Conformational properties of rigid-chain amphiphilic macromolecules: The phase diagram

The coil-globule transition in rigid-chain amphiphilic macromolecules was studied by means of computer simulation, and the phase diagrams for such molecules in the solvent quality-persistence length coordinates were constructed. It was shown that the type of phase diagram depends to a substantial extent on the degree of polymerization of a macromolecule. Relatively short amphiphilic macromolecules in the poor-solvent region always form a spherical globule, with the transition to this globule involving one or two intermediate conformations. These are the disk globule if the Kuhn segment is relatively large and the string of spherical micelles or the disk globule in the case of relative flexible chains. The phase diagram of a long rodlike amphiphilic chain turned out to be even more complex. Namely, three characteristic regions were distinguished in the region of a poor solvent, depending on the chain rigidity: the region of a cylindrical globule without certain order in the main chain, the region of the cylindrical globule with blobs having the collagen ordering of the chain, and the region of coexistence of collagen-like and toroidal globules. In the intermediate transitional region, not only conformations of strings of spherical micelle beads but also the necklace conformations in which the polymer chain in each bead has collagen ordering can occur in this case.     

Semiflexible amphiphilic polymers: cylindrical-shaped, collagenlike, and toroidal structures

A coarse-grained model is used to study the conformational properties of semiflexible polymers with amphiphilic monomer units containing both hydrophilic and hydrophobic interaction sites. The hydrophobically driven conformational transitions are studied using molecular dynamics simulations for the chains of varying stiffness, as characterized by intrinsic Kuhn segment lengths that vary over a decade. It is shown that the energy of hydrophobic attraction required for the realization of the coil-to-globule transition increases with increasing chain stiffness. For rather stiff backbone, the coil-to-globule transition corresponds to a first order phase transition. We find that depending on the chain stiffness, a variety of thermodynamically stable anisometric chain morphologies are possible in a solvent selectively poor for hydrophobic sites of amphiphilic monomer units. For flexible chains, the amphiphilic polymer forms a cylindrical globule having blob structure with nearly spherical blobs. With increasing stiffness, the number of blobs composing the globule decreases and the shape of blobs transforms into elongated cylinder. Further increase in stiffness leads to compaction of macromolecules into a collagenlike structure when the chain folds itself several times and different strands wind round each other. In this state, the collagenlike structures coexist with toroidal globules, both conformations having approximately equal energies.     

Amphiphilic comb macromolecules with different distribution statistics of side-chain grafting sites: Mathematical modeling

The influence of the distribution statistics of side-chain grafting sites on the conformational properties of amphiphilic comblike macromolecules immersed in a solvent that is poor for the main chain and good for the side chains was studied. It was shown that the coil-globule transition for macromolecules with the protein-like distribution of side-chain grafting sites occurs at higher temperatures, wherein the size of the proteinlike macromolecules is generally smaller than that of the corresponding regular macromolecules. Regardless of distribution statistics of side-chain grafting sites, the coil-globule transition of comb macromolecules passes through the step of the formation of the beads-on-a-string conformation composed of micelle-like beads. The temperature dependence curves of the heat capacity exhibit at least two maximums associated with the coil-globule transition per se and the coalescence of the beads into a single globule. The coil-globule transition temperature is slightly dependent upon the degree of polymerization of the main chain and drops with a decrease in the degree of polymerization of the side chains. It was found that comb macromolecules can form spherical, disklike, or cylindrical globules, depending on the structural parameters.     

Semiflexible grafted polymers in poor solvents: toroidal, archway, and tower micelles

We study a system of grafted semiflexible polymers in a poor solvent which form toroidal or rodlike conformations in the bulk. However, because of the physical constraint of surface grafting, macrophase separation is inhibited and a number of different polymer aggregates (or micelles) form which can be related to the chains' stiffness and their affinity for each other. In contrast to the fully flexible Gaussian case, we observe a number of novel micelle structures, including tower micelles, archway micelles, and spider micelles. We also attempt to develop a phase diagram for the occurrence of these structures with respect to the variables of chain length, chain stiffness, and polymer grafting density.     

Secondary globular structure of copolymers containing amphiphilic and hydrophilic units: Computer simulation analysis

The coil-globule transition in copolymers composed of amphiphilic and hydrophilic monomer units has been studied by the computer simulation technique. It has been shown that the structure of globules formed in such systems substantially depends on the rate at which the solvent quality worsens. The globule resulting from slow cooling is cylindrical, and its core contains a large amount of hydrophilic groups. The globule formed upon rapid cooling takes the helical conformation, in which all hydrophilic groups are displaced to the periphery. One helix turn of such globules contains 3–5 units. In both cases, the backbone of the polymer chain forms a typical zigzag-shaped structure with an average angle between neighboring bond vectors of about 60°. This fact implies that globules of copolymers consisting of amphiphilic and hydrophilic units comprise secondary structure components.     

Stoichiometric polyelectrolyte complexes as comb copolymers

The collapse behavior of a single comblike copolymer chain has been studied by Monte Carlo simulations. It has been supposed that the solvent is good for the side chains but the solvent quality for the backbone chain changes. It has been shown that depending on the structural parameters of the comb copolymer (the lengths of the backbone and side chains, grafting density of the side chains) various thermodynamically stable morphologies of the collapsed backbone chain can be realized. In addition to ordinary spherical globule we have observed elongated structures as well as necklace-like conformations. The proposed model can be used to describe conformational behavior of stoichiometric complexes between block copolymers with a polyelectrolyte short block and oppositely charged linear homopolymers.     

Solvent property induced morphological changes of ABA amphiphilic triblock copolymer micelles in dilute solution: A self-consistent field simulation study

The morphological changes of ABA amphiphilic triblock copolymer micelles in dilute solution were systematically studied by tuning the solvent property using self-consistent field simulation. The solvent property was tuned by changing the Flory-Huggins interaction parameters between each type of blocks and solvent, respectively. The simulation results show that by changing the solvent properties, a series of micelle morphologies such as vesicle, cage-like, ring-shaped, rod-like and spherical micelle morphologies can be obtained. Variations of the free energy of the solution system and the surface area of micelles with the Flory-Huggins interaction parameters were calculated to better understand the effect of solvent property on micelle morphologies. In addition, a phase diagram showing the morphological changes of micelles with the Flory-Huggins interaction parameters is provided.     

Influence of the block hydrophilicity of AB2 miktoarm star copolymers on cluster formation in solutions

We investigated the formation of various micelle shapes of lipid-like amphiphilic AB(2) miktoarm star copolymers in a solution, by performing dissipative particle dynamics simulations. AB(2) miktoarm star copolymer molecules are modeled with coarse-grained structures that consist of a relatively hydrophilic head (A) group with a single arm and a hydrophobic tail (B) group with double arms. A decrease in the hydrophilicity of the head group leads to a reduction of the polymer-solvent contact area, causing cluster structure changes from spherical micelles to vesicles. Consequently, a spherical exterior with multi-lamellar or cylindrical phase interior structures forms under poor solvent conditions without the introduction of spherical hard-wall containers. Furthermore we observed that, for small head group lengths, vesicles were formed in much wider range of solvent-head interaction strength than for long head groups, indicating that molecules with short head group offer a superior vesicle forming property. A phase diagram, the structure and kinetics of the cluster formation, a density profile, and a detailed shape analysis are presented to discuss the molecular characteristics of potential candidates for drug carriers that require superior and versatile vesicle forming properties. We also show that, under certain solvent-hydrophilic head group interaction conditions, initially formed cylindrical micelles transform to bilayer fragments through redistribution of copolymers within the cluster.     

Discontinuous molecular dynamics simulation study of polymer collapse

Discontinuous molecular dynamics simulations were used to study the coil-globule transition of a polymer in an explicit solvent. Two different versions of the model were employed, which are differentiated by the nature of monomer-solvent, solvent-solvent, and nonbonded monomer-monomer interactions. For each case, a model parameter lambda determines the degree of hydrophobicity of the monomers by controlling the degree of energy mismatch between the monomers and solvent particles. We consider a lambda-driven coil-globule transition at constant temperature. The simulations are used to calculate average static structure factors, which are then used to determine the scaling exponents of the system in order to determine the theta-point values lambda(theta) separating the coil from the globule state. For each model we construct coil-globule phase diagrams in terms of lambda and the particle density rho. Additionally, we explore for each model the effects of varying the range of the attractive interactions on the phase boundary separating the coil and globule phases. The results are analyzed in terms of a simple Flory-type theory of the collapse transition.     

Intramolecularly ordered globules and the collapse of short chains

We investigate the poor-solvent collapse of short chains having different stiffness through self-consistent minimization of the intramolecular free energy under the constraint of fixed segment lengths between adjacent beads. At first the chains form the Random Gaussian Globule, where the beads are distributed at random at the same average distance from the centre of mass, while the segments show very little correlation. At a larger attractive potential, this collapsed globule undergoes a transition to one or more ordered compact states, depending on the chain stiffness. Under very strong contraction, all chains are described as a Compact Ordered Globule: the beads are again at a constant average distance from the centre of mass, while the segments jump back and forth at the globule's wall with a very large correlation. At intermediate contraction, the thinner and stiffer chains form the Oscillating Ordered Globule wherein the beads are alternatively distributed on two concentric on two concentric shells. In this case, we also find metastable states with nonsymmetrical conformations of the chain with respect to its ends. We also briefly discuss the thermodynamics of the coil-globule and globule-globule transitions, showing that in long polymer chains these ordered conformations cannot involve the whole chain. However, we suggest that they might still be found as local globules that form for kinetic reasons.     

Microstructuring of a polymer globule in solution in the presence of an amphiphilic substance

Microstructuring in the bulk of a polymer globule in a solution that contains dimeric amphiphilic molecules, in particular, surfactants, is studied in terms of the weak-segregation theory. An inhomogeneous structure can result from a decrease in free energy with the orientation of amphiphilic molecules in the region of inhomogeneity owing to the interaction of hydrophobic and polar parts of the molecules with the solvent. For the sake of simplicity, we discuss the case of identical second virial coefficients of the interaction of monomer units and amphiphilic molecules with different energies of interaction of the hydrophobic and polar parts of the molecule with the solvent. By comparing the free energy for different types of microstructures, we predict that, with deterioration in the quality of the solvent, there is an initial formation of a homogeneous globule followed by formation of a body-centered cubic structure; a hexagonal cylindrical structure; and, finally, a lamellar structure. For a low degree of amphiphilicity, the transition from a homogeneous globule to only a lamellar structure occurs. An increase in the concentration of the amphiphilic substance in the surrounding solution hinders the formation of a globule but facilitates its microstructuring, which is also promoted by an increase in the volume of the amphiphilic molecule and the difference in the interaction energies of its hydrophobic and polar parts with the solvent. Phase diagrams of a globule??s state at different values of model parameters are plotted.     

Structures of stiff macromolecules of finite chain length near the coil‐globule transition: A Monte Carlo simulation

Using a coarse‐grained model of a semiflexible macromolecule, the equilibrium shapes of the chain have been studied varying both the temperature and the chain stiffness. We have applied Monte Carlo techniques using the bond fluctuation model for a chain length of N = 80 effective monomers, and two different types of interactions: a potential depending on the angle between successive bonds along the chain to control the chain stiffness, and an attractive interaction between non‐bonded effective monomers to model variable solvent quality. In a diagram of states where chain stiffness and inverse temperature are used as variables, we find regions where the chain exists as coil, as spherical globule, and as toroidal globule, respectively. Some of these regions are not limited by sharply defined boundaries, but rather wide two‐state coexistence regions occur in between them, where also intermediate metastable structures (such as rods and disks) occur. Recording histograms of energy, orientational order parameters, etc., which exhibit a two‐peak structure in the two‐state coexistence regions, we perform a subensemble analysis of the individual structures corresponding to these peaks.     

Dense orientationally ordered states of a single semiflexible macromolecule: an expanded ensemble Monte Carlo simulation

Using a coarse-grained model we perform a Monte Carlo simulation of the state behavior of an individual semiflexible macromolecule. Chains consisting of N = 256 and 512 monomer units have been investigated. A recently proposed enhanced sampling Monte Carlo technique for the bond fluctuation model in an expanded ensemble in four-dimensional coordinate space was applied. The algorithm allows one to accelerate the sampling of statistically independent three-dimensional conformations in a dense globular state. We found that the temperature of the intraglobular liquid-solid transition decreases with increasing chain stiffness. We have investigated the possible intraglobular orientationally ordered (i.e., liquid-crystalline) structures and obtained a diagram of states for chains consisting of N = 256 monomer units. This diagram contains regions of stability of coil, two spherical globules (liquid and solid), and rod-like globule conformations. Transitions between the globular states are rounded first-order ones since the states of liquid, solid, and cylinder-like globules do have different internal symmetry.     

Spontaneous generation of amphiphilic block copolymer micelles with multiple morphologies through interfacial Instabilities

We introduce a method for the formation of block copolymer micelles through interfacial instabilities of emulsion droplets. Amphiphilic polystyrene-block-poly(ethylene oxide) (PS-PEO) copolymers are first dissolved in chloroform; this solution is then emulsified in water and chloroform is extracted by evaporation. As the droplets shrink, the organic solvent/water interface becomes unstable, spontaneously generating a new interface and leading to dispersion of the copolymer as micellar aggregates in the aqueous phase. Depending on the composition of the copolymer, spherical or cylindrical micelles are formed, and the method is shown to be general to polymers with several different hydrophobic blocks: poly(1,4-butadiene), poly(-caprolactone), and poly(methyl methacrylate). Using this method, hydrophobic species dissolved or suspended in the organic phase along with the amphiphilic copolymer can be incorporated into the resulting micelles. For example, addition of PS homopolymer, or a PS-PEO copolymer of different composition and molecular weight, allows the diameter and morphology of wormlike micelles to be tuned, while addition of hydrophobically coated iron oxide nanoparticles enables the preparation of magnetically loaded spherical and wormlike micelles.     

无规共聚物自组装球形胶束表面亲水性的耗散粒子动力学模拟

建立了含不同亲疏水粒子比的双亲性无规共聚物粗粒化模型. 采用耗散粒子动力学方法模拟了两亲性无规共聚物选择性溶剂自组装球形胶束表面的亲水性能. 模拟结果表明, 无规共聚物在选择性溶剂中自组装得到实心球形胶束, 球形胶束表面的亲水性与聚合物链亲水粒子含量、溶剂的选择性有关. 随着聚合物链所含亲水粒子增加, 球形胶束表面的亲水性增强. 球形胶束表面的亲水性随着疏水粒子与溶剂粒子间的排斥参数增大而增强, 模拟结果与实验结论一致. 该模拟方法给出的胶束微结构信息可以为双亲无规共聚物分子设计及自组装双亲胶束制备提供一定的理论指导.     

A Monte Carlo study of amphiphilic dendrimers: spontaneous asymmetry and dendron separation

We study via Monte Carlo simulation the conformation of amphiphilic dendrimers for which terminal monomers (t) and internal monomers (i) interact differently with the solvent (s). Specifically, we have studied g = 3,6 dendrimers as a function of chi(it), chi(is), and chi(ts) (chi is the differential contact energy between the different particles) for parameter values chi(it) = 0, +/-1 and -1 < chi(is), chi(ts) < 1. We have allowed negative chi values in order to model attractive polar interactions (e.g., hydrogen bonding) which are believed to be important in many dendrimer/solvent systems. We find the "phase diagram" of dendrimer conformations to be extremely rich and to be a strong function of g, chi(is), and chi(ts) but only a weak function of chi(it), For chi(is), chi(ts) > 0, we observe dendrimer conformations, such as unimolecular normal micelles and inverted loopy micelles. However, for chi(is) < 0 or chi(ts) < 0, we observe more exotic molecular conformations, for example, the spontaneous development of asymmetry and dendron separation. These properties are analyzed in terms of snapshots as well as more quantitatively in terms of the radii of gyration, radial density profiles, pair-correlation functions, degree of asymmetry, and dendron overlap factor. By exploiting the dramatic conformational changes under different solvent conditions, we suggest the possibility of using amphiphilic dendrimers as stimuli-responsive smart materials.     

Molecular dynamics simulations of polyelectrolyte brushes: from single chains to bundles of chains

Using molecular dynamics simulations in combination with scaling analysis, we have studied the effects of the solvent quality and the strength of the electrostatic interactions on the conformations of spherical polyelectrolyte brushes in salt-free solutions. The spherical polyelectrolyte brush could be in one of four conformations: (1) a star-like conformation, (2) a "star of bundles" conformation in which the polyelectrolyte chains self-assemble into pinned cylindrical micelles, (3) a micelle-like conformation with a dense core and charged corona, or (4) a conformation in which there is a thin polymeric layer uniformly covering the particle surface. These different brush conformations appear as a result of the fine interplay between electrostatic and monomer-monomer interactions. The brush thickness depends nonmonotonically on the value of the Bjerrum length. This dependence of the brush thickness is due to counterion condensation inside the brush volume. We have also established that bundle formation in poor solvent conditions for the polymer backbone can also occur in a planar polyelectrolyte brush. In this case, the grafted polyelectrolyte chains form hemispherical aggregates at low polymer grafting densities, cylindrical aggregates at an intermediate range of the grafting densities, and vertically oriented ribbon-like aggregates at high grafting densities.     

Simulation study of the coil-globule transition of a polymer in solvent

Molecular dynamics simulations are used to study the coil-globule transition for a system composed of a bead-spring polymer immersed in an explicitly modeled solvent. Two different versions of the model are used, which are differentiated by the nature of monomer-solvent, solvent-solvent, and nonbonded monomer-monomer interactions. For each case, a model parameter lambda determines the degree of hydrophobicity of the monomers by controlling the degree of energy mismatch between the monomers and solvent particles. We consider a lambda-driven coil-globule transition at constant temperature. The simulations are used to calculate average static structure factors, which are then used to determine the scaling exponents of the system in order to determine the theta-point values lambdatheta separating the coil from the globule states. For each model we construct coil-globule phase diagrams in terms of lambda and the particle density rho. The results are analyzed in terms of a simple Flory-type theory of the collapse transition. The ratio of lambdatheta for the two models converges in the high density limit exactly to the value predicted by the theory in the random mixing approximation. Generally, the predicted values of lambdatheta are in reasonable agreement with the measured values at high rho, though the accuracy improves if the average chain size is calculated using the full probability distribution associated with the polymer-solvent free energy, rather than merely using the value obtained from the minimum of the free energy.     

水溶液中Pluronic嵌段共聚物聚集行为的介观模拟

通过介观动力学方法(MesoDyn)研究了低浓度下的三嵌段共聚物PEO27PPO61PEO27 (P104)水溶液的聚集行为, 讨论了聚合物浓度、模拟时间对P104水溶液相行为的影响. 在聚合物浓度较低(φ<35%)的情况下, 可以形成三种不同的胶束聚集体：球形胶束(spherical micelle)、胶束簇(micellar cluster)和盘状胶束(disk-like micelle). (1) 球形胶束(5%-10%, φ), 模拟的胶束结构表明疏水的PPO嵌段形成球形内核(micellar core), 而亲水的PEO嵌段形成核壳(micellar corona), 并有水分子存在内核和核壳之中；(2) 胶束簇(11%-15%, φ), 由于球形胶束之间的缔合, 形成直径明显高于球形胶束的聚集体, 其半径比球形胶束大1 nm左右；(3) 盘状胶束(16%-25%, φ), 胶束簇核壳PEO嵌段之间的相互缠绕, 形成了成串的类似盘状的胶束. 模拟中有序参数随浓度的变化证明了这种结构划分的合理性.     

Microphase Separation within a Comb Copolymer with Attractive Side Chains: A Computer Simulation Study

Computer simulation modelling of a flexible comb copolymer with attractive interactions between the monomer units of the side chains is performed. The conditions for the coil‐globule transition, induced by the increase of attractive interaction, ε, between side chain monomer units, are analysed for different values of the number of monomer units in the backbone, N, in the side chains, n, and between successive grafting points, m. It is shown that the coil‐globule transition of such a copolymer corresponds to a first‐order phase transition. The energy of attraction (ε) required for the realisation of the coil‐globule transition decreases with increasing n and decreasing m. The coil‐globule transition is accompanied by significant aggregation of side chain units. The resulting globule has a complex structure. In the case of a relatively short backbone (small value of N), the globule consists of a spherical core formed by side chains and an enveloping shell formed by the monomer units of the backbone. In the case of long copolymers (large value of N), the side chains form several spherical micelles while the backbone is wrapped on the surfaces of these micelles and between them.