Stretching globular polymers. I. Single chains

We review the force-extension behavior of polymers collapsed in poor solvent, modified to include the effects of semiflexibility and considered for globules with "ordered" and "disordered" internal structures. A series of ordered globules is used as a model for the unbinding of a disordered globule beneath its glass transition and for multiple-repeat proteins such as the poly-Ig-domain titin used in atomic force microscopy studies. These single-chain results form the foundation for the treatment of cross-linked networks of globular polymers.     

A Monte Carlo simulation of the aggregation, phase-separation, and gelation of model globular molecules

Monte Carlo computer simulation on a square 3-D lattice is used to model state behavior of globular copolymers. Two types of globular molecules were defined. One consisted of a single type of subunit (a homopolymer) while the second contained a core of strongly attractive subunits and an outer layer of less strongly attractive subunits (a heteropolymer). Systems of globules were simulated at varied volume fraction (V(F)) and reduced temperature (T(R)), and state diagrams were constructed. These state diagrams contained state boundaries defined by the V(F)/T(R) combinations at which the system formed a percolating network and at which the various component subunits in the globule unfolded. Simulated systems could exist in a number of states (between 4 and 7), depending on the V(F), T(R), whether the molecule was a homo- or heteroglobule and whether the globules were allowed to interact with each other or not. All systems exhibited a gelation/crossover line that resembled a lower critical solution temperature. All systems also exhibited a critical gelation concentration, above which a continuous network was formed. The critical gelation concentration varied between about 2-4% V(F) depending on the type of system. This is comparable to experimental critical gelation concentrations of in the region of 4% (w/w) for a range of associating polymers and biopolymers such as globular proteins and polysaccharides. Other states were formed which included one where elongated, fibril-like aggregated strands were formed, and a micelle-like aggregated state. The results are discussed in terms of the known state behavior of associating polymers and biopolymers (proteins and polysaccharides).     

Stretching globular polymers. II. Macroscopic cross-linked networks

We expand upon the results for the force-extension behavior of single-collapsed polymer chains to consider the mechanical response of networks of cross-linked globular polymers in poor solvent. Force-strain curves are obtained under the affine deformation approximation for networked globules with both disordered and ordered globule conformations. Due to their large stored lengths, these networks would be capable of reaching extremely large strains. They also show anomalous nonmonotonic force-strain response, as a consequence of the nonmonotonic force-extension curves of their constituent globules. Finally, we consider the stability of ordered and disordered globules in these networks and propose means taken from biological and colloid science to stabilize networked globules.     

Structure of salted and discharged globules of hydrophobic polyelectrolytes adsorbed from aqueous solutions

In this article, we compare structures of protonated poly(2-vinylpyridine) globules (2D compact coils on the surface) adsorbed on the mica surface from aqueous solution when the shrinking is brought about either by discharging the molecules at an elevated pH or by adding monovalent and polyvalent salts. We study the structure of the PE coils using in situ atomic force microscopy experiments in aqueous solutions in a liquid cell. The abrupt coil-to-globule transition caused by pH changes and the discharge of polymer chains resulted in compact globules. If the pH corresponding to extended coil conformation remains unchanged, the coil shrinks due to the added salt. The size of the globule in the latter case corresponds to the unperturbed dimension of the polymer coil. There is no essential difference in the dimensions of the globules as obtained in the presence of monovalent and multivalent counterions for the studied ionic strength. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1623–1627, 2010     

Infrared studies of the potential controlled adsorption of sodium dodecyl sulfate at the Au(111) electrode surface

Quantitative subtractively normalized interfacial Fourier transform infrared reflection spectroscopy (SNIFTIRS) was used to determine the conformation and orientation of sodium dodecyl sulfate (SDS) molecules adsorbed at the single crystal Au(111) surface. The SDS molecules form a hemimicellar/hemicylindrical (phase I) structure for the range of potentials between -200 ≤ E < 450 mV and condensed (phase II) film for electrode potentials ≥500 mV vs Ag/AgCl. The SNIFTIRS measurements indicate that the alkyl chains within the two adsorbed states of SDS film are in the liquid-crystalline state rather than the gel state. However, the sulfate headgroup is in an oriented state in phase I and is disordered in phase II. The newly acquired SNIFTIR spectroscopy measurements were coupled with previous electrochemical, atomic force microscopy, and neutron reflectivity data to improve the current existing models of the SDS film adsorbed on the Au(111) surface. The IR data support the existence of a hemicylindrical film for SDS molecules adsorbed at the Au(111) surface in phase I and suggest that the structure of the condensed film in phase II can be more accurately modeled by a disordered bilayer.     

Effect of the coil-globule transition on the free-energy barrier for intrachain crystal nucleation

The rate of crystal nucleation of colloids and globular proteins can be enhanced by critical density fluctuations. It has been argued that a closely related phenomenon influences the rate of intramolecular "crystallization" of single-chain polymers. We report Monte Carlo simulations of the free-energy barrier that separates the crystalline state of a homopolymer chain from the disordered state. The simulations show that the barrier for nucleation of the ordered state is drastically lowered as the disordered state changes from a coil to a globule. We discuss the relation of the present findings to intramolecular nucleation of heteropolymers, such as proteins.     

Chain conformation in two-dimensional dense state

In an effort to provide evidence concerning the conformation of many chains in strict two-dimensional (2D) dense state, we synthesized polymer chains of diameter of nanometers through an anionic polymerization process. The conformational characteristics of the long chain molecules in films of thickness h corresponding to the chain diameter a were directly obtained from atomic force microscopy observations. In 2D dispersed state, the conformations of the long chain molecules were typical Gaussian. However, in 2D dense state the long chain molecules were strongly interpenetrated. Their conformations were largely perturbed by the presence of neighbor chains and were not Gaussian. This result was in contradiction with the segregated globule model predicted by de Gennes. The central reason is that 2D space cannot be filled to normal density with 2D Gaussian globules; either the area must be greatly increased with consequently large voids, or the globule conformation must be expanded by allowing chains to interpenetrate each other.     

Reversible collapse of brushlike macromolecules in ethanol and water vapours as revealed by real-time scanning force microscopy

Environment-controlled scanning force microscopy allowed us to study adsorption and desorption of single poly(methacrylate)-graft-poly(n-butyl acrylate) brush molecules on mica in real time. The molecules transform reversibly from a two-dimensional, extended wormlike state to a compact globular state. The dynamics of the conformational transition was sufficiently slow in order to allow its observation by scanning force microscope in real time. The reversible transformation is effected by coadsorption of water or ethanol, the latter introduces the collapse. Adsorbing ethanol and water from the vapour atmosphere results in a change of the surface properties of mica, either favouring adsorption or desorption of the graft polymer. When the extended, tightly adsorbed poly(n-butyl acrylate) brush molecules are exposed to ethanol vapour, the macromolecules swell and contract to form compact globules. Exchanging the ethanol vapour to a humid atmosphere caused the molecules to extend again to a wormlike two-dimensional conformation. Coexistence of collapsed and extended strands within the same molecule indicates a single-molecule first-order transition in agreement with observations on Langmuir films previously reported.     

STM vizualization of thiol-containing peptide dendrimers on Au(111)

Peptide dendrimers assembled by solid-phase peptide synthesis using a branching diamino acid at every 2(nd) or 3(rd) position provide readily accessible synthetic model systems for proteins and enzymes. They adopt a globular shape by topology rather than by folding. Peptide dendrimers of 2(nd) and 3(rd) generation functionalized with a cysteine or cystine residue in the core were adsorbed on Au(111) surface and imaged by STM at air, under UHV, or in solution. The dendrimers appear as globular features with dimensions suggesting an extended flattened conformation, forming both single globules and ordered arrays on the surface. These images represent the first direct visualization of peptide dendrimer enzyme models.     

Dynamics of collapsed polymers under the simultaneous influence of elongational and shear flows

Collapsed polymers in solution represent an oft-overlooked area of polymer physics, however recent studies of biopolymers in the bloodstream have suggested that the physics of polymer globules are not only relevant but could potentially lead to powerful new ways to manipulate single molecules using fluid flows. In the present article, we investigate the behavior of a collapsed polymer globule under the influence of linear combinations of shear and elongational flows. We generalize the theory of globule-stretch transitions that has been developed for the specific case of simple shear and elongational flows to account for behavior in arbitrary flow fields. In particular, we find that the behavior of a globule in flow is well represented by a two-state model wherein the critical parameters are the transition probabilities to go from a collapsed to a stretched state P(g-s) and vice versa P(s-g). The collapsed globule to stretch transition is described using a nucleation protrusion mechanism, and the reverse transition is described using either a tumbling or a relaxation mechanism. The magnitudes of P(g-s) and P(s-g) govern the state in which the polymer resides; for P(g-s) ≈ 0 and P(s-g) ≈ 1 the polymer is always collapsed, for P(g-s) ≈ 0 and P(s-g) ≈ 0 the polymer is stuck in either the collapsed or stretched state, for P(g-s) ≈ 1 and P(s-g) ≈ 0 the polymer is always stretched, and for P(g-s) ≈ 1 and P(s-g) ≈ 1 the polymer undergoes tumbling behavior. These transition probabilities are functions of the flow geometry, and we demonstrate that our theory quantitatively predicts globular polymer conformation in the case of mixed two-dimensional flows, regardless of orientation and representation, by comparing theoretical results to Brownian dynamics simulations. Generalization of the theory to arbitrary three-dimensional flows is discussed as is the incorporation of this theory into rheological equations.     

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.     

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.     

Effects of surface curvature and surface chemistry on the structure and activity of proteins adsorbed in nanopores

The interactions of proteins with the surface of cylindrical nanopores are systematically investigated to elucidate how surface curvature and surface chemistry affect the conformation and activity of confined proteins in an aqueous, buffered environment. Two globular proteins, lysozyme and myoglobin, with different catalytic functions, were used as model proteins to analyze structural changes in proteins after adsorption on ordered mesoporous silica SBA-15 and propyl-functionalized SBA-15 (C(3)SBA-15) with carefully controlled pore size. Liquid phase ATR-FTIR spectroscopy was used to study the amide I and II bands of the adsorbed proteins. The amide I bands showed that the secondary structures of free and adsorbed protein molecules differ, and that the secondary structure of the adsorbed protein is influenced by the local geometry as well as by the surface chemistry of the nanopores. The conformation of the adsorbed proteins inside the nanopores of SBA-15 and C(3)SBA-15 is strongly correlated with the local geometry and the surface properties of the nanoporous materials, which results in different catalytic activities. Adsorption by electrostatic interaction of proteins in nanopores of an optimal size provides a favorably confining and protecting environment, which may lead to considerably enhanced structural stability and catalytic activity.     

A new equation for the size distribution of emulsion particles

Summary A study of experimental data from the literature provided grounds for believing that the particle size distributions of emulsions can be represented by a single general size distribution equation. In the present paper this distribution equation, which contains two parameters, is derived statistically. Verification with published experimental data on several oil-in-water emulsions and with own data on water-in-oil emulsions yielded very good agreement for mechanically prepared emulsions.

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Zusammenfassung Ein Studium der experimentellen Ergebnisse aus dem Schrifttum legt nahe, daß die Teilchengrößenverteilungen von Emulsionen durch eine einzige generelle Verteilungsgleichung dargestellt werden können. Die vorliegende Arbeit gibt eine statistische Ableitung dieser Verteilungsfunktion, die zwei Parameter enthält. Die PrÜfung mit veröffentlichten experimentellen Ergebnissen an verschiedenen öl-in Wasser-Emulsionen und mit eigenen Experimenten an Wasser- in öl-Emulsionen ergab fÜr mechanisch präparierte Emulsionen sehr gute Übereinstimmungen.

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List of symbols A constant - a parameter of the equation; characteristic diameter - constant - constant - D sum of the diameters of all globules - dd sum of the diameters of the globules in the diameter interval fromx tox +dx - m number of categories - N total number of globules - n _i number of globules ini-th category - dn number of globules in the diameter interval fromx tox +dx. - _i number of volume elements in thei-th category - P probability - p number of volume elements in volumeV - S total surface area of the globules - s surface area of a globule - s _i surface area of a globule in thei-th category - ds surface area of the globules in the diameter interval fromx tox +dx - V total volume of the globules - v volume of a globule - v _i volume of a globule in thei-th category - v _x cumulative volume below sizex - dv volume of the globules in the diameter interval fromx tox +dx - w specific surface area of a globule - w _i specific surface area of a globule in thei-th category - X parameter of the equation; largest globule occurring - x variable globule diameter - X _i diameter of a globule in thei-th category.     

Development of equations for differential and integral enthalpy change of adsorption for simulation studies

We present equations to calculate the differential and integral enthalpy changes of adsorption for their use in Monte Carlo simulation. Adsorption of a system of N molecules, subject to an external potential energy, is viewed as one of transferring these molecules from a reference gas phase (state 1) to the adsorption system (state 2) at the same temperature and equilibrium pressure (same chemical potential). The excess amount adsorbed is the difference between N and the hypothetical amount of gas occupying the accessible volume of the system at the same density as the reference gas. The enthalpy change is a state function, which is defined as the difference between the enthalpies of state 2 and state 1, and the isosteric heat is defined as the negative of the derivative of this enthalpy change with respect to the excess amount of adsorption. It is suitable to determine how the system behaves for a differential increment in the excess phase adsorbed under subcritical conditions. For supercritical conditions, use of the integral enthalpy of adsorption per particle is recommended since the isosteric heat becomes infinite at the maximum excess concentration. With these unambiguous definitions we derive equations which are applicable for a general case of adsorption and demonstrate how they can be used in a Monte Carlo simulation. We apply the new equations to argon adsorption at various temperatures on a graphite surface to illustrate the need to use the correct equation to describe isosteric heat of adsorption.     

THE ADSORPTION OF AN ANIONIC SURFACTANT AT THE OIL WATER INTERFACE DURING EMULSION HOMOGENIZATION

Adsorption of sodium dodecylbenzene sulfonate (NaDBS) on the surfaces of dispersed oil globules during homogenization of paraffin oil in water emulsions has been studied. NaDBS concentration was changed over a wide interval comprising critical micelle concentration. For the emulsions homogenized for different time intervals the total quantity and the percentage of NaDBS adsorbed, the amount and number of NaDBS molecules adsorbed per unit inter-facial area, as well as the specific surface area of dispersed phase and the area per emulsifier molecule have been determined.

The amount adsorbed and density of the emulsifier layer, I.e., the area per NaDBS molecule adsorbed on the oil globule surfaces, depend not only on Initial NaDBS concentration but also, on the homogenization time and the homogenization action. This makes a difference between the adsorption behaviour under the conditions of emulsion formation and its subsequent homogenization, and the adsorption behaviour of the emulsifier at a plane quiescent Interface.     

Adsorption and order formation of colloidal nanoparticles on a substrate: a Brownian dynamics study

Adsorption process and order formation of electrostatically stabilized colloidal particles with a radius of 50 nm onto a planar surface with countercharge are examined. We perform Brownian dynamics simulations with a new three-dimensional cell model, in which the particle-particle and particle-substrate interactions are modeled based on the DLVO theory. The simulations yield the following results: (1) a larger bulk concentration would be required for larger kappaa to reach order formation to compensate for the decrease in the bulk potential; (2) the phase transition from a disordered to an ordered structure of the adsorbed particles on the substrate is considered to be of the Kirkwood-Alder type of transition through the examination of the two-dimensional pressure of the adsorbed particles; (3) the adsorbed particles are found to form a hexagonally ordered array, only if what we call "one-directional average force" acting on an adsorbed particle exceeds a critical value, which is independent of the ionic strength, or the interaction potentials. The critical value of the one-directional average force is interpreted as the force needed to keep an ordered structure by localizing adsorbed particles at fixed positions. In addition, the critical force is used to develop a new model to estimate the surface coverage at the order-disorder transition and it is demonstrated that the new model gives better estimation than other models previously reported.     

Kinetics and Isotherms of Cationic Polyelectrolyte Adsorption on Quartz

The kinetics of the formation of quartz surface charge in the solutions of a cationic polyelectrolyte, poly(styrene-co-dimethyl aminopropylmaleimide) with the molecular mass M = 20000 is studied in the concentration range from 10^–5 to 0.5 g/l in 10^–4 M KCl background solution at pH 6.5. Quartz capillaries with the radius from 5 to 10 m and molecularly smooth surface are used as model systems. Characteristic times of the formation of the surface charge at equilibrium with the solution are calculated from the data on the kinetics of adsorption; these times are equal to 40–50 min for the region of electrostatic adsorption (before the surface charge reversal) and 20–25 min, for the region of hydrophobic adsorption upon the formation of the second adlayer. Based on the steady values of the surface charge, the isotherms and potentials of adsorption of cationic polyelectrolyte are calculated. Electrostatic adsorption isotherm is described by the Langmuir equation with the energy of molecular adsorption of 25.4kT. It is shown that, at polymer concentration above 10^–2 g/l, the conformation of adsorbed molecules ceases to be planar. However, even in this case, we succeed in calculating the surface charge using the Helmholtz and Gouy equations and applying the pressure drops at the capillary ends higher than 10 atm, when under the loading of increasing shear stress in the surface layer the conformation of adsorbed molecules approaches the planar shape. Based on the two-layer model of the formation of surface charge developed earlier, it is shown that the energy of hydrophobic adsorption is smaller than that of electrostatic adsorption and is equal to 17.7kT. Possible physical mechanisms of electrostatic and hydrophobic adsorption of cationic polyelectrolyte molecules on quartz are discussed.