Diagram of State of Stiff Amphiphilic Macromolecules

Summary: We studied coil-globule transitions in stiff-chain amphiphilic macromolecules via computer modeling and constructed phase diagrams for such molecules in terms of solvent quality and persistence length. We showed that the shape of the phase diagram essentially depends on the macromolecule degree of polymerization. Relatively short amphiphilic molecules always form a spherical globule in a poor solvent, and the coil-globule transition includes one or two intermediate conformations, depending on the chain's stiffness. These are a disk-like globule in case of high enough Kuhn segment length, and a pearl necklace-like structure of spherical micelles and a disk-like globule in case of relatively flexible chains. The phase diagram of a long stiff amphiphilic chain was found to be more complex still. Thus three specific regions can be distinguished in the poor solvent region, depending on the chain stiffness. These correspond to a cylindrical globule without any specific backbone ordering, a cylindrical globule containing blobs with collagen-like ordering of the chain, and co-existence of collagen-like and toroidal globules. In the intermediate transition region in this case, apart from the pearl necklace-like conformations with spherical micelles, necklace conformations can be also observed where the polymeric chain has collagen-like ordering within each bead.     

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.     

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.     

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.     

Comb macromolecules with attracting functional groups in side chains

The conformational behavior of a single comb-shaped macromolecule with associating groups in side chains was studied by means of Monte Carlo simulation. The side chains contain two types of units, type A representing nonfunctional units (main chain units are likewise classified with type A) and type B representing functional (attracting) units. As a result of an increase in attraction energy between associating groups, the transition of the macromolecule from coil to the globule state takes place. The coil-globule transition is accompanied by segregation of unlike units; as a result, the globule has a complex structure: the core of the globule is formed by attracting groups of side chains, and the envelope is formed from soluble units of both main and side chains. The dependence of the size and shape of the macromolecule on its structural parameters, such as the length of main and side chains and the graft density of side chains, and on the position of the functional groups in side chains was examined. Along with the single globule, conformations in which the attracting units of side chains formed several bead globules were observed.     

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.     

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.     

pH-induced reversible conformational and morphological regulation of polyleucine grafted polyallylamine assembly in solution

One of the essential parts in the molecular mechanism of biological properties is the structural changes of proteins induced by stimuli. An amphiphilic copolymer, poly(L-leucine) grafted polyallylamine as a simple model of proteins, has been prepared by NCA polymerization with free amino groups of polyallylamine as an initiator. Here, we report the pH-induced reversible conformational and morphological regulation of the amphiphilic copolymer, whose hydrophobic peptide graft chains have no pH-sensitive groups, in an aqueous solution containing 50 vol % trifluoroethanol. The conformation of the poly(L-leucine) graft chain was found to be strongly pH dependent. Under acidic conditions, where electrostatic repulsion existed between the neighboring protonated amine moieties of the polyallylamine main chain, the rapid aggregation of the poly(l-leucine) graft chains was disturbed, and the peptide graft chains formed a beta-sheet structure owing to the intramolecular hydrogen bonding among the graft chains. Under this condition, the amphiphilic polymer formed amyloid-like fibrils, and then the fibrils grew into a planer plate composed of staked beta-sheets. On the other hand, under basic conditions, the poly(L-leucine) graft chains showed conformational transitions from a beta-sheet structure to an alpha-helical conformation owing to a distortion of the regular arrangement of the peptide graft chains by the conformational change of the polyallylamine main chain, whose amino groups were deprotonated. The conformational transition resulted in a disturbance of the regular sheet assembly of the amphiphilic copolymer and induced morphological changes to the amorphous globular aggregates. The pH-induced conformational and morphological changes of the poly(L-leucine) graft polyallylamine were reversible and synchronized with the protonation of the polyallylamine main chain.     

Monte Carlo Simulation of Coil-to-Globule Transition of Compact Polymer Chains: Role of Monomer Interacting

Coil-to-globule transitions are fundamental problems existing in polymer science for several decades; however, some features are still unclear, such as the effect of chain monomer interaction. Herein, we use Monte Carlo simulation to study the coil-to-globule transition of simple compact polymer chains. We first consider the finite-size effects for a given monomer interaction, where the short chain exhibits a one-step collapse while long chains demonstrate a two-step collapse, indicated by the specific heat. More interestingly, with the decrease of chain monomer interaction, the critical temperatures marked by the peaks of heat capacity shift to low values. A closer examination from the energy, mean-squared radius of gyration and shape factor also suggests the lower temperature of coil-to-globule transition.     

Polyelectrolyte Complexes Consisting of Macromolecules With Varied Stiffness: Computer Simulation

Monte Carlo simulations are employed in order to analyze the structure of polyelectrolyte complexes consisting of two identical but oppositely charged macroions with varying chain stiffness. It is shown that two complex structures can arise depending on the stiffness of the constituent chains. Stiff chains are organized into a “ladder” structure in which chains are located parallel to each other and monomeric units are arranged into ionic pairs according to their position in the chain. Flexible chains form a globular “scrambled‐egg” structure with a disordered position of monomer units. The conformational transition between the two structures proceeds as a phase transition.

     

Destruction of globules of Co- and homopolymer macromolecules in the presence of an amphiphilic substrate

The destruction of a globule in the presence of a dimeric substrate composed of a hydrophilic group OP and a hydrophobic group H with a high affinity to hydrophobic H units of a macromolecule has been studied. Globules of the homopolymer H macromolecule and the macromolecule of the HP copolymer with proteinlike statistics of monomer unit distribution along a chain have been investigated. The destruction of a globule in such systems begins with the transformation of the globule’s shape from spherical to disklike. At high substrate concentrations, the globule of the proteinlike copolymer is completely destroyed; under the same conditions, the homopolymer macromolecule forms a structure composed of two beads having a shape close to that of the oblate ellipsoid that are located symmetrically about a string connecting them.     

Microstructure and lateral diffusion in monolayers of polymerizable amphiphiles

Lipid analogue amphiphilic molecules containing polymerizable units were investigated in monolayers at the air/water interface by using film balance measurements, fluorescence microscopy, and photobleaching techniques. The polymerizable groups (diene-, diyne-, and methacrylate units) were introduced into the hydrophobic alkyl chains or into the polar head of the amphiphilic molecules.In the case of the diene- and diyne-containing compounds the polymerizable units are incorporated into the hydrophobic alkyl chains, enabling them to form a two-dimensional network. Due to the free chain flexibility of the monomers the lateral mobility was comparable to that of saturated lipid analogues and decreases upon polymerization proportionally to the dose of UV irradiation. In addition, fluid/solid phase transitions of compounds with polymerizable groups in the hydrophobic part tend to vanish during the formation of the polymers. However, the direct observation of the growth of polymeric crystalline domains can be followed by using diacetylene lipid analogues.In the case of the methacrylate derivatives the polymerizable unit was coupled to the polar part via a flexible spacer. For these systems the characteristics of the monomeric phase transition are retained after polymerization. However, it shows a significant, strong decrease of the in-plane mobility already in the fluid-expanded phase of the polymer. The quantitative measurements of the lateral diffusion in the monolayers can be correlated with fluorescence microscopic images of their structure.     

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.     

高分子研究中的一个知识问题——柔性链“从线团到小球”的构象变化

一条大分子链由许多小分子通过共价键连接而成.正是这一"连接"导致了大分子一些独特的物理性质及相关问题.本文希望阐明的就是这样一个小分子物理中没有的知识问题:小分子在溶剂中仅有溶或不溶2个状态;而自60年代起,理论学家们就预言一条柔性大分子链在溶解的状态下,其构象随着溶剂性质变差可以从无规线团蜷缩成一个单链小球.为了证明这一构象变化,实验学家们从70年代末起进行了大量的研究,直至90年代初期仍未观察到稳定的单链蜷缩小球.实验上这一长期悬而未解的问题困惑着众多研究者.甚至有理论学家在1993年报道,当今的样品制备和实验手段无法观察到一个热力学稳定的单链蜷缩小球.中国钱人元先生和一些其他研究者自80年代末期也开始关注与单链有关的问题.我们实验室从1993年开始另辟蹊径,通过制备和采用窄分布的热敏性水溶性高分子超长链,终于在1995年利用激光光散射首次观察到理论上预测的"线团到小球"的构象变化.随后,又揭示了变化过程中存在着一个全新的"融化球"构象以及在单链蜷缩小球中并无理论上预计的额外链互穿和打结.从得到的稳定单链蜷缩小球出发,我们又首次在实验上研究了"小球到线团"的过程,意外地观察到其在准理想状态附近滞后于"线团到小球"的构象变化,并证明该滞后可归于链蜷缩过程中形成的额外链内氢键.最后,借用红外纳秒脉冲激光加热的方法研究了"线团到小球"的蜷缩动力学,并发现其包含了在单个高分子链上"成核"和"粗化"先后2个过程.其中,"成核"过程与链长无关.经过近20年的努力,我们终于基本解决了这一近代高分子物理研究中与知识有关的重要问题,揭示了与其相关的一些大分子特有的物理性质.     

Effect of branching and confinement on star-branched polymeric systems

The effect of confinement, number of branches (functionality), and size of the molecules on various properties as a function of temperature of star-branched polymers confined between two walls was studied using Monte Carlo simulations with the parallel tempering technique. The coil-to-globule transition and the liquidlike to solidlike transition, similar to those observed for linear chains, were characterized in all systems by changes in the heat capacity, internal energy, and radius of gyration. The transitions were also characterized by the most probable isomeric structure at a given temperature. The radius of gyration of the star polymers was smaller than the values of linear chains when the number of arms f increased. For star chains with more than f=5 arms the values of the radius of gyration, and therefore the size of the molecules, were similar for every condition of confinement studied, especially at higher temperatures. As confinement was increased, the difference in the radius of gyration of linear chains and star polymers became even larger. The coil-to-globule transition temperatures shifted to higher temperatures as the size of the chains and the number of arms in a molecule were increased. Effects of confinement were higher on the properties of the system at the smallest separations (less than twice the monomer diameter), where the coil-to-globule transition shifted to lower temperatures. The liquidlike to solidlike transition was present at almost the same temperature for different conditions of confinement, chain size, and number of arms. The behavior of the systems for separations between the walls greater than five bead diameters was similar to the behavior in the unconfined case. Hence, no considerable effect of confinement was found above this separation.     

仿细胞膜结构共聚物的合成及涂层性能

采用饥饿法将2-甲基丙烯酰氧乙基磷酰胆碱(MPC)分别与甲基丙烯酸十八烷基酯(SMA)、 甲基丙烯酸十二烷基酯(LMA)及甲基丙烯酸正丁酯(BMA)聚合, 通过改变投料比例和沉淀剂种类, 合成了一系列含磷酰胆碱基团的仿细胞膜结构的两亲性二元随机共聚物. ¹H NMR和元素分析结果表明, 合成的两亲性二元随机共聚物的组成与投料比相近. DSC结果表明, 聚合物具有较低的玻璃化转变温度. 表面张力及水的动态接触角(DCA)研究发现, 聚合物涂层表面具有明显的两亲性及表面结构易变性, 在空气中憎水基团在表面取向, 在水环境中亲水的磷酰胆碱基团则迁移取向到涂层表面形成仿细胞外层膜结构界面, 最终形成不溶于水的仿细胞膜结构涂层.     

Macromolecules in a blend of poor and amphiphilic solvents

The globular state of the homopolymer macromolecule in a blend composed of a poor solvent and an amphiphilic solvent (substrate), whose molecules tend to be aligned with the solvent concentration gradient in the inhomogeneity region, was theoretically studied. The size of a homogeneous globule and the substrate concentration in its volume were calculated in terms of a bulk approximation. After the transition of the macromolecule from the coil to the globule state, its volume first decreases with a decrease in temperature and then begins to grow due to substrate molecules penetrating the globule. The substrate concentration in the globule insignificantly exceeds that outside the globule at identical second virial coefficients of interaction between monomer units and between substrate molecules. The expression for the free energy functional depending on the volume fractions of the components and on the orientation of substrate molecules was examined in the ground-state approximation. The orientation effect leads to narrowing of the surface layer and to a decrease in the surface tension of the homogeneous globule, thereby increasing its stability with respect to the transition to the unfolded-coil state.     

Secondary structure of globules of copolymers consisting of amphiphilic and hydrophilic units: Effect of potential range

The relation of the coil-globule transition in macromolecules consisting of amphiphilic and hydrophilic monomer units to the radius of action of the interaction potential is investigated by the method of computer-assisted experiments. The internal structure of globules formed by such macromolecules is significantly dependent on the radius of action of the potential. In the case of the long-range potential, the globule is characterized by the blob structure, while in the case of the short-range potential, a quasi-helical structure forms. In this structure, the skeleton of a macromolecule forms a helical turn, and the direction of twisting may vary from one turn to another. The coil-globule transition in such macromolecules proceeds through formation of the necklace conformation from quasi-helical micelle beads. For sufficiently long macromolecules, the dimensions of such globules are linearly dependent on the degree of polymerization.     

Simulation analysis of the temperature dependence of lignin structure and dynamics

Lignins are hydrophobic, branched polymers that regulate water conduction and provide protection against chemical and biological degradation in plant cell walls. Lignins also form a residual barrier to effective hydrolysis of plant biomass pretreated at elevated temperatures in cellulosic ethanol production. Here, the temperature-dependent structure and dynamics of individual softwood lignin polymers in aqueous solution are examined using extensive (17 μs) molecular dynamics simulations. With decreasing temperature the lignins are found to transition from mobile, extended to glassy, compact states. The polymers are composed of blobs, inside which the radius of gyration of a polymer segment is a power-law function of the number of monomers comprising it. In the low temperature states the blobs are interpermeable, the polymer does not conform to Zimm/Stockmayer theory, and branching does not lead to reduction of the polymer size, the radius of gyration being instead determined by shape anisotropy. At high temperatures the blobs become spatially separated leading to a fractal crumpled globule form. The low-temperature collapse is thermodynamically driven by the increase of the translational entropy and density fluctuations of water molecules removed from the hydration shell, thus distinguishing lignin collapse from enthalpically driven coil-globule polymer transitions and providing a thermodynamic role of hydration water density fluctuations in driving hydrophobic polymer collapse. Although hydrophobic, lignin is wetted, leading to locally enhanced chain dynamics of solvent-exposed monomers. The detailed characterization obtained here provides insight at atomic detail into processes relevant to biomass pretreatment for cellulosic ethanol production and general polymer coil-globule transition phenomena.     

Semiflexible polymers grafted to a solid planar substrate: changing the structure from polymer brush to "polymer bristle"

Monte Carlo simulations are presented for a coarse-grained model of polymer brushes with polymers having a varying degree of stiffness. Both linear chains and ring polymers grafted to a flat structureless non-adsorbing substrate surface are considered. Applying good solvent conditions, it is shown that with growing polymer stiffness the brush height increases significantly. The monomer density profiles for the case of ring polymers (chain length N(R) = 64) are very similar to the case of corresponding linear chains (N(L) = 32, grafting density larger by a factor of two) in the case of flexible polymers, while slight differences appear with increasing stiffness. Evidence is obtained that the chain dynamics in brushes is slowed down dramatically with increasing stiffness. Very short stiff rings (N(R) ≤ 16) behave like disks, grafted to the substrate such that the vector, perpendicular to the disk plane, is oriented parallel to the substrate surface. It is suggested that such systems can undergo phase transitions to states with liquid crystalline order.