Geometries in Diblock Copolymer/Homopolymer Blends

AbstractIt is well‐known that A‐B diblock copolymers in selective solvents or A‐homopolymers can form micelles of different shapes. The critical micelle concentration (CMC) of three basic micelle shapes (lamellar, cylindrical, and spherical) are calculated using the self‐consistent field theory formulated in the grand canonical ensemble. For a given set of molecular parameters, the stable micelle morphology is determined by a comparison of the CMC. The results confirm that micelles undergo a sequence of shape transitions, lamellar → cylindrical → spherical, when the A‐block of the diblock copolymer becomes longer. The results also reveal details about the micelle structure, such as the core radius and corona thickness. This information can be used to understand the effect of homopolymer molecular weight and monomer–monomer interaction on the micelle morphologies.magnified image

A systematic coarse-graining strategy for semi-dilute copolymer solutions: from monomersto micelles

A systematic coarse-graining procedure is proposed for the description and simulation ofAB diblock copolymers in selective solvents. Each block is represented by a small number,nA ornB, of effective segments or blobs, containing a large number of microscopic monomers.nA andnB are unequivocally determined by imposing that blobs do not, on average, overlap,even if complete copolymer coils interpenetrate (semi-dilute regime). Ultra-softeffective interactions between blobs are determined by a rigorous inversionprocedure in the low concentration limit. The methodology is applied to anathermal copolymer model where A blocks are ideal (theta solvent), B blocksself-avoiding (good solvent), while A and B blocks are mutually avoiding. Themodel leads to aggregation into polydisperse spherical micelles beyond a criticalmicellar concentration determined by Monte Carlo simulations for several size ratiosf of the two blocks. The simulations also provide accurate estimates of the osmotic pressureand of the free energy of the copolymer solutions over a wide range of concentrations. Themean micellar aggregation numbers are found to be significantly lower than those predictedby an earlier, minimal two-blob representation (Capone et al 2009 J. Phys. Chem. B 113 3629).

Effect of conformational asymmetry on the self-assembly of amphiphilic diblock copolymer in selective solvent

Three dimensional real-space self-consistent field theory is employed to study the effect of conformational asymmetry on the self-assembly of amphiphilic diblock copolymer in selective solvent. The phase diagrams in wide ranges of interaction parameters and conformational asymmetry were obtained in present study. The results indicate that the conformational asymmetry is an important factor that determines the self-assembly of amphiphilic diblock copolymer in solution. The self-assembled morphology changes from sphere to rod, then to vesicle with an increase of the degree of conformational asymmetry. We found that the entropic contribution of the core-forming block is the main reason for this transition.

Effect of Solvent Molecular Size on the Self‐Assembly of Amphiphilic Diblock Copolymer in Selective Solvent

AbstractReal‐space self‐consistent field theory (SCFT) is employed to study the effect of solvent molecular size on the self‐assembly of amphiphilic diblock copolymer in selective solvent. The phase diagrams in wide ranges of interaction parameters and solvent molecular size were obtained in present study. The results indicate that the solvent molecular size is a key factor that determines the self‐assembly of amphiphilic diblock copolymer. The self‐assembled morphology changes from circle‐like micelle to line‐like micelle, then to loop‐like micelle by decreasing the solvent molecular size in a wide range of solvent selectivity. We analyze and discuss this change in terms of the solvent solubility and the entropy contribution.magnified image

A Theoretical Study of Phase Behaviors for Diblock Copolymers in Selective Solvents

A self-consistent mean-field theory (SCMFT) study on the phase behaviors of AB-diblock copolymer solutions is presented. All of the possible thermodynamically stable ordered structures verified by experiments are considered and the phase diagrams are generated. This work mainly focuses on the cases of selective solvents. The results show that a series of phase transitions occurs upon dilution. In particular, large windows of lamellae + cylinder coexistence are located for the cases of highly asymmetric diblock copolymers in strongly selective solvents, which is in agreement with previous experimental observations. The transitions between the “inverted” fcc structure and the “inverted” bcc structure are also observed. The calculation indicates that the copolymer−solvent interaction plays important roles in these transitions.

Monte Carlo Phase Diagram of Symmetric Diblock Copolymer in Selective Solvent

With a lattice Monte Carlo method, we investigate 16−16 symmetric diblock in selective solvent, A-b-B/A, at 10 volume fractions from 1.0 to 0.1, and for each volume fraction, we perform simulations at up to 54 temperatures, using simulation boxes of different sizes. We report temperature dependencies for a number of quantities such as energy, specific heat, and mean-squared end-to-end distances and construct a phase diagram using the thermodynamic and structural quantities as well as snapshots of the selected configurations. The simulated phase diagram is compared with the experimental data of Lodge and co-workers for nearly symmetric poly(styrene-b-isoprene) mixed with dimethyl phthalate.

On the selection of FCC and BCC lattices in poly(styrene-b-isoprene) copolymer micelles

Spherical micelles of poly(styrene-b-isoprene) (SI) diblock copolymers in selective solvents have been reported to pack onto either face-centered cubic (fcc) or body-centered cubic (bcc) lattices. The selection rule for fcc and bcc lattices has been understood in terms of the intermicellar potentials, and they have been quantified using the ratio of the corona layer thickness to the core radius,L/R c , as suggested by McConnell and Gast. In order to test the validity of the McConnell-Gast criterion, this study compared theL/R c values from various solutions i.e. nine SI copolymers in several different selective solvents. The McConnell-Gast criterion was not found to be a determining factor, even though it could explain the fcc/bcc selection qualitatively. From the phase diagrams, the transition between fcc and bcc phases was also considered as a function of concentration and temperature, and their physical mechanisms are discussed based on the recent mean-field calculation reported by Grason.

Ordered phases of diblock copolymers in selective solvent

The authors propose a mean-field model to explore the equilibrium coupling between micelle aggregation and lattice choice in neutral copolymer and selective solvent mixtures. They find both thermotropic and lyotropic transitions from face-centered cubic to body-centered cubic ordered phases of spherical micelles, in agreement with experimental observations of these systems over a broad range of conditions. The stability of the nonclosed packed phase can be attributed to two physical mechanisms: the large entropy of lattice phonons near crystal melting and the preference of the intermicelle repulsions for the body-centered cubic structure when the lattice becomes sufficiently dense at higher solution concentrations. Both mechanisms are controlled by the decrease of micelle aggregation and subsequent increase of lattice density as solvent selectivity is reduced. These results shed new light on the relationship between micelle structure--"crewcut" or "hairy"--and long-range order in micelle solutions.

Micellization of ω-Functionalized Diblock Copolymers in Selective Solvent. Study on the Effect of Hydrogen Bonds

Two series of ω-functionalized diblock copolymers polystyrene-b-polyisoprene, PS−PI, having hydroxyl end groups either at the PS (PI−PS−OH) or at the PI (PS−PI−OH) block were synthesized by living anionic polymerization. The samples had similar molecular weights but different compositions. Employing suitable post-polymerization reactions the hydroxyl groups were transformed to the corresponding 2-ureido-4-pyrimidinone (UPy) functions. The UPy group is known to dimerize strongly in a self-complementary array of four cooperative hydrogen bonds. The micellization properties of the unfunctionalized and the ω-functionalized polymers having either hydroxyl or UPy end groups were studied in n-decane, which is a selective solvent for the PI block, by static and dynamic light scattering and dilute solution viscometry. A distinct micellar behavior was obtained depending on the nature of the end group and their location either at the core-forming or the corona-forming block. To confirm the results regarding the effect of the hydrogen bonds the solid-state properties of the copolymers were studied by differential scanning calorimetry and thermogravimetric analysis. Furthermore, the dilute solution properties were investigated in chloroform, which is a common good solvent for both the PS and PI blocks but nonpolar, thus allowing the formation of hydrogen bonds.

Simulated annealing study of morphological transitions of diblock copolymers in solution

The simulated annealing method was applied to study the self-assembling process of diblock copolymers in selective solvents for one block. The simulation results illustrated that the morphologies of the copolymer aggregates strongly depend on the interactions between the core-forming blocks and the solvents and on the length of the corona-forming blocks. Multiple morphological transitions were observed in one system. The transition sequence (disordered state-spherical micelles-short rodlike micelles-long rodlike micelles-onionlike aggregates) was observed for copolymers with increasing core-solvent interaction. Similar transitions were observed with the decrease of the length of the corona-forming blocks. The mechanisms of these transitions are investigated. The simulation results are compared with experiments and other simulations.

Diblock Copolymer Micelles in a Dilute Solution

We performed theoretical and experimental investigations of dilute solutions of micelles of neutral amorphous diblock copolymers in selective solvents. The ranges of thermodynamic stability of spherical, cylindrical, and lamellar morphologies along with the equilibrium sizes and aggregation numbers of micelles are calculated and measured. For high molecular weight copolymers it is shown that the sphere-to-cylinder transition as well as precipitation of the micelles associated with cylinder-to-lamella transition occurs when aggregates have a crew-cut structure with the thickness of the corona smaller than the radius of the core. Similar to starlike micelles with corona larger than the core, the equilibrium parameters of crew-cut micelles are determined by the balance between the free energy of the corona and the surface energy of the core. The elastic free energy of the core remains small compared to the corona and surface free energies; however, it determines the transitions between different morphologies...

Order−Disorder Transition and Critical Micelle Temperature in Concentrated Block Copolymer Solutions

The phase behavior of symmetric styrene−isoprene (SI) diblock copolymers in selective solvents in the vicinity of the order−disorder transition (ODT) was investigated by small-angle neutron scattering (SANS). Particular emphasis is placed on the region just above the ODT, where a disordered phase of micelles is observed. To understand morphological changes in more detail, one of the blocks is deuterated, i.e., PS−dPI and dPS−PI, and the scattering length density (SLD) of the solvents used were identical to the SLD of the corona chains. Two approaches for the analysis of SANS data were taken: the generalized indirect Fourier transformation (GIFT) and direct model fitting with relevant form and structure factors. With increasing temperature, the micellar aggregation number decreases, and the core radius is roughly maintained by the increased solvent swelling of the core. The critical micelle temperature (cmt) is experimentally described in the present study by an abrupt decrease in the size, aggregation number, and volume fraction of micelles. The micelles were found to dissociate into free chains approximately 20−30 °C higher than the TODT, and the cmt is found to be quite close to the mean-field spinodal temperature TS. A mean-field temperature, TMF, is located by the crossover temperature from the linear behavior of Imax-1 vs T-1 plot, and the structure factor above the experimentally determined TMF is also found to be in good agreement with the Leibler−Landau-type mean-field theory. We examined two different ODTs: body-centered cubic lattices to disorder and hexagonal cylinders to disorder, with similar results in both cases.

Self-assembly behaviour of amphiphilic diblock copolymer in selective solvents studied by synchrotron small-angle x-ray scattering

The aggregation behaviour of styrene-vinyl benzoic acid (PSm-b-PVBAn) amphiphilic diblock copolymers in selective solvents with different m and n was investigated by synchrotron small-angle x-ray scattering (SAXS). We have carried out a detailed analysis of scattering intensity, dimension, shape and microstructure of the diblock copolymers of narrow distribution in water, methanol, ethanol and isopropanol selective solvents, respectively. We have found that the aggregation behaviour of the copolymer depends on the nature of the solvent and the micelle forms flat disc objects with the ratio of radius ω=0.4. The average radius gyration Rg of the copolymer decreases as solvents change from isopropanol to ethanol and to methanol and increases with increasing pH in aqueous solution, but decreases with the addition of CoCl2 in ethanol solvent. The scattering intensity of diblock copolymer micelle follows I(h)∝h-α in different selective solutions, suggesting that the PSm-b-PVBAn coils have self-similar structure behaviour or a fractal structure in the selective solvents. All of these revealed that the aggregation behaviour of the diblock copolymer changes dramatically with experimental condition in the selective solvent. The increase of mass fractal dimension (Dm) from 2.12 to 2.47 indicates that the copolymer chain changes from a swollen coil to a rather compact disc in the course of changing solvents, decreasing surface fractal dimension (Ds) from 2.98 to 2.58 indicates that the copolymer micelle change from a rather rough surface to a smooth form in the course of increasing pH in aqueous solutions and increasing Dm and Ds from 2.29 to 2.35 and 2.70 to 2.90, respectively, indicates the shrinkage of copolymer micelle to a rather compact and rough disc form by adding CoCl2 in ethanol solvents.