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We study the effect of polydispersity on the compression and interpenetration properties of two opposing polymer brushes by numerical self-consistent field approach and by analytical theory. Polydispersity is represented by an experimentally relevant Schulz–Zimm chain-length distribution. We focus on three different polydispersities representing sharp, moderate, and extremely wide chain length distributions and derive approximate analytical expressions for the pressure–separation curves, Π(D). We study the brush interpenetration and quantify it in terms of the overlap integral, Γ, representing the number of interbrush contacts, and interpenetration length, δ. For the case of moderate densities where the equation of state is dominated by the second virial term with coefficient υ, we demonstrate that the pressure, the overlap integral, and the interpenetration length are related by a simple equation, Π/kBT = υΓ/δ, where kBT represents the thermal energy. We propose a scaling form for δ(D) for the three poly...

We propose a novel class of responsive polymer brushes, where the effective grafting density can be controlled by external stimuli. This is achieved by using end-grafted polymer chains that have an affinity to the substrate. For sufficiently strong surface interactions, a fraction of chains condenses into a near-surface layer, while the remaining ones form the outer brush. The dense layer and the more tenuous outer brush can be seen as coexisting microphases. The effective grafting density of the outer brush is controlled by the adsorption strength and can be changed reversibly and in a controlled way as a response to changes in environmental parameters. The effect is demonstrated by numerical SCF calculations and analyzed by scaling arguments. Since the thickness of the denser layer is about a few monomer sizes, its capacity to form a microphase is limited by the product of the brush chain length and the grafting density. We explore the range of chain lengths and grafting densities where the effect is most pronounced. In this range, the SCF studies suggest that individual chains inside the brush show large rapid fluctuations between two states that are separated by only a small free energy barrier. The behavior of the brush as a whole, however, does not reflect these large fluctuations, and the effective grafting density varies smoothly as a function of the control parameters., Comment: To appear in J. Chem. Phys

We study the effect of polydispersity on the structure of polymer brushes by analytical theory, a numerical self-consistent field approach, and Monte Carlo simulations. The polydispersity is represented by the Schulz-Zimm chain-length distribution. We specifically focus on three different polydispersities representing sharp, moderate and extremely wide chain length distributions and derive explicit analytical expressions for the chain end distributions in these brushes. The results are in very good agreement with numerical data obtained with self-consistent field calculations and Monte Carlo simulations. With increasing polydispersity, the brush density profile changes from convex to concave, and for given average chain length $N_n$ and grafting density $\sigma$, the brush height $H$ is found to scale as $(H/H_{\mathrm{mono}}-1)\propto(N_w/N_n-1)^{1/2}$ over a wide range of polydispersity indices $N_w/N_n$ (here $H_{\mathrm{mono}}$ is the height of the corresponding monodisperse brush. Chain end fluctuations are found to be strongly suppressed already at very small polydispersity. Based on this observation, we introduce the concept of the brush as a near-critical system with two parameters (scaling variables), $(N_{n}\sigma^{2/3})^{-1}$ and $(N_w/N_n-1)^{1/2}$, controlling the distance from the critical point. This approach provides a good description of the simulation data. Finally we study the hydrodynamic penetration length $l_\mathrm{p}$ for brush-coated surfaces in flow. We find that it generally increases with polydispersity. The scaling behavior crosses over from $l_\mathrm{p}\sim N_\mathrm{n}^{1/2}\sigma^{-1/6}$ for monodisperse and weakly polydisperse brushes to $l_\mathrm{p}\sim N_{n}^{2/3}$ for strongly polydisperse brushes., Comment: 21pages, 9 figures. Accepted for publication in Macromolecues

Using molecular dynamics simulations, we study and compare the pressure, P, and the surface tension, γ, of linear chains and of ring polymers at the hard walls confining both melts into a slit. We examine the dependence of P and γ on the length (i.e., molecular weight) N of the macromolecules. For linear chains, we find that both pressure and surface tension are inversely proportional to the chain length, P(N)−P(N→∞)∝N−1,γ(N)−γ(N→∞)∝N−1, irrespective of whether the confining planes attract or repel the monomers. In contrast, for melts comprised of cyclic (ring) polymers, neither the pressure nor the surface tension is found to depend on molecular weight N for both kinds of wall-monomer interactions. While other structural properties as, e.g., the probability distributions of trains and loops at impenetrable walls appear quantitatively indistinguishable, we observe an amazing dissimilarity in the probability to find a chain end or a tagged monomer of a ring at a given distance from the wall in both kinds o...

In this paper, we discuss the elastic behavior of an isolated macromolecule in conjugated and non-conjugated ensembles during different modes of applying a mechanical force to the chain ends, namely, the mechanical effects corresponding to the methods of atomic force microscopy, magnetic levitation, and stretching of a macromolecule in an isotropic force field. Recently published results on the Langevin dynamics computer simulation of the stretching of a Gaussian polymer chain in different ensembles are analyzed. An analytical description of all the results of this simulation is given to show that the conclusion made by the authors of those studies about the nonequivalence of conjugated ensembles for Gaussian chains is not quite correct. A theoretical examination of the stretching of individual semirigid chains, which exhibit interesting behavior because of manipulations with actin molecules and microtubules, which are components of the cytoskeleton of most cells, is performed. We present rigorous analytical results about the stretching of chains composed of two or three freely jointed rods of equal length without consideration for excluded-volume inter-actions. It is shown that the stress-strain curves of these chains differ not only quantitatively but also qualitatively in different ensembles and that these curves for a chain of two freely jointed rods have an anomalous shape. These results on the different behavior of stress-strain for different modes of external mechanical impacts can be useful for interpreting experiments on the stretching of individual polymer molecules with different structures obtained via different methods, such as atomic-force microscopy and magnetic levitation.

This review is concerned with the response of an isolated polymer chain subjected to the action of the two different modes of the mechanical impact on the chain ends. In one mode, the end-to-end distance is changed in a controlled fashion and the fluctuating response force is measured; in the second case, an external stress field is applied to the chain end, and the measured response of the system is the fluctuating end-to-end distance. The main attention is focused on the results of the computer-aided simulation experiments and theoretical results. Upon stretching of an ideal chain, a real chain in a good solvent, or a globule, the resultant strain-force and force-strain dependences are shown to be different for chains with finite length L; however, this difference diminishes with an increase in the length of a molecule. When the anchored Gaussian chain is separated from the adsorbing surface, this difference disappears in the limit of high L; however, in the neighborhood of the phase transition, some characteristics (fluctuations, distribution functions) appear to be critically different under different impact modes even in the thermodynamic limit. The example of an abnormal system is discussed: The behavior of a polymer chain compressed by a small piston is different in the conjugated ensembles, and, as the system increases in size, this difference becomes even more pronounced.

We present a scaling theory and Monte Carlo (MC) simulation results for a flexible polymer chain slowly dragged by one end into a nanotube. We also describe the situation when the completely confined chain is released and gradually leaves the tube. MC simulations were performed for a self-avoiding lattice model with a biased chain growth algorithm, the pruned-enriched Rosenbluth method. The nanotube is a long channel opened at one end and its diameter $D$ is much smaller than the size of the polymer coil in solution. We analyze the following characteristics as functions of the chain end position $x$ inside the tube: the free energy of confinement, the average end-to-end distance, the average number of imprisoned monomers, and the average stretching of the confined part of the chain for various values of $D$ and for the number of monomers in the chain, $N$. We show that when the chain end is dragged by a certain critical distance $x^*$ into the tube, the polymer undergoes a first-order phase transition whereby the remaining free tail is abruptly sucked into the tube. This is accompanied by jumps in the average size, the number of imprisoned segments, and in the average stretching parameter. The critical distance scales as $x^*\sim ND^{1-1/\nu}$. The transition takes place when approximately 3/4 of the chain units are dragged into the tube. The theory presented is based on constructing the Landau free energy as a function of an order parameter that provides a complete description of equilibrium and metastable states. We argue that if the trapped chain is released with all monomers allowed to fluctuate, the reverse process in which the chain leaves the confinement occurs smoothly without any jumps. Finally, we apply the theory to estimate the lifetime of confined DNA in metastable states in nanotubes., Comment: 13pages, 14figures

Using a combination of analytical theory, Monte Carlo simulations, and three dimensional self-consistent field calculations, we study the equilibrium properties and the switching behavior of adsorption-active polymer chains included in a homopolymer brush. The switching transition is driven by a conformational change of a small fraction of minority chains, which are attracted by the substrate. Depending on the strength of the attractive interaction, the minority chains assume one of two states: An exposed state characterized by a stem-crown-like conformation, and an adsorbed state characterized by a flat two-dimensional structure. Comparing the Monte Carlo simulations, which use an Edwards-type Hamiltonian with density dependent interactions, with the predictions from self-consistent-field theory based on the same Hamiltonian, we find that thermal density fluctuations affect the system in two different ways. First, they renormalize the excluded volume interaction parameter $v_\mathrm{\tiny bare}$ inside the brush. The properties of the brushes can be reproduced by self-consistent field theory if one replaces $v_\mathrm{\tiny bare}$ by an effective parameter $v_{\mathrm{\tiny eff}}$, where the ratio of second virial coefficients $B_{\mathrm{\tiny eff}}/B_\mathrm{\tiny bare}$ depends on the range of monomer interactions, but not on the grafting density, the chain length, and $v_\mathrm{\tiny bare}$. Second, density fluctuations affect the conformations of chains at the brush surface and have a favorable effect on the characteristics of the switching transition: In the interesting regime where the transition is sharp, they reduce the free energy barrier between the two states significantly. The scaling behavior of various quantities is also analyzed and compared with analytical predictions., Comment: 15 pages, 14 figures

The coil-bridge transition in a self-avoiding lattice chain with one end fixed at height H above the attractive planar surface is investigated by theory and Monte Carlo simulation. We focus on the details of the first-order phase transition between the coil state at large height H ⩾ Htr and a bridge state at H ⩽ Htr, where Htr corresponds to the coil-bridge transition point. The equilibrium properties of the chain were calculated using the Monte Carlo pruned-enriched Rosenbluth method in the moderate adsorption regime at (H/Na)tr ⩽ 0.27 where N is the number of monomer units of linear size a. An analytical theory of the coil-bridge transition for lattice chains with excluded volume interactions is presented in this regime. The theory provides an excellent quantitative description of numerical results at all heights, 10 ⩽ H/a ⩽ 320 and all chain lengths 40 < N < 2560 without free fitting parameters. A simple theory taking into account the effect of finite extensibility of the lattice chain in the strong adsorption regime at (H/Na)tr ⩾ 0.5 is presented. We discuss some unconventional properties of the coil-bridge transition: the absence of phase coexistence, two micro-phases involved in the bridge state, and abnormal behavior in the microcanonical ensemble.

We propose a design for polymer-based sensors and switches with sharp switching transition and fast response time. The switching mechanism involves a radical change in the conformations of adsorption-active minority chains in a brush. Such transitions can be induced by a temperature change of only about ten degrees, and the characteristic time of the conformational change is less than a second. We present an analytical theory for these switches and support it by self-consistent field calculations and Brownian dynamics simulations., Highlighted as APS focus story in Physics 7, 83 (2014)

The initial stages of colonization of wheat roots by cells ofAzospirillum brasilense strains 75 and 80 isolated from soils of the Saratov oblast were studied. The adsorption of azospirilla on root hairs of soft spring wheats rapidly increased in the first hours of incubation, going then to a plateau phase. Within the first 15 h of incubation, exponential-phase cells were adsorbed more intensively than stationary-phase cells. Conversely, stationary-phase cells were adsorbed more intensively than exponential-phase cells, if the period of azospirilla incubation with the wheat roots was extended. As the time of incubation increased, the attachment of azospirilla to the wheat roots became stronger. The effect of cell attachment to root hairs was strain-dependent; the number of adsorbed cells of a given strain of azospirilla was greater in the case of host wheat cultivars. The deformation of wheat root hairs was affected by the polysaccharide-containing complexes isolated from the capsular material of azospirilla. The suggestion is made that common receptor systems are involved in the adsorption of azospirilla on roots and in root hair deformation

It was shown that Azospirillum brasilense strains Sp7, Sp107, Sp245, and S17 when cultivated in a liquid synthetic malate medium to the end of the exponential phase of growth, produced at least two complex polysaccharide-containing components. The components were arbitrarily called lipopolysaccharide-protein complex and polysaccharide-lipid complex. These complexes were shown to interact with a wheat germ agglutinin. From polysaccharide-lipid complexes, acidic polysaccharides were isolated and their specific rotation, molecular masses, affinity for wheat germ agglutinin, and monosaccharide composition were determined. The polysaccharides of all strains contained rhamnose, galacturonic acid, and glucosamine, while the polysaccharides of strains Sp7 and S17 included additional fucose and mannose, respectively, and both had galactose. It is suggested that lipopolysaccharide-protein complexes, polysaccharide-lipid complexes, and polysaccharides may be involved in the process of interaction of azospirilla with wheat root surfaces.

This paper reviews the results obtained in studies of the extracellular polysaccharides, lipopolysaccharide-protein complexes, polysaccharide-lipid complexes, lipopolysaccharides, and O-specific polysaccharides from bacteria of the genus Azospirillum. On the basis of present knowledge, the possible roles of the extracellular polysaccharides and polysaccharide-containing complexes of azospirilla in interaction with the roots of plants are discussed. Some pieces of evidence are considered in light of the lectin hypothesis originally proposed for the legume-Rhizobium symbiosis. In the context of these views of Azospirillum-cereal associative pairs, a key process at the early stages of the interaction is the specific reaction of cereal root lectins with the extracellular polysaccharide components, containing N-acetyl-d-glucosamine as part of their structure.

Full adsorption of flexible chains onto typical solid substrates occurs at a surface interaction energy of (5–10) kBT. The corresponding detachment force is in the range 10–50 pN. In contrast to “bare” solid substrates common to non-living materials, surfaces coated with brush-like polymer layers are very common in biological soft matter. We employ a simple mean-field approach to describe the effects of weak attraction between a floating long macromolecule and the brush. We show that even for a moderately thick brush a very small effective attraction is enough to produce complete binding of the long chain. The detachment force scales as , where W is the brush thickness. Hence the force could be 1 to 2 orders of magnitude smaller than in the case of typical solid substrates.

Two exopolysaccharide complexes hereafter termed lipopolysaccharide-protein complex and polysaccharide-lipid complex were isolated by means of washing-off with physiological solution from the cell surface of Azospirillum brasilense Spl07, Sp245, S17, 8, 15, 55, 75 and 80 of a complex biopolymer mixture followed by separation. On exposure to wheat seedling root hairs (Triticum aestivum cv. Saratovskaya 29) LPPCs and PSLCs were shown to cause root hair deformations similar to morphological changes of root hairs under the effect of bacterial cells. The data indicating the ability of complexes to bind to WGA, localized on wheat seedling roots were obtained by means of studying LPPCs and PSLCs inhibition in agglutination test under the effect of WGA. PSs containing GlcN, specifically interacting with WGA, were isolated from PSLCs.

A rigorous theory of adsorption of a Gaussian chain of infinite length into cylindrically shaped pores and onto cylindrical surfaces of arbitrary diameter, D, has been developed for any energy of interaction −ϵ. The change in the conformational free energy of a chain arriving inside the pores from an unrestricted volume is proportional to (D∗)−2 (D∗ is the effective pore width) over the entire molecular-sieve range (−ϵ −ϵc, the conformational free energy of the chain is virtually independent of the width and shape of the pores and is determined mainly by the value of −ϵ. At the critical point, −ϵ = −ϵc, the probability of the arrival of a polymer chain in the pore is independent of both the width and shape of the pore and is determined only by the ratio of geometrical volumes of the free volume to the pore volume. For cylindrical pores, a weak dependence of −ϵc on D is observed only for narrow pores. This dependence virtually disappears on passing to adsorbents with wide pores. Consideration of the adsorption of the macromolecule on the outer surface of the cylinder showed that at any finite value of the diameter of the cylinder, D, adsorption occurs as an ‘infinite-order’ phase transition. The maximum value of the specific heat (Cpmaxk=253=ϵ2c does not depend on D. The degree of bonding of the macromolecule to the adsorbent increases with decreasing curvature of the surface, rapidly attaining values characteristic of chain adsorption on a plane.

Substituted 1,3-thiazinoazoles were obtained by treating benzimidazole-2-thione, 4,5-diphenylimidazole-2-thione, and 1,2,4-triazole-3-thione with tertiary cyanoacetylenic alcohols and their acetals in the presence of lithium hydroxide. Treatment of the 1,3-thiazinobenzimidazoles with base destroyed the thiazino ring forming benzimidazol-2-one.

Nitration of 1,2-dihydropyrrolizine and its homologs with a mixture of nitric acid and acetic anhydride has been shown to give a mixture of 5-, 6-, and 7-nitro-1,2-dihydropyrrolizines. The distribution of isomers with respect to the position of alkyl substituents in the nonaromatic portion of the bicyclic is discussed.

Mixtures of isomeric 5-, 6-, and 7-carbethoxymethyl-1,2-dihydropyrrolizines were obtained by reaction of 1,2-dihydropyrrolizines with ethyl diazoacetate. The effect of the position of the alkyl groups in the two-membered ring on the ratio of isomers in the reaction products is demonstrated. A method for the isolation of 5-carbethoxymethyl-1,2-dihydropyrrolizines from the mixtures of isomers based on the difference in their reactivities in diazo coupling is described. The preferred conformations of the two-membered rings in the 5-carbethoxymethyl-1,2-dihydropyrrolizines are judged from the PMR spectral data.

The general method of obtaining the partition function and thermodynamic characteristics of polymer chains near an adsorbing surface, simulated by random walks on a lattice, is developed. The method takes into account the effect of short-range interactions in polymer chains, in particular, the chain stiffness and secondary structure. The theory of adsorption of chains of different stiffness is developed, and the process of adsorption which occurs when the external conditions change is shown to be always a second-order phase transition. The critical adsorption energy decreases and the sharpness of transition grows when the chain stiffness increases. A simple model of a chain with “virtual” steps is proposed which simplifies the treatment; the results obtained are in good agreement with exact theories. A general scheme of analysis of adsorption of chains with a given secondary structure is set forth and the analogy between the stiffness of a noncooperative chain and the presence of helical segments in a polypeptide chain is discussed.

A strict analytical theory has been developed describing the behavior of a model lattice polymer chain of arbitrary stiffness in a slitlike pore at polymer–adsorbent interaction energies –e. The thermodynamic characteristics of the system were calculated. It was shown that the transition of the macromolecule from the solution volume inside a pore occurs by the first-order phase transition with evolution of latent heat of adsorption. The transition point –e = –ec is determined by the chain stiffness and is independent of the pore width D. It is shown that in the precritical range, –e < –ec, the free energy ΔF of the macromolecules in the pores is adequately described by the universal dependence ΔF = ΔF(D*/A), where D* is some effective pore width depending on the value of –e, and A is the length of the Kuhn segment. At high attraction energies, –e ≫ –ec, the macromolecules are bonded to the pore walls by a great number of units and their free energy depends only on –e and the chain stiffness, ΔF = ΔF(A, e). Close to the critical energy –e ≃ –ec (transition range), ΔF is determined by both the stiffness of the macromolecule and the pore width D: ΔF ∼ A2D−1 for fairly high values of A and D. The possibilities of using porous media as protein stabilizers are discussed, and the value of the stabilizing effect depending on the chain stiffness is estimated.

Substituted 1,3-thiazinoazoles were obtained by treating benzimidazole-2-thione, 4,5-diphenylimidazole-2-thione, and 1,2,4-triazole-3-thione with tertiary cyanoacetylenic alcohols and their acetals in the presence of lithium hydroxide. Treatment of the 1,3-thiazinobenzimidazoles with base destroyed the thiazino ring forming benzimidazol-2-one.

Opening of the 1,3-oxathiolane ring with the formation of 8-mercaptoalkylcarbamate II evidently occurs in the first step under the influence of the amine; the subsequent dimerization of II via the addition of the mercapto group of one molecule to the double bond of a second molecule leads to intermediate III. This is followed by intramolecular substitution of the carbamoyl grouping with the formation of the 1,3-dithiolane ring.

During the reaction of l-cyano-3-methyl-3-hydroxy-l-pentyne (I) with Na2S'9H20 in the presence of potassium hydroxide (in the ratio of 0.4:1:1; 20~ dioxane), 2-methyl-2-ethyl3,4-di(cyanomethylene)oxetane (III), a product of the autoheterocyclization of carbinol I, was obtained instead Of the expected sulfide according to [i]. It is possible that cyanoethylene, formed as the result of the inverse Favorski reaction, is added in the form of an anion to the triple bond of the initial carbinol, which is very electrophilic in character. Then, the intermediate carbinol II cyclizes into III in a yield of 55%, mp 89~ (from ether). IR spectrum (KBr): 1650 (C----CH), 2220 cm -~ (CN); PMR spectrum (i00 MHz, CDCI3): 1.65 (s, 2-CH~); 1.20 (t, 2-CH2-CH3) and 1.88 (qu, 2-CH2); 5.55 (s, 3'-CH); 5.13 ppm (s, 4'-CH), f3',4' = 0.6 Hz.