The Morphology of Symmetric Triblock Copolymer Melts Confined in a Slit: A Monte Carlo Simulation

Monte Carlo simulations based on a modified bond‐fluctuation and vacancy‐diffusion algorithm on a simple cubic lattice were employed to examine the morphology of thin films of the symmetric A_mB_2nA_m triblock copolymer confined between two hard homogeneous parallel walls. The walls preferred either segment A or segment B. Parallel lamellae, parallel cylinders and perpendicular cylinders morphologies, dependent on the composition, film thickness and interaction energies, were identified in these simulations, in agreement with the experimental observations of several researchers.     

Electrophoretic flow of interacting polymer chains: Effects of temperature,polymer concentration,and porosity

Using a Monte Carlo simulation in three dimensions, we studied the variation of the root-meansquare (rms) displacement (R_rms) of polymer chains with time and the rates of their mass transfer (j) as a function of biased field (B), polymer concentration (p), chain length (L_c), porosity (p_s), and temperature (T). In homogeneous/annealed system, the rms displacement of the chains shows a drift-like behavior, R_rms ∼ t, in the asymptotic time regime preceded by a subdiffusive power-law (R_rms ∼ t^k, with k < 1/2) at high p. The subdiffusive regime expands on increasing L_c and p but reduces on increasing T or B. In quenched porous media, the drift-like behavior of R_rms persists at low barrier concentration (p_b) and high T. However, at high p_b and/or low T, chains relax into a subdrift and/or subdiffusive behavior especially with high p or long L_c. Flow of chains is measured via an effective permeability (σ) using a linear response assumption. In annealed system, σ increases monotonically with B at high T and low p but varies nonmonotonically at low T, high p and high L_c. We find that σ decays with L_c, σ ∼ L, where α depends on B, p and T with a typical value a α ∼ 0.43−0.64 for p = 0.1-0.3 at B = 0.5. Further, σ decays with p, σ ∼ − Cp with a decay rate C sensitive to T and B. In quenched porous media, even at low pb and high T, σ varies nonmonotonically with bias, i.e., the increase of σ is followed by decay on increasing the bias beyond a characteristic value (B_c). This characteristic bias seems to decrease logarithmically with barrier concentration, B_c ∼ −klnp_b. The prefactor k depends on the chain length, k ≈ 0.35 for shorter chains (L_c = 20, 40) and ≈ 0.15 for longer chains (L_c = 60). Scaling dependence of σ on L_c similar to that in annealed system is also observed in porous media with different values of exponent α. The current density shows a nonlinear power-law response, j ∼ B^σ, with a nonuniversal exponent δ ≈ 1.10−1.39 at high temperatures and low barrier concentrations.     

SOLUBILIZATION OF OIL IN DISCONTINUOUS CUBIC LIQUID CRYSTAL IN POLY(OXYETHYLENE)n OLEYL ETHER SYSTEMS

The structural change of the discontinuous cubic (I₁) phase upon addition of oil (heptane, decane, and hexadecane) is investigated by small-angle x-ray scattering. In polyoxyethylene oleyl ether (C_18.1EO_n) systems having long polyoxyethylene chain (n =19.2, 30.1, and 50.8), the I ₁ phase is formed in a wide concentration range. Only in C_18.1EO_nEO_19.2EO_n systems, the structure of the I₁ phase changes from body-centered to face centered cubic lattice upon addition of oil. According to the analysis of the change in effective cross-sectional area, the solubilization of hexadecane increases the repulsion between polyoxyethylene chains, while solubilization of heptane makes it decrease. The solubilization of decane keeps the repulsion constant. Since the repulsion hampers the curvature change due to the solubilization, the solubilization capacity is in the order, heptane>decane>hexadecane. The oil penetration and nonpenetration into the palisade layer are also discussed in term of the change in the effective volume of the lipophilic part in the surfactant molecule.     

Kinetics of the reaction of sodium arylthiolates with nitro-carboxybenzyl halide derivatives

The rate constants for the reactions of 4-halomethyl-3-nitrobenzoic acids, the nonnitro derivatives, and their ethyl esters with arylthiolates were measured at different temperatures. It was found that the retardation in rate constants compared to benzyl halides is due to the electrostatic repulsion between the electronegative substituents (COO⁻ and/or NO₂) in the substrates and thiolate ions. Good correlations between log k₂ values of the acids and carbon basicities of thiolates were found while log k₂ values of the esters show good straight lines with Hammett σ constants, pk_a, and carbon basicities of arylthiolates. © 1996 John Wiley & Sons Inc     

Unmixing of polymer blends confined in ultrathin films: crossover between two-dimensional and three-dimensional behavior

The interplay between chain conformations and phase separation in binary symmetric polymer mixtures confined into thin films by "neutral" hard walls (i.e., walls that do not preferentially attract or repel one of the two components of the mixture) is studied by Monte Carlo simulations. Using the bond fluctuation model on a simple cubic lattice in the semi grand canonical ensemble, we locate the critical temperature of demixing via finite size scaling methods for a wide range of chain lengths (16 infinity, and hence T(c) proportional, variant N. However, strong deviations from the Flory-Huggins theory occur as long as the unperturbed chain dimension exceeds D, and the critical behavior falls in the universality class of the two-dimensional Ising model for any finite value of D.     

Monte Carlo Simulations of the Morphologies and Conformations of Triblock Copolymer Thin Films

Summary: The morphologies and conformations of triblock copolymer (ABA and ABC) thin films confined between two identical walls were investigated by Monte Carlo simulation using bond length fluctuation and cavity diffusion algorithm on cubic lattice. Effects of the wall‐block interactions, copolymer chain composition and film thickness on morphologies, as well as on the fraction of chain “bridge” conformation f_bridge are presented in detail. In ABA thin film, column, parallel, perforated and perpendicular lamellas were discriminated, furthermore, the transition of morphology and the variation of f_bridge of ABA film along with the increase of thickness were revealed. In ABC thin film, lamella especially perpendicular lamella morphologies are predominant in varying the wall‐block interactions and the thickness. The results are consistent with some theoretical predictions such as DDFT and simulations reported in literature.

Isodensity profile of A₅B₅A₅ thin film.     

Properties of surfactant monolayers in relation to microemulsion phase behaviour

The relationship between the properties of surfactant monolayers at oil-water interfaces and the phase behaviour in bulk of mixtures of oil + water + surfactant is discussed. Such monolayer properties include the spontaneous curvature, c_o the interfacial tension, I γ, the elasticity K (or rigidity) associated with the mean curvature, and the elasticity K associated with the Gaussian curvature. The model system chosen for investigation is the anionic surfactant AOT + aqueous NaCl + n-alkane at 20°C. In such systems, inversion of microemulsion type from oil-in-water (o/w) to water-in-oil (w/o) is possible with increasing electrolyte concentration. The tension, γ, passes through an ultralow minimum value at conditions corresponding to the formation of three phases. Using small angle neutron scattering, we have determined the structure of surfactant-rich third phases (c_o ~ 0) formed with the different alkanes. Lamellar phases consisting of surfactant monolayers separated alternately by oil and water appear with short alkanes, whereas L₃ and bicontinuous phases form in systems containing longer alkanes. The bending elasticity K has been measured for planar monolayers at the oil-water interface by ellipsometry. K is independent of salt concentration but depends markedly on alkane chain length N, falling from ~ 1 k_BT for N < 11 to ~0.1 k_BT for N = 14. This is discussed in terms of the differing extents of oil penetration into the surfactant chains. Higher rigidities favouring lamellar phases and lower rigidities favouring bicontinuous microemulsions are in line with the theoretical predictions of de Gennes and Taupin. Estimates of the constant K have been obtained in droplet microemulsions (w/o) from a knowledge of their size, K and γ. The sign of the constant is in agreement with the geometry of the phases formed in three phase systems. Finally, the ideas and concepts developed in the oil-water systems described above are used to explain the wetting behaviour by alkanes of AOT monolayers at the air-water surface.     

AN INVESTIGATION ON FOLD STRUCTURE IN POLYETHYLENE LAMELLA WITH DIAMOND LATTICE MODEL

Based on perfect rotational isomeric state model of polyethylene chainwithout any torsional stretch or chain twisting, the separation distance between a zig-zagsegment and its re-entry ones in lamella has been investigated. The intervals were definedby a pair of quantum numbers (k_x, k_y) according to the formula: D=0.153/(3~(1/2))((8k_x~2+16l_y~2)~(1/2))(nm)k_x and k_y are integers just as the lattice coordinates on the respective & and α- axes ofthe crystal lattices for polyethylene. The crystal lattices of polyethylene can be accessibleby the re-entry stems, whether it is adaceni fold or not. Conformations, until 14-bondfold, of the fold part were investigated. The sequence TTGTTG' G' TTGGTTG possessesthe lowest average conformation energy per bond for (110) fold, and TGTTG'G'TTTG'for (020) fold, TTTGGTGGTTGTG' etc. for (200) fold.     

Emulsion polymerization. V. Lowest theoretical limits of the ratio kt/kp

It is assumed that the propagating polymeric radicals have no diffusive mobility in the very highly viscous medium within latex particles. Chain growth takes place on a lattice when the polymeric radical reacts with a monomer present on a lattice site adjacent to that occupied by the reactive chain end. For termination, two radical chain ends must be positioned on adjacent lattice sites at the same instant. The k_t/k_p ratios calculated with this model are either similar to or somewhat lower than the values determined in emulsion polymerization experiments. A minimum value of k_t/k_p can be calculated with the aid of the rate equation of Part III by assuming that only “living” polymer is produced during emulsion polymerization. This value of k_t/k_p is significantly lower than that calculated by the lattice model. Since the value corresponding to the lattice model gives the slowest practically achievable termination rate, it is concluded from these calculations that emulsion polymerization cannot be carried out under conditions in which chain termination is completely suppressed.     

The “Inverted Bonds” Revisited: Analysis of “In Silico” Models and of [1.1.1]Propellane by Using Orbital Forces

This article dwells on the nature of “inverted bonds”, which refer to the σ interaction between two sp hybrids by their smaller lobes, and their presence in [1.1.1]propellane. Firstly, we study H₃C−C models of C−C bonds with frozen H-C-C angles reproducing the constraints of various degrees of “inversion”. Secondly, the molecular orbital (MO) properties of [1.1.1]propellane and [1.1.1]bicyclopentane are analyzed with the help of orbital forces as a criterion of bonding/antibonding character and as a basis to evaluate bond energies. Triplet and cationic states of [1.1.1]propellane species are also considered to confirm the bonding/antibonding character of MOs in the parent molecule. These approaches show an essentially non-bonding character of the σ central C−C interaction in propellane. Within the MO theory, this bonding is thus only due to π-type MOs (also called “banana” MOs or “bridge” MOs) and its total energy is evaluated to approximately 50 kcal mol⁻¹. In bicyclopentane, despite a strong σ-type repulsion, a weak bonding (15–20 kcal mol⁻¹) exists between both central C−C bonds, also due to π-type interactions, though no bond is present in the Lewis structure. Overall, the so-called “inverted” bond, as resulting from a σ overlap of the two sp hybrids by their smaller lobes, appears highly questionable.     

Features of the kinetics of the liquid-phase oxidation of cyclohexanol

The kinetics of oxygen uptake in the cumyl peroxide-initiated oxidation of cyclohexanol (373 K, o-dichlorobenzene) is studied. The parameters of the oxidizability of k _p (2k _t )^?0.5 (which depend on [RH]) and the rate constants of the bi- and trimolecular reactions of chain initiation (k ₀ = 1.25 × 10^?8 L/(mol s) and k′₀ = 2.5 × 10^?9 L²/(mol² s), respectively) are determined by solving the inverse kinetic problem. It is demonstrated that the quadratic-law recombination of peroxyl radicals during cyclohexanol oxidation also occurs without chain termination. The recombination rates of peroxyl radicals with and without chain termination (k′/k _t ) are found to grow with increasing [RH], reaching their maxima at [RH] = 1.0 mol/L, and to diminish subsequently. We conclude that this can be attributed to changes in the ratio between the propagating peroxyl radicals (hydroperoxyl and 1-hydroxycyclohexylperoxyl) in the reaction medium.     

Influence of the linking chain length on the recombination kinetics of covalently bonded triplet radical pairs and magnetic field effects

Nanosecond laser flash photolysis technique is used to study the formation and decay kinetics of covalently linked triplet radical pairs (RP) formed after photoinduced electron transfer in the series of 21 zinc porphyrin—chain—viologen (Pph—Sp_n—Vi²⁺) dyads, where the number of atoms (n) in the chain increases from 2 to 138. In poorly viscous polar solvents (acetone, CHCl₃—CH₃OH (1 : 1) mixture), the dependence of the rate constant of RP formation on n can be described by the equation k _e = k _e ⁰ n ^–a at k _e ⁰ = 2.95·10⁸ s^–1 anda = 0.8. In the zero magnetic field, the RP recombination rate constant (k _r(B = 0)) is significantly lower than k _e and ranges from 0.7·10⁶ to 8·10⁶ s^–1. The dependence of k _r(B = 0) on n is extreme. The dependence k _r(B = 0) reaches a maximum at n = 20. In the strong magnetic field (B = 0.21 T), the significant retardation of triplet RP recombination is observed. The chain length has an insignificant effect on k _r(B = 0.21 T), which ranges from 0.3·10⁶ to 0.9·10⁶ s^–1. The regularities found are discussed in terms of the interplay of molecular and spin dynamics.     

Transient free-exciton luminescence and exciton—lattice interaction in pyrene crystals

Time-resolved spectra and luminescence decay time in pyrene crystals have been studied by a time-correlated photon-counting technique over the temperature range 295−136 K (above the phase-transition point). Transient free-exciton luminescence is observed as well as thermally activated free-exciton luminescence. The rate of decay of transient free-exciton luminescence σ is proportional to exp(− E_B/kT, where k is the Boltzmann constant and T the temperature. The ST barrier height E_B is found to be 260 cm⁻¹. The ratio of the ST barrier height against the exciton bandwidth is found to be 0.1. The lower bound of the time required for excitons to tunnel through the ST barrier is estimated to be 36 ps.     

Cage‐Like B41+ and B422+: New Chiral Members of the Borospherene Family

The newly discovered borospherenes B₄₀^?/0 and B₃₉^? mark the onset of a new class of boron nanostructures. Based on extensive first‐principles calculations, we introduce herein two new chiral members to the borospherene family: the cage‐like C₁ B₄₁⁺ ( 1 ) and C₂ B₄₂²⁺ ( 2 ), both of which are the global minima of the systems with degenerate enantiomers. These chiral borospherene cations are composed of twelve interwoven boron double chains with six hexagonal and heptagonal faces and may be viewed as the cuborenes analogous to cubane (C₈H₈). Chemical bonding analyses show that there exists a three‐center two‐electron σ bond on each B₃ triangle and twelve multicenter two‐electron π bonds over the σ skeleton. Molecular dynamics simulations indicate that C₁ B₄₁⁺ ( 1 ) fluctuates above 300 K, whereas C₂ B₄₂²⁺ ( 2 ) remains dynamically stable. The infrared and Raman spectra of these borospherene cations are predicted to facilitate their experimental characterizations.     

Monte Carlo study of the coil-to-globule transition of a model polymeric system

Monte Carlo computer simulations of single, flexible, self-avoiding chains on a cubic lattice have been performed upon conditions of increasing segment–segment cohesive energy (deteriorating solvent quality). The simulations spanned a wide range of chain lengths (20–10,000, i.e., up to molecular weights of a few millions) and cohesive energies (0.0–0.45k_BT, i.e., from athermal to very poor solvents). The chain length dependence of the chain size in poor solvents was characterized by a wide plateau of almost null growth for intermediate chain lengths. This plateau was linked to the development of the incipient constant density core, while genuine power law dependence (1/3) was not reached even for the longest chains and poorest solvents simulated here. The mere appearance of a core required substantial chain lengths (higher than 1000; molecular weights of a few hundred thousands), while short chains underwent a gradual densification devoid of any qualitative changes in the density distribution. Sufficiently long chains became more but not quite spherical and underwent a reasonably sharp second order phase transition. The findings were generally in agreement with predictions of mean-field theory and with the use of the standard scaling variables, despite slight inconsistencies. Nevertheless, the results stress the fact that short chains never form a constant density core and that core-dominance on the globule's properties (“volume approximation”) is only valid for extraordinarily long chains [molecular weight of O(10⁹)], an effect linked to the relatively diffuse nature of the surface layer and originating from chain connectivity in conjunction with spherical geometry. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3651–3666, 2006     

Dynamic Elasticity of Cubic Diamond

Previously, the structure of the carbon allotrope glitter has been disclosed, and a theory accompanying the structural report as to its bulk modulus at pressure predicted it would be among the hardest materials possible. The dynamic elasticity theory developed in that paper, involving the forces generated in elastic chemical bond deformations resulting from applied mechanical forces, is here applied to the cubic diamond lattice. Stresses, both lateral and axial, contribute to the bulk modulus of cubic diamond at pressure. The ultimate strength of the cubic diamond lattice, in the approximations of the dynamic elasticity theory presented in this paper, is estimated to be in excess of 1 TPa, at modest bond length deformations of about 0.1 ?, and when including the zero pressure bulk modulus B ₀ in the computation. In particular, the dynamic elasticity model predicts the hardest direction of cubic diamond will be for an isotropic mechanical force applied along 〈111〉 directions of the structural unit cell.     

Boron-Made N2: Realization of a B≡B Triple Bond in the B2Al3− Cluster

Until now, all B≡B triple bonds have been achieved by adopting two ligands in the L→B≡B←L manner. Herein, we report an alternative route of designing the B≡B bonds based on the assumption that by acquiring two extra electrons, an element with the atomic number Z can have properties similar to those of the element with the atomic number Z+2. Specifically, we show that due to the electron donation from Al to B, the negatively charged B≡B kernel in the B₂Al₃⁻ cluster mimics a triple N≡N bond. Comprehensive computational searches reveal that the global minimum structure of B₂Al₃⁻ exhibits a direct B–B distance of 1.553 Å, and its calculated electron vertical detachment energies are in excellent agreement with the corresponding values of the experimental photoelectron spectrum. Chemical bonding analysis revealed one σ and two π bonds between the two B atoms, thus confirming a classical textbook B≡B triple bond, similar to that of N₂.