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.     

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.     

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.     

激光光散射研究聚(N-异丙基丙烯酰胺)单链及其智能凝胶微球在水中的相变(下)

（接上期）２聚（Ｎ－异丙基丙烯酰胺）微凝胶在水中的体积相变２．１理论部分凝胶体积相变热力学：聚合物凝胶的溶胀和蜷缩可以用膨胀因子α＝（Ｖ／Ｖ０）１／３＝（ΦＴ／ΦΘ）１／３来表征，其中ΦΘ的ΦＴ分别是温度Θ和Ｔ下凝胶网络的体积分数。在平均场理论中，中...     

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.     

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.     

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.     

Effect of the degrees of polymerization of an enzyme and a substrate on the catalytic activity of the enzyme

It is shown that, as the degree of polymerization of an enzyme molecule is decreased, its enzymatic activity declines and subsequently vanishes at the triple point of the state diagram of a macromolecule. As the degree of polymerization of the enzyme molecule is increased, its enzymatic activity becomes higher owing to an increase in the density of loops in the fringelike surface layer of the globule. An expression for the turnover number of the enzyme that allows for effects of the chemical structures of the enzyme and the substrate on enzymatic activity is obtained.     

The effect of surface polarity of glass on liquid crystal alignment

The effects of the surface polarity of a glass substrate on the orientation of nematic liquid crystals (LCs) were studied using the polarised optical microscope and Fourier-transform infrared spectroscopy. On the surface of oxygen plasma treated glass, a homeotropic alignment of LCs was induced for LCs with negative dielectric anisotropy. This suggests that vertical orientation of LCs could be induced on a polar glass substrate without using an LC alignment layer. Upon cooling towards the isotropic–nematic transition, E7 with positive dielectric anisotropy changes its LC arrangement to isotropic, homeotropic, planar orientations in order. The nematic LC anchoring transition of E7 was interpreted by considering the competition between van der Waals forces and dipole interactions that control the alignment of LC molecules on a polar glass surface.     

Transition in swollen polymer networks induced by intramolecular condensation

It is predicted that the net repulsion between the segments of a polymer network and a poor solvent can cause a phase transition marked by a sudden change in the degree of swelling. This is analogous to the “coil–globule” transition recently predicted by Ptitsyn to occur for a macromolecule in solution. The critical conditions for the transition. as well as phase diagrams, are calculated for the gel in free swelling and under uniaxial tension, which facilitates the transition. The transition depends on the gel being formed of chains crosslinked while greatly swollen by a diluent and also having a high degree of crosslinking. It is concluded that it would be difficult to attain the conditions necessary for the transition in the free-swelling case, but that it should be possible for gel under tension.     

The features of structurization of the dilute aqueous solution of lithium chloride at the near-critical and supercritical conditions

Method of integral equations in the RISM approximation was used for the study of the structural properties of the dilute aqueous solution of lithium chloride in the near-critical and supercritical state. The following general trends of structural changes in the solution at its transition from the standard conditions to the supercritical conditions were revealed: destruction of the solvent tetrahedral lattice, thermal dehydration of the cation and anion, and an increase in the contact association. We found that the effect of temperature on the decrease in the fraction of the hydrogen-bonded solvent molecules and the value of the thermal dehydration of the ions is comparable with the influence of the density on the same characteristics. The process of ion association is affected predominantly by temperature, the effect is maximal in the subcritical region.     

Structure and Properties of Polymer Biocomposite Materials

Results of studying the structure and properties of biocomposite materials are summarized. The materials in question include an enzyme (laccase, peroxidase), an ion- or electron-conducting polymer (Nafion, polymethylpyrrole), and a carbon substrate (compact, disperse). It is shown that the orientation of a large number of enzyme molecules in an enzyme/Nafion composite material on the substrate surface favors direct bioelectrocatalysis. During co-immobilization of an enzyme and polymethylpyrrole, conditions are realized under which the polymer takes part in the electron transfer between the active center of the enzyme and the surface of the electroconducting substrate. A fresh approach to constructing a biocomposite material is developed. The material is based on an extremely finely divided carbon material (colloidal graphite), which ensures a high specific activity of laccase immobilized on it. The size of colloidal-graphite particles is commensurate with that of the laccase molecule, owing to which the enzyme macromolecule is surrounded by carbon particles. As a result, practically all adsorbed enzyme molecules are electrochemically active and participate in direct bioelectrocatalysis.     

Effect of low-molecular impurity on the melting of DNA-type macromolecules

Thermodynamics of the melting of a DNA-type macromolecule is studied theoretically. Elements of the macromolecule are able to annex a low-molecular impurity from the solvent (e.g., metal ions). Two models of the annexing of the impurity to the macromolecule are analyzed. It is shown that the concentration dependence of the helix-coil phase transition temperature is describable by a non-monotonic function in the case of certain relations between parameters.     

Simulating the equation of state of model globular proteins adsorbed at a surface

Monte Carlo computer simulation is used to follow the adsorption of a model globular and disordered protein at a hard surface and to simulate the surface equation of state for these molecules. The simulation utilizes the deformable globule model where the "protein" is treated as a collection of interacting subunits. Disordered globules are modeled as athermal molecules, whereas globular molecules have a strong attractive interaction between subunits. The surface equation of state is modeled by applying a known pressure to an adsorbed globule and following the changes in adsorbed conformation. Simulated equations of state for the disordered and globular molecules show features that are observed in experimental surface pressure versus area plots. In particular the simulated equations of state show "kinks" that correspond to regions where the adsorbed globules undergo conformational changes as they lift away from the surface in response to the increased pressure. The model proteins follow Bull's equation at low surface pressures in a way that is broadly in line with results from experiment, and the changes in conformation as a function of surface pressure are in line with predictions by DeFeijter and Benjamins made using a soft-particle model for adsorbed proteins.     

New theory of equation of state for surface monolayer

A novel statistical-thermodynamic approach to deriving an equation of state for a surface monolayer has been elaborated on the basis of excluded area. A master differential equation relating surface (two-dimensional) pressure to excluded area has been derived to generate equations of state for a surface monolayer. The crudest solution (the zero approximation) of the master equation reproduces the known van Laar and Frumkin equations of state. The first approximation yields the two-dimensional van der Waals equation. The second, third, and fourth approximations lead to new and more accurate equations of state. The particular result of the fourth approximation is a precise equation of state for hard disks with deviation not more than 0.46% from data obtained by Monte Carlo and molecular-dynamics simulations within the whole range of surface density. The role of the third dimension for surface equations of state is discussed. An orientation equation of state has been proposed for monolayers containing anisometric particles. It follows from the orientation equation obtained that the orientation effect creates possibility for a two-dimensional phase transition.     

Conformational relaxation dynamics of a poly(N-isopropylacrylamide) aqueous solution measured using the laser temperature jump transient grating method

We observed phase transition and phase relaxation processes of a poly(N-isopropylacrylamide) (PNIPAM) aqueous solution using the heterodyne transient grating (HD-TG) method combined with the laser temperature jump technique. The sample temperature was instantaneously raised by about 1.0 K after irradiation of a pump pulse to crystal violet (CV) molecules for heating, and the phase transition was induced for the sample with an initial temperature just below the lower critical solution temperature (LCST); the following phase relaxation dynamics was observed. Turbidity relaxation was observed in both the turbidity and HD-TG responses, while another relaxation process was observed only in the HD-TG response, namely via the refractive index change. It is suggested that this response is due to formation of globule molecules or their assemblies since they would have nothing to do with turbidity change but would affect the refractive index, which is dependent on the molar volume of a chemical species. Furthermore, the grating spacing dependence of the HD-TG responses suggests that the response was caused by the counter propagating diffusion of the coil molecules as a reactant species and the globule molecules as a product species and the lifetime of the globule molecules ranged from 1.5 to 5 seconds. Thus, we conclude that the turbidity reflects the dynamics of aggregate conditions, not molecular conditions. The coil and globule sizes were estimated from the obtained diffusion coefficient. The sizes of the coil molecules did not change at the initial temperatures below the LCST but increased sharply as it approaches LCST. We propose that the coil-state molecules associate due to hydrophobic interaction when the initial temperature was higher than LCST minus 0.5 K and that the globule-state molecules generated from the coil-state molecules showed a similar trend in temperature. The phase transition was also induced by heating under a microscope, and the relaxation process was followed using the fluorescence peak shift of a fluorescent molecule-labeled PNIPAM. The result also supports the existence of a globule molecule or its assembly remains for several seconds in the phase relaxation.     

Surface-enhanced Raman scattering interaction of p-aminobenzoic acid on a silver-coated alumina substrate

The adsorption behavior of p-aminobenzoic acid (PABA) molecules on a silver-coated alumina surface-enhanced Raman scattering (SERS) substrate was investigated. For spotted PABA and PABA in non-polar solvents, the PABA molecule is adsorbed flat on the surface of the SERS substrate. In this orientation, the benzene ring is π-bonded to the substrate, and the molecule is further anchored to the substrate by the binding of the lone pairs of NH₂ and COO⁻ groups onto the metal surface. On the other hand, the adsorption behavior of PABA in a polar solvent is greatly influenced by the hydrogen bonding of the amine group with the polar solvent. In this orientation, the molecule is preferentially adsorbed through the COO^± and assumes a non-flat orientation on the metal surface.     

Correlation of molecular orientation and packing density in a dsDNA self-assembled monolayer observable with surface-enhanced Raman spectroscopy

Observations of two spectrally distinct ring breathing modes of guanine and adenine in the surface-enhanced Raman spectrum (SERS) of a dsDNA self-assembled monolayer on an Au nanoshell SERS substrate provide information concerning the orientation of its constituent molecules. The two modes vary with DNA concentration in a highly systematic manner, consistent with studies suggesting DNA molecules tend toward a more horizontal orientation at low-surface concentrations and a more vertical conformation at high concentrations. The introduction of small molecular spacers coadsorbed onto the Au nanoshell surface to "raise" the DNA molecules yields a SERS spectrum consistent with a more upright molecular orientation.     

Coil-globule transition: Self-assembly of a single polymer chain

The coil collapse problem is of interest not only because it represents the simplest model of protein folding, but also because of its fundamental importance as related to polymer nanostructures and fractionation. It is extremely difficult to observe the coil-to-globule transition experimentally because at finite concentrations in a poor solvent, the macromolecules tend to aggregate due to phase separation when the collapsed state is being achieved. In the mid-1980s, two-stage kinetics of a single-chain collapse was proposed theoretically.^1,2 The first successful experimental observation of a two-stage coil-to-globule transition was achieved by quenching a dilute solution of polystyrene (PS) in cyclohexane.³ By using a thinnest capillary tube cell with a wall thickness of 0.01 mm and a diameter of 5 mm for dynamic light scattering, two relaxation times, τ_crum for the crumpled globule state and τ_eq for the compact globule state, were determined⁴ for the first time. The relaxation times were much slower than expected. From the size of the crumpled globule and that of the compact globule and by assuming the intraglobular density to be uniform, the volume fraction of the PS chain in the crumpled globule state, ϕ_crum, and that in the compact globule state, ϕ_comp, can be estimated, with ϕ_crum = 0.02 and ϕ_comp ∼ 0.24-0.4 at 28°C for polystyrene in cyclohexane. The results imply that a single-chain globule contains a large amount of solvent. It should also be noted that ϕ_comp is temperature dependent, i.e., one would have to go to hypothetically low temperatures in order to squeeze out all the solvent (cyclohexane) in the compact PS globule. The single-chain coil collapse state could be achieved under equilibrium conditions by using a high molecular weight, M_w ∼ 1.08 × 10⁷ g/mol; M_w/M_n < 1.06) poly(N-isopropylacrylamide) (PNIPAM) in water,<⁵ even though the ten million molecular weight for PNIPAM was substantially lower than that for polystyrene (M_w ∼ 50 × 10⁶ g/mole).⁶ Under equilibrium conditions, it was feasible to determine both the hydrodynamic radius R_h and the radius of gyration R_g. The ratio of R_g/R_h changed from 1.45 to 0.77, clearly demonstrating the transition from the theta coil state to the compact globule state. At the maximum value of the scaled expansion factor α_s³ |τ| M_w^1/2, R_g/R_h = 1.33 where α_s = R_g/R_g (θ) and τ = |T-θ| / θ with θ being the theta temperature. In the compact globule, R_g/R_h was of the order of 0.7, implying that the PNIPAM compact globule in water still contained ∼80% water, of the same order of magnitude as the PS compact globule in cyclohexane at 7° below its theta temperature (35°C).     

The size of a polymer in a symmetric solvent

Using a simple thermodynamic model, we derive an expression for the excluded volume parameter v of a polymer chain in a symmetric solvent (solvated by its own monomers). For a chain with a given segment length and number of monomers, this parameter determines whether the chain is collapsed or expanded. For the latter it determines the degree of expansion. Using a simple off-lattice version of Flory's model [P. J. Flory, Principles of Polymer Chemistry (Cornell University Press, Ithaca, 1953)] and relaxing the assumption of incompressibility, we obtain the result v=(1-kappa)rho(0), where kappa is the dimensionless compressibility and rho(0) the number density of solvent. In the incompressible limit (in the sense that kappa-->0) the chain is expanded and the inverse of the solvent number density determines the degree of expansion of the chain. Using the van der Waals equation of state to estimate kappa (allowing for nonzero compressibility in a system that can undergo a gas-liquid phase transition), the model predicts that upon raising the temperature at constant pressure there is both a lower (coil to globule) and upper (globule to coil) Flory temperature. This is in quantitative agreement with experiment and computer simulations.