Elastic behavior of short compact chains confined in double parallel boundaries

Adsorption of short two-dimensional compact chains confined in the double attractive parallel planar boundaries is investigated by using enumeration calculation method in this paper. First, we calculate the chain size and shape of adsorbed compact chains, such as mean-square end-to-end distance per bond R²/N, mean-square radii of gyration per bond S²_x/N and S²_y/N, shape factor δ and fraction of adsorbed segments f_a to illuminate that how the size and shape of adsorbed compact chains changes during the process of tensile elongation. There are some special behaviors in the chain size and shape for strong attraction interaction. In the meantime, compact chains can reach to the stable state with large distance between two parallel boundaries D. On the other hand, some thermodynamic properties, such as average energy per bond, Helmholtz free energy per bond, elastic force f and energy contribution to elastic f_U are also investigated in order to study the elastic behavior of compact chains adsorbed on the double attractive parallel planar boundaries. These investigations may provide some insights into the thermodynamic behaviors of adsorbed compact chains.     

三维吸附紧密高分子单链的力学性质研究

采用PERM(pruned-enriched Rosenbluth method)算法,研究了吸附在界面附近的紧密高分子链力学行为.发现当界面的吸附能比较大时,紧密高分子链从紧贴于吸附界面到逐渐远离的过程中,其外形会经历4种典型的变化.同时紧密高分子链的尺寸大小如/N、xy/N、z/N,形状参数<δ*>,热力学性质如每个键的平均自由能A/N,平均相互作用能/N等,甚至所受外力的大小都会同时做出相应的变化,其出现变化的位置也一致.特别是随着紧密高分子链离开吸附界面的过程中,作用于高分子链上的外力明显出现几个力学平台,这与实验得到的结果完全一致.同时还研究了弱吸附能的情况,在这种情况下实验是很难进行的.     

Polymer fracture—A simple model for chain scission

A simple model for calculating the fracture process for a single extended-chain molecule such as polyethylene is considered. The model consists of a chain of N coupled Morse oscillators. There exists a critical overall extension ΔL_c below which the fracture is energetically unfavorable but above which fracture is favored both energetically and kinetically. This elongation ΔL_c scales as N^1/2. For the critically stretched chain, the activation energy for rupture increases with N. Long chains must be stretched beyond this critical value to fail within experimentally meaningful times. Chains of all lengths subjected to the same force will fail with the same activation energy, provided this force is large enough to stretch each chain to ΔL > ΔL_c. Observed activation energies are less than 1/3D_e, where D_e is the bond energy.     

SEGMENT DENSITY PROFILES OF COMPACT POLYMER CHAINS CONFINED BETWEEN TWO PARALLEL PLANE WALLS

We use the pruned-enriched Rosenbluth method to investigate systematically the segment density profiles of compact polymer chains confined between two parallel plane walls.The non-adsorption case of adsorption interaction energyε=0 and the weak adsorption case ofε=-1 are considered for the compact polymer chains with different chain lengths N and different separation distances between two walls D.Several special entropy effects on the confined compact polymer chains,such as a damped oscillation in the segment density profile for the large separation distance D,are observed and discussed for different separation distances D in the non-adsorption case.In the weak adsorption case,investigations on the segment density profiles indicate that the competition between the entropy and adsorption effects results in an obvious depletion layer.Moreover,the scaling laws of the damped oscillation period T_d and the depletion layer width L_d are obtained for the confined compact chains.Most of these results are obtained for the first time so far as we know,which are expected to understand the properties of the confined compact polymer chains more completely.     

Phase behavior of a single polyethylene chain confined between two adsorption walls

The phase behavior of a single polyethylene chain confined between two adsorption walls is investigated by using molecular dynamics simulations. In the free space, it is confirmed in our calculation that the isolated polymer chain exhibits a disordered coil state at high temperatures, and collapses into a condensed state at low temperatures, that is, the coil‐to‐globule transition, and the finite chain length effects are considered since the critical region depends on chain lengths. When the chain is confined between two attractive walls, however, the equilibrium properties not only depend on the chain length but also depend on the adsorption energy and the confinement. Mainly, we focus on the influence of polymer chain length, confinement, and adsorption interaction on the equilibrium thermodynamic properties of the polyethylene chains. Chain lengths of N = 40, 80, and 120 beads, distances between the two walls of D = 10, 20, 30, 50, and 90 Å, and adsorption energies of w = 1.5, 2.5, 3.5, 6.5, and 8.5 kcal/mol are considered here. By considering the confinement–adsorption interactions, some new folding structures are found, that is, the hairpin structure for short chain of N = 40 beads, and the enhanced hairpin or crystal like structures for long chains of N = 80 and 120 beads. The results obtained in our simulations may provide some insights into the phase behaviors of confined polymers, which can not be obtained by previous studies without considering confinement–adsorption interactions. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 370–387, 2008     

Characterization of Polylactides with Different Stereoregularity Using Electrospray Ionization Ion Mobility Mass Spectrometry

We investigated the effect of stereoregularity on the gas-phase conformations of linear and cyclic polylactides (PLA) using electrospray ionization ion mobility mass spectrometry (ESI-IM-MS) combined with molecular dynamics simulations. IM-MS analysis of PLA ions shows intriguing difference between the collision cross section (Ω_D) value of poly-L-lactide (PLLA) and poly-LD-lactide (PLDLA) ions with respect to their chain architecture and stereoregularity. In the singly sodiated linear PLA (l-PLA?Na⁺) case, both l-PLLA and l-PLDLA up to 11mer have very similar Ω_D values, but the Ω_D values of l-PLLA are greater than that of l-PLDLA ions for larger ions. In the case of cyclic PLA (c-PLA), c-PLLA?Na⁺ is more compact than c-PLDLA?Na⁺ for short PLA ions. However, c-PLLA exhibits larger Ω_D value than c-PLDLA for PLA ions longer than 13mer. The origin of difference in the Ω_D values was investigated using theoretical investigation of PLAs in the gas phase. The gas-phase conformation of PLA ions is influenced by Na⁺-oxygen coordination and the weak intramolecular hydrogen bond interaction, which are more effectively formed in more flexible chains. Therefore, the less flexible PLLA has a larger Ω_D value than PLDLA. However, for short c-PLA, concomitant maximization of both Na⁺-oxygen coordination and hydrogen bond interaction is difficult due to the constricted chain freedom, which makes the Ω_D value of PLAs in this range show a different trend compared with other PLA ions. Our study facilitates the understanding of correlation between stereoregularity of PLAs and their structure, providing potential utility of IM-MS to characterize stereoisomers of polymers. Figure

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Modulation of ionization and structural properties of weak polyelectrolytes due to 1D, 2D,and 3D confinement

What is the impact of reducing the space available to molecules onto their properties is a fundamental question for capillary systems, molecular biology and transport, protein and material sciences. Possibly influenced by space restriction, ionization degree has rarely been studied for confined polyelectrolytes; Monte Carlo titrations and coarse‐grained models are thus used to investigate structural and ionization changes induced on a single polyelectrolyte chain by confinement into slit (1D), cylindrical (2D), or spherical (3D) cavities. Four polyelectrolyte models differing in chain stiffness and the possible formation of charged hydrogen bonds (c? H? bonds) are studied. Low pH effective ionization constants (pK_a ) of confined chains are lower than for the free species if c? H? bonds can be formed. This is especially evident for 3D‐confined stiff chains, a finding rationalized by the impact of global compression onto chain conformations. If no c? H? bonds are allowed, chain ionization is largely unaffected by 1D or 2D confinement, while it is depressed by 3D. Chain confinement Helmholtz energy (ΔA _conf) was computed as a function of both pH and confining width (W) to gauge the impact of ionization‐induced stiffening onto ΔA _conf versus W behavior, the partition coefficient governing absorption, and the average number of c? H? bond formed. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55 , 1088–1102     

Quinolin‐6‐ol at 100 K

The title compound, C₉H₇NO, has two symmetry‐independent molecules in the asymmetric unit, which have different conformations of the hydroxy group with respect to the quinoline ring. One of the molecules adopts a cis conformation, while the other shows a trans conformation. Each type of independent molecule links into a separate infinite O—H...N hydrogen‐bonded chain with the graph‐set notation C(7). These chains are perpendicular in the unit cell, one extended in the a‐axis direction and the other in the b‐axis direction. There is also a weak C—H...O hydrogen bond with graph‐set notation D(2), which runs in the c‐axis direction and joins the two separate O—H...N chains. The significance of this study lies in the comparison drawn between the experimental and calculated data of the crystal structure of the title compound and the data of several other derivatives possessing the hydroxy group or the quinoline ring. The correlation between the IR spectrum of this compound and the hydrogen‐bond energy is also discussed.     

Model Bridging Effects of Asymmetrical Triblock Copolymers

Summary: We have performed Monte Carlo simulations to study the bridging of symmetrical or asymmetrical triblock copolymers confined between two similar or different solid surfaces based on a simple lattice model. The influence of the molecular structure, surface separation, adsorption energy, chain composition, and the chain concentration on the fractions of chains with bridge, loop and dangling configurations are reported in detail. The results show that the largest bridging fraction is given only when symmetrical triblock copolymers are confined between two parallel surfaces with the same adsorption energy. The bridge fraction is decreased so long as the asymmetry of the copolymers or the difference between the two surfaces is enhanced. It was found also that the bridging fraction increases as the adsorption energy increases. The bridging fraction Ω_bridge under different separations, L_z, can be expressed as in various situations. On the other hand, by introducing a symmetry index ν, the influence of molecular structure of copolymers on the bridges can be illustrated approximately by a relation when the two surfaces are similar and the adsorption energy is not too high. Combining the two expressions, data of the bridge fractions for copolymers of different symmetries confined between surfaces with different separations can be described with a single equation, which, in some occasion, can be used for prediction.

Influence of molecular structure on the bridging fraction for .     

Rigidity percolation model of polymer fracture

A theory of the fracture of polymers with network microstructure was developed that was based on the vector, or rigidity percolation (RP) model of Kantor and Webman, in which the modulus, E, is related to the lattice bond fraction p, via E ～ [p ? p_c]^τ. The Hamiltonian for the lattice was replaced by the strain energy density function of the bulk polymer, U = σ²/2E, where σ is the applied stress and p was expressed in terms of the lattice perfection via the bond density ν, with the entanglement molecular weight, ν = ρ/M_e and appropriate measures of crosslink density for rubber, thermosets, and carbon nanotubes. The stored mechanical energy, U, was released by the random fracture of νD_o[p ? p_c] over stressed hot bonds of energy D_o ≈ 330 kJ/mol. The polymer fractured critically when p approached the percolation threshold p_c, and the net solution was obtained as σ = (2EνD_o [p ? p_c])^1/2 with a fracture energy, G_1c ～ [p ? p_c]. The fracture strength of amorphous and semicrystalline polymers in the bulk was well described by, σ = [ED_oρ/16 M_e]^1/2, or σ ≈ 4.6 GPa/M_e^1/2. Fracture by disentanglement was found to occur in a finite molecular weight range, M_c < M < M*, where M*/M_c ≈ 8, such that the critical draw ratio, λ_c = (M/M_c)^1/2, gave the molecular weight dependence of the fracture as G_1c ～ [(M/M_c)^1/2 ? 1]². The critical entanglement molecular weight, M_c, is related to the percolation threshold, p_c, via M_c = M_e/(1 ? p_c). Fracture by bond rupture was in accord with Flory's suggestion, G/G* = [1 ? M_c/M], where G* is the maximum fracture energy. Fracture of an ideal rubber with p = 1 was determined not to occur without strain hardening at λ > 4, such that the maximum stress, σ = E (λ ? 1/λ) = 3.75E. The fracture properties of rubber were found to behave as σ ～ ν, σ ～ E, and G_1c ～ ν. For highly crosslinked thermosets, it was predicted that σ ～ (Eν)^1/2, σ ～ (X ? X_c)^1/2, and G_1c ～ ν^?1/2, where X is the degree of reaction of the crosslinking groups and X_c defines the gelation point. When applied to carbon nanotubes (SWNT and MWNT) of diameter d and hexagonal bond density ν = j/b², the nominal stress as a function of diameter is σ(d) = [16 ED_o(p ? p_c) j/b]^1/2/d ≈ 211/d (GPa.nm) and the critical force, F_c(d) ≈ 166 d (nN/nm), in which j = 1.15, b = 0.142 nm, E ≈ 1 Tpa, and D_o = 518 kJ/mol. For polymer interfaces with Σ chains per unit area of length L and width X ～ L^1/2, G_1c is then ～ [p ? p_c], where p ～ ΣL/X. The results predicted by the RP fracture model were in good agreement with a considerable body of fracture data for linear polymers, rubbers, thermosets, and carbon nanotubes. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 168–183, 2005     

Molecular geometry and chain entanglement: parameters for the tube model

The tube diameter in the reptation model is the distance between a given chain segment and its nearest segment in adjacent chains. This dimention is thus related to the cross-sectional area of polymer chains and the nearest approach among chains, without effects of thermal fluctuation and steric repulsion. Prior calculated tube diameters are much larger, about 5 times, than the actual chain cross-sectional areas. This is ascribed to the local freedom required for mutual rearrangement among neighboring chain segments. This tube diameter concept seems to us to infer a relationship to the corresponding entanglement spacing. Indeed, we report here that the critical molecular weight, M_c, for the onset of entanglements is found to be M_c = 28 A/(〈R²〉₀/M), where A is the chain cross-sectional area and 〈R²〉₀ the mean-square end-to-end distance of a freely jointed chain of molecular weight M. The new, computed relationship between the critical number of backbone atoms for entanglement and the chain cross-sectional area of polymers, N_c = A^0,44, is concordant with the cross-sectional area of polymer chains being the parameter controlling the critical entanglement number of backbone atoms of flexible polymers.     

Polymer chains confined into tubes with attractive walls: A Monte Carlo simulation

A bead-spring off-lattice model of a polymer chain with repulsive interactions among repeating units confined into straight tubes of various cross sections, D_T², is studied by Monte Carlo simulation. We are also varying the chain length from N = 16 to 128 and the strength of a short-range attractive interaction between the repeating units and the walls of the tube. Longitudinal and perpendicular static linear dimensions of the chains are analyzed, as well as the density profile of repeating units across the tube. These data are interpreted in terms of scaling concepts describing the crossover between three-dimensional and quasi-one-dimensional chain conformations and the adsorption transition of chains at flat infinite walls, respectively. We also study the time-dependent mean-square displacements of repeating units and obtain various relaxation times. It is shown that both relaxation times scaling proportional to N² and to N³ play a role in the reptative motion of the chain in the tubes.     

Crystal structure of polyisobutylene

The crystal structure of polyisobutylene was determined by x-ray analysis. The orthorhombic cell, with a = 6.88 Å, b = 11.91 Å, c (fiber axis) = 18.60 Å (space group: P2₁2₁2₁ ? D), contains two molecular chains each consisting of eight monomeric units in the fiber identity period. The chain conformation is essentially an (8/3) helix, but deviates appreciably from the exact (8/3) helix symmetry. The symmetry of the molecular chain is only a twofold screw axis in exact sense, and a crystallographic asymmetric unit consists of four monomeric units. The torsional angles are where M denotes the methyl group. The averaged skeletal C? CH₂? C and C? CM₂? C bond angles are 128° and 110°, respectively. The large C? CH₂? C bond angles may be due to steric respulsion between the adjacent methyl groups, giving intramolecular distances larger than 3.09 Å.     

ADSORPTION OF SHORT TWO-DIMENSIONAL COMPACT CHAINS

Short two-dimensional compact chains adsorbed on the attractive surface at different temperatures were investigated by using the enumeration calculation method. First we investigate the chain size and shape of adsorbed chains, such as characteristic ratios of mean-square radii of gyration 〈S^2〉x/N and 〈S^2〉y/N, shape factor 〈δ〉, and the orientation of chain bonds 〈cos^2 θ〉 to illuminate how the size and shape of adsorbed compact chains change with increasing temperatures. There are some special behaviors for the chain size and shape at low temperature, especially for strong attraction interaction. In the meantime, adsorbed compact chains have different behaviors from general adsorbed polymer chains. Some thermodynamics properties are also discussed here. Heat capacity changes non-monotonously, first increases and then reduces. The transition temperature Tc is nearly 1.0, 1.4, 2.0 and 4.2 （in the unit of To） for the case of ε = 0, -1, -2 and -4 （in the unit of kTo）, respectively. Average energy per bond increases while average Helmholtz free energy per bond decreases with increasing temperatures. From these two thermodynamics parameters we can also get another transition temperature Tc＇, and it is close to 0.7, 1.1, 1.5 and 3.4 for ε= 0, -1, -2, and -4, respectively. Therefore, Tc is greater than Tc＇ under the same condition. These investigations may provide some insights into the thermodynamics behaviors of adsorbed protein-like chains.     

Elastic behavior of single polymer chains adsorbed on rough surfaces

In this paper, elastic behaviors of single polymer chains adsorbed on the rough surfaces with a substrate and some periodically tactic pillars are investigated by the pruned-enriched-Rosenbluth method (PERM). In our simulation, a single polymer chain is firstly adsorbed on the substrate and then pulled along the z-axis direction, which is vertical to the substrate. We investigate the chain size and shape of polymer chains, such as mean-square radii of gyration per bond 〈S²〉_xy/N, 〈S²〉_z/N and shape factor 〈δ^∗〉 in order to show how the size and shape of adsorbed polymer chains change during the desorption process. Due to the occurrences of separation of the chains from the substrate, farther adsorption on the upper surfaces of pillars and complete separation from the whole rough surfaces in the elastic process, the changes of 〈S²〉_xy/N, 〈S²〉_z/N and 〈δ^∗〉 during the process are complicated. On the other hand, some thermodynamic properties such as average energy per bond, average Helmholtz free energy per bond, elastic force f are investigated, and our aim is to study the elastic behaviors of polymer chains adsorbed on the rough surface during the elasticity process. Elastic force f has some plateaus during the desorption process for strong adsorption interaction. If there is no adsorption interaction, the chains can get away from the rough surfaces spontaneously. These investigations can provide some insights into the elastic behaviors of polymer chains adsorbed on the rough surface.     

SCF Wave functions for (CuO2)n lamella in crystal field of T′–Nd2CuO4

An SCF analysis has been carried for ensembles that simulate the CuO₂ conduction layer in the tetragonal layer crystal T′—Nd₂CuO₄ (Fig. 1). In this work, the CuO₂ layer is described by a planar macromolecule, (CuO₂)_n, subject to the crystal field produced by the point charges in the ionic layers of D_4h symmetry The computations were carried out using the KGNMOL, HONDO, and KGNGRAF codes in MOTECC -91. The computations were carried out with different oxygen and copper basis sets and energy convergence to less than 10^?8 Hartrees. The purpose of the SCF computation was to estimate the cohesive energy of the ensembles, the electron density for the individual molecular orbitals, and the excess correlation energy, to ascertain the nature of the Cu? O bond in the conduction layer. The results indicate the following: (1) The cohesive energy of the ensembles (measured by the SCF energy plus the correlation energy, above the atomic values): ΔU_c ≡ ΔE_SCF + ΔE_C = ?4.35 to ?4.17 Hartrees per CuO bond as n increases from 4 to 9. Further insight was obtained by considering the electrostatic energy contributions to ΔU_c; E_{electrostatic} (ensemble) → E_Modeling (infinite lattice) were evaluated by replacing the oxygen and copper atoms by point charges determined by a Mullion population analysis. The larger oxygen basis set (13, 8/5,3) gave consistent results for the different ensembles of ΔE_covalent ≡ ΔU_c ? E_{electrostatic} = ?1.1 Hartrees per CuO bond. (ii) The electron density indicates that covalent bonds are formed and that the oxygen atoms play an important role in the structure stability. The covalent bonds formed indicate that nominal ionic valences do not apply. Mulliken population analyses gave valences of the order of one at the copper and oxygen atoms. The CuO bond orders are 0.47 between neighboring atoms and 0.048 for those separated by two atoms. (iv) The covalent nature of the CuO bonds in (CuO₂)_n was compared to that for the H₂ molecule using as a measure the electron density and the excess correlation energy. The excess correlation energy per CuO bond above the atomic values is one order of magnitude lower that that for the H₂ molecule and that for the C?C bond in alternant hydrocarbons. © 1993 John Wiley & Sons, Inc.     

Statistics of stiff polymer chains near an adsorbing surface

The exact solution of the problem of adsorption of a long ideal polymer chain with variable degree of stiffness on a plane surface is presented. It is shown that the adsorption of stiff polymer chains is a second-order phase transition; in the adsorbed state “train” (i.e. adsorbed) sections are relatively longer and loop sections relatively shorter than for flexible chains. This effect is very pronounced: already for moderately stiff chains the number of Kuhn segment lengths in one “train” section at the temperature T = T_cr/2 (T_cr is the critical temperature for adsorption transition) can reach several thousands, and deviation from the surface occurs only in the form of small “hairpins”. The maximum length of the chain, which at the given conditions would flatten completely on the surface, is estimated.     

Degeneracy of confined D‐dimensional harmonic oscillator

Using the mathematical properties of the confluent hypergeometric functions, the conditions for the incidental, simultaneous, and interdimensional degeneracy of the confined D‐dimensional (D > 1) harmonic oscillator energy levels are derived, assuming that the isotropic confinement is defined by an infinite potential well and a finite radius R_c. Very accurate energy eigenvalues are obtained numerically by finding the roots of the confluent hypergeometric functions that confirm the degeneracy conditions. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Carbon–nitrogen bond dissociation energy values in C-nitrosocompounds

Measurements of the D(R? NO) bond strength in some C-nitrosocompounds have been made using an electron impact method. The appearance potential of the radical ion (R⁺) has been determined, the D(R? NO) bond energy being obtained from the relation The values obtained are: D(C₆H₅? NO) = 41 kcal/mole, D(t-C₄H₉? NO) = 34 kcal/mole, D(t-C₅H₁₁? NO) = 36 kcal/mole and D(i-C₃H₇? NO) = 36.5 kcal/mole. These values are in good agreement with the numerous estimations of Benson and coworkers and confirm that the C? N bond strength in C-nitrosocompounds is very much less than in nitrocompounds or in amines.     

Equilibrium anionic polymerization of β-methoxypropionaldehyde

Anionic polymerization of β-methoxypropionaldehyde (MPA) was carried out in tetrahydrofuran (THF) by using benzophenone–monolithium complex as an initiator. An equilibrium between polymerization and depolymerization was observed at a temperature range of ?90 to ?70°C. From the temperature dependence of the equilibrium monomer concentration, thermodynamic parameters for the polymerization of MPA in THF were evaluated as follows: ΔH_ss = ?4.8 ± 0.2 kcal/mole, ΔH_SS = ?22.4 ± 1.3 cal/mole-deg, and (T_c)_ss = ?59°C. The thermodynamic change upon the conversion of liquid monomer to condensed polymer was computed from both the partial mixing energy of MPA with THF and the linear relationship between the equilibrium volume fraction of MPA monomer and that of the resulting polymer: ΔH_1c = ?4.7 ± 0.2 kcal/mole, ΔS_1c = ?19.5 ± 1.3 cal/mole-deg, and (T_c)_1c = ?35°C.