Hindered interdiffusion in asymmetric polymer-polymer junctions

We discuss theoretically the diffuse interface formed when a long (L) polymer is put into contact with shorter chains (S) of the same material (all chains being entangled). At time t shorter than the reptation time T_L of the long chains, the L chains behave like a gel swollen by the S chains. The “penetration factor” ψ (i.e. the volume fraction of S near the gel surface) is controled by a balance between the osmotic pressure of the swollen L chains, and the elastic tension ψ due to swelling. If t is larger than T_S (the reptation time of the short chains), ψ is of order N_e/N_S (where N_e is the number of monomers between entanglement points, and N_S is the degree of polymerisation of the short chains). On the other hand, if t < T_S, N_S must be replaced by the average number s (t) of monomers of an S chain which have entered the L region, and ψ ∼ N_e/ s (t) ∼t^−1/2. The width of the mixed region e(t) increases like s ^1/2(t) at T_S, and like (D_St)^1/2 (where D_S is the reptation diffusion constant of the S chains) at t>T_S.     

Hydrogen‐bonded sheets in benzylmethylammonium hydrogen maleate

In the title compound, C₈H₁₂N⁺·C₄H₃O₄⁻, there is a short and almost linear but asymmetric O—H...O hydrogen bond in the anion. The ions are linked into C₂²(6) chains by two short and nearly linear N—H...O hydrogen bonds and the chains are further weakly linked into sheets by a single C—H...O hydrogen bond.     

Gelation Studies on a Radical Chain Cross‐Linking Copolymerization Process: Comparison of the Critical Exponents Obtained by Dynamic Light Scattering and Rheology

Summary: The sol–gel transition of a radical chain cross‐linking copolymerization system [N‐vinylcaprolactam/2‐hydroxylethyl methacrylate/allyl methacrylate] has been studied using in situ time‐resolved dynamic light scattering (DLS) and in situ rheology. A critical dynamic behavior was observed near the sol–gel transition, which was characterized by the presence of a power‐law spectra over three decades in the time–intensity correlation function g₂(t) − 1 ∼ t^−μ and over two decades in the oscillatory shear experiment G′(ω) ∼ G″(ω) ∼ ωⁿ. A comparison of the obtained critical exponents μ ≈ 0.62 and n ≈ 0.75 was made. The theory predicts a relationship between these exponents, but up to now no experimental comparison has been done. The experimental results favor the percolation model, with a fractal dimension d_f of the gel clusters of 1.67.

Double‐logarithmic plot of time–intensity correlation functions g₂(t) − 1 versus the delay time t.     

A one‐dimensional copper(II) coordination polymer incorporating succinate and N,N‐diethylethylenediamine ligands: crystallographic analysis,vibrational and surface features,and DFT analysis

Transition metal atoms can be bridged by aliphatic dicarboxylate ligands to produce chains, layers and frameworks. The reaction of copper sulfate with succinic acid (H₂succ) and N ,N‐ diethylethylenediamine (deed) in basic solution produces the complex catena‐poly[[[(N ,N‐diethylethylenediamine‐κ²N ,N ′)copper(II)]‐μ‐succinato‐κ²O ¹:O ⁴] tetrahydrate], {[Cu(C₄H₄O₄)(C₆H₁₆N₂)]·4H₂O}_n or {[Cu(succ)(deed)]·4H₂O}_n . Each carboxylate group of the succinate ligand coordinates to a Cu^II atom in a monodentate fashion, giving rise to a square‐planar coordination environment. The succinate ligands bridge the Cu^II centres to form one‐dimensional polymeric chains. Hydrogen bonds between the ligands and water molecules link these chains into sheets that lie in the ab plane. Density functional theory (DFT) calculations were used to support the experimental data. From these calculations, a good linear correlation was observed between the experimental and theoretically predicted structural and spectroscopic parameters (R ² ∼ 0.97).     

A Novel Polymeric Lead(II)‐Azido Compound: Synthesis,Structural Characterization,and DFT Calculations of [Pb(dmp)(N3)2]n

A novel 1D Pb^II coordination polymer containing Pb₂‐(μ‐N₃)₂ unit [Pb(dmp)(N₃)₂]_n (dmp =  2,9‐dimethyl‐1,10‐phenanthroline) has been prepared and characterized. Single‐crystal X‐ray diffraction analyses show that the coordination number for Pb^II ions is six, PbN₆, with “stereochemically active” electron lone pairs and the coordination sphere being hemidirected. The single‐crystal X‐ray data show the chains interact with each other through the π–π stacking interactions, which create a 3D framework. The structure of title complex has been optimized by density functional theory. Structural parameters and IR spectra for the complex are in agreement with the crystal structure.     

Branched polymer via free radical polymerization of chain transfer monomer: A theoretical and experimental investigation

A simple mathematic model for the free radical polymerization of chain transfer monomers containing both polymerizable vinyl groups and telogen groups was proposed. The molecular architecture of the obtained polymer can be prognosticated according to the developed model, which was validated experimentally by homopolymerization of 4‐vinyl benzyl thiol (VBT) and its copolymerization with styrene. The chain transfer constant (C_T) of telogen group in a chain transfer monomer is considered to play an important role to determine the architecture of obtained polymer according to the proposed model, either in homopolymerization or copolymerization. A highly branched polymer will be formed when the C_T value is around unity, while a linear polymer with a certain extent of side chains will be obtained when the C_T value is much bigger or smaller than unity. The C_T of VBT was determined to be around 15 by using the developed model and ¹H NMR monitored experiments. The obtained poly(VBT) and its copolymers were substantiated to be mainly consisted of linear main chain with side branching chains, which is in agreement with the anticipation from the developed model. The glass transition temperature, number average molecular weight, and its distribution of those obtained polymer were primarily investigated. This model is hopefully to be used as a strategy to select appropriate chain transfer monomers for preparing hyperbranched polymers. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1449–1459, 2008     

The configurational free energy of a polymer chain

The configurational, or elastic, free energy A_el of a polymer chain is discussed in terms of the Fourier configurational approach. The importance of accounting for all degrees of freedom of the chain is shown in comparison with affine mean-field theories and with scaling theories of chain expansion and contraction. In case of strong contraction the chain does show neither affinity nor self-similarity, and we get A_el ∼ N^1/3, N being the number of chain bonds. Conversely, in case of good-solvent expansion we find A_el ∼ N. The same result holds in the vicinity of the Θ-temperature, where A_el is also proportional to [(T − Θ)/T]².     

On the Anion Distribution in Zr7O8N4

The effect of anion distribution on the stability of β‐zirconium oxide nitride Zr₇O₈N₄ (trigonal, ; a = 953.80(2) pm, c = 884.98(3) pm, Z=3) has been investigated quantum‐chemically. In agreement with experimental results for the structurally related β′‐type zirconium oxide nitride (Zr₇O₁₁N₂) nitride anions occupy sites in the central polyhedron of a Bevan cluster (A₇X₁₂ unit) in the most stable configurations. Other relevant structural ordering parameters are minimization of N^3?···N^3? contacts and of the number of quasi‐linear N–Zr–N bonds. The calculated electronic structure of β‐Zr₇O₈N₄ is in qualitative agreement with experimental observations.     

3‐[(E)‐(3‐tert‐Butyl‐1‐phenyl‐1H‐pyrazol‐5‐yl)iminomethyl]quinolin‐2(1H)‐one: chains built by π‐stacking of hydrogen‐bonded R22(8) dimers

In the title compound, C₂₃H₂₂N₄O, there is evidence for some bond fixation in the aryl component of the quinolinone unit. Pairs of molecules related by inversion are linked into R₂²(8) dimers by almost linear N—H...O hydrogen bonds, and dimers related by inversion are linked into chains by a single aromatic π–π stacking interaction.     

The one‐dimensional structure of Cu(dmen)2Pd(CN)4 (dmen is N,N‐di­methyl­ethyl­enedi­amine)

The title compound, catena‐poly­[[μ‐cyano‐1:2κ²C:N‐dicyano‐1κ²C‐bis(N,N‐di­methyl­ethyl­enedi­amine‐2κ²N,N′)­pallad­ium(II)­copper(II)]‐μ‐cyano‐1:2′κ²C:N], [CuPd(CN)₄(C₄H₁₂N₂)₂]_n, consists of infinite quasi‐linear chains with all metal positions on centers of symmetry. The paramagnetic [Cu(dmen)₂]²⁺ cations are linked by diamagnetic [Pd(CN)₄]²⁻ anions via bridging cyano groups, which occupy trans positions in both cation and anion, giving rise to 2,2‐TT‐type chains. The coordination polyhedron of the paramagnetic Cu atom is an octahedron exhibiting typical elongation due to the Jahn–Teller effect, with two longer Cu—N([triple‐bond]C) bonds in the axial positions [2.5528 (13) Å] and four shorter Cu—N_dmen bonds (dmen is N,N‐dimethylethylenediamine) in the equatorial plane [1.9926 (11) and 2.1149 (12) Å]. The Cu—N[triple‐bond]C angle is 138.03 (12)°. Neighboring chains form weak N—H⋯NC hydrogen bonds.     

On the lowest electronic states of the C2F radical

The adiabatic energy surfaces of the lowest three electronic states [²(²A′ and ²A′)] and ²Σ⁺[²A′] of the C₂F radical were investigated by the Hartree-Fock multiconfiguration self-consistent field (HF—MCSCF) ab initio method using a large set of atomic natural orbitals (ANO) and an extended configuration space, and the results were shown to be in agreement with the predictions of valence theory for this radical. The electronic ground state was found to have a bent equilibrium structure, hence contradicting the Walsh rule which predicts for the isoelectronic molecules a ² linear state. The three states were found to be nearly degenerate and the potential energy surfaces of the two lowest electronic states exhibit an avoided crossing at an energy ∼2000 cm⁻¹ above the ground-state minimum, lower than the highest vibrational fundamental. The strong adiabatic interaction which is responsible for the ordering of the electronic states and their equilibrium geometry involves not only the bending coordinate as normally found for Renner-Teller pairs of states, but also the C—C stretching coordinate, due to the near degeneracy of the ²Σ⁺ and the ² lowest electronic states at linear geometries. © 1996 John Wiley & Sons, Inc.     

Molecular Weight Development in Free‐Radical Polymerization with Polyfunctional Chain‐Transfer Agents, 1. Equal Reactivity Model

The analytic expression for the weight‐average molecular weight development in free‐radical polymerization that involves a polyfunctional chain‐transfer agent is proposed. Free‐radical polymerization is kinetically controlled; therefore, the probability of chain connection with a polyfunctional chain‐transfer agent as well as the primary chain‐length distribution changes during the course of polymerization. We consider the primary chains formed at different times as different types of chains, and the heterochain branching model is used to obtain the weight‐average chain length at a given conversion level in a matrix formula, described as P_w = W { D _w + ( I + T ) SP ( I – TSP )^–1 D_f }. Because the primary chains are formed consecutively, the number of chain types N is extrapolated to infinity, but such extrapolation can be conducted with the calculated values for only three different N values. The criterion for the onset of gelation is simply described as a point at which the largest eigenvalue of the product of matrixes, TSP reaches unity, i. e., det  ( I – TSP ) = 0. The present model can readily be extended for the star‐shaped polyfunctional initiators, and the relationships between the model parameters and kinetic rate expression for such reaction systems are also shown.     

Modeling the Synthesis of Butyl Methacrylate Macromonomer by Sequential ATRP‐CCTP

The atom transfer radical polymerization of butyl methacrylate mediated by Cu(I)Br/N,N,N′,N″,N″‐pentamethyldiethylenetriamine in anisole at 70 °C with the subsequent addition of bis(difluoroboryldiphenylglyoximato)cobalt(II) after 2 h is modeled using Predici software, to gain additional insight to the system used experimentally to produce macromonomer chains with narrow dispersity. The mechanistic model, using kinetic coefficients from the literature and activation and deactivation rate coefficients estimated from this work, provides a good representation of experimental results. The simulations demonstrate that the time (conversion) at which cobalt chain transfer agent is added to the system is critical to control the number‐average molar mass of the final product and also confirm that chains of higher length in the final product are more likely to be nonfunctionalized, in agreement with experimental observations. The model predicts the production of a significant fraction of macromonomer oligomers with lengths of 1–3 units, also consistent with experiments.     

Sonochemical Synthesis of a Novel Nanoscale Lead(II) Coordination Polymer: Synthesis,Crystal Structure,Thermal Properties,and DFT Calculations of [Pb(dmp)(μ‐N3)(μ‐NO3)]n with the Novel Pb2(μ‐N3)2(μ‐NO3)2 Unit

A new nanostructured coordination polymer of divalent lead with the ligand 2,9‐dimethyl‐1,10‐phenanthroline (dmp), [Pb(dmp)(μ‐N₃)(μ‐NO₃)]_n ( 1 ), was synthesized by sonochemical methods. The polymer was characterized by scanning electron microscopy, X‐ray powder diffraction, IR, ¹H NMR, and ¹³C NMR spectroscopy, and elemental analyses. Compound 1 was structurally characterized by single‐crystal X‐ray diffraction. The single‐crystal analysis shows that the coordination number of Pb^II ions is seven, (PbN₄O₃) has a “stereo‐chemically active” electron lone pair, and the coordination sphere is hemidirected. The chains interact with each other through π–π stacking interactions to create a 3D framework. The structure of the title complex was optimized by density functional calculations. The calculated structural parameters and the IR spectrum of the title complex are in agreement with the crystal structure.     

Bond length alternation in cyclic polyenes. VII. Valence bond theory approach

The problem of bond length alternation in linear extended ϕ-electron systems with conjugated double bonds is examined using the valence bond theory applied to a simple model of cyclic polyenes C_NH_N with N = 4v and N = 4v + 2 sites as described by the Pariser-Parr-Pople Hamiltonian. Overlap enhanced atomic orbitals are employed in order to achieve the optimal treatment with only two Kekulé structures. The predicted bond length alternation and its magnitude are in good agreement with earlier molecular orbital based calculations and with experiment. Special attention is given to the discussion of the origin of bond length alternation in long polyenic chains and to the role of the resonance energy leading to stabilization of undistorted, symmetric structures for small aromatic (N = 4v + 2) cycles. © 1996 John Wiley & Sons, Inc.     

Computer simulation of three‐arm star polymers

We show that Shaffer's version of the bond fluctuation model can be used to simulate three‐arm star polymers. We report a simulation study of both single stars and melts of star polymers with arm lengths up to 90 monomer units (approximately twice the entanglement crossover length for linear chains). Center‐of‐mass self‐diffusion of single stars is Rouse‐like (D ˜ N^–1). Due to a limited range of molecular weights we cannot distinguish between a power‐law and an exponential dependence of the star‐melt self‐diffusion coefficient on arm length.     

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.     

Three‐Dimensional Antiferromagnetic Order of Single‐Chain Magnets: A New Approach to Design Molecule‐Based Magnets

Two one‐dimensional compounds composed of a 1:1 ratio of Mn^III salen‐type complex and Ni^II oximato moiety with different counter anions, PF₆^? and BPh₄^?, were synthesized: [Mn(3,5‐Cl₂saltmen)Ni(pao)₂(phen)]PF₆ ( 1 ) and [Mn(5‐Clsaltmen)Ni(pao)₂(phen)]BPh₄ ( 2 ), where 3,5‐Cl₂saltmen^2?=N,N′‐(1,1,2,2‐tetramethylethylene)bis(3,5‐dichlorosalicylideneiminate); 5‐Clsaltmen^2?=N,N′‐(1,1,2,2‐tetramethylethylene)bis(5‐chlorosalicylideneiminate); pao^?=pyridine‐2‐aldoximate; and phen=1,10‐phenanthroline. Single‐crystal X‐ray diffraction study was carried out for both compounds. In 1 and 2 , the chain topology is very similar forming an alternating linear chain with a [‐Mn^III‐ON‐Ni^II‐NO‐] repeating motif (where ‐ON‐ is the oximate bridge). The use of a bulky counteranion, such as BPh₄^?, located between the chains in 2 rather than PF₆^? in 1 , successfully led to the magnetic isolation of the chains in 2 . This minimization of the interchain interactions allows the study of the intrinsic magnetic properties of the chains present in 1 and 2 . While 1 and 2 possess, as expected, very similar paramagnetic properties above 15 K, their ground state is antiferromagnetic below 9.4 K and paramagnetic down to 1.8 K, respectively. Nevertheless, both compounds exhibit a magnet‐type behavior at temperatures below 6 K. While for 2 , the observed magnetism is well explained by a Single‐Chain Magnet (SCM) behavior, the magnet properties for 1 are induced by the presence in the material of SCM building units that order antiferromagnetically. By controlling both intra‐ and interchain magnetic interactions in this new [Mn^IIINi^II] SCM system, a remarkable AF phase with a magnet‐type behavior has been stabilized in relation with the intrinsic SCM properties of the chains present in 1 . This result suggests that the simultaneous enhancement of both intrachain (J) and interchain (J′) magnetic interactions (with keeping J ? J′), independently of the presence of AF phase might be an efficient route to design high temperature SCM‐based magnets.     

Determination of chain stiffness and polydispersity from static light-scattering

Chain stiffness is often difficult to distinguish from molecular polydisperity. Both effects cause a downturn of the angular dependence at large q² (q = (4π/λ)sin θ/2) in a Zimm plot. A quick estimation of polydisperity becomes possible from a bending rod (BR) plot in which lim (c → 0) qRθ/Kc is plotted against q(〈S²〉_z)^1/2 = u. Flexible and semiflexible chains show a maximum whose position is shifted from u_max = 1.41 for monodisperse chains towards larger values as polydispersity is increased, while simultaneously, the maximum height is lowered. Stiff chains display a constant plateau at large q, its value is πM_L where M_L is the linear mass density. Using Koyama's theory, the number of Kuhn segments can be determined from the ratio of the maximum height to the plateau height, if the polydispersity index z = (M_w/M_n ? 1)^?1 is known. Thus, if the weight-average molecular weight M_w, is known, the contour length L_w, the number of Kuhn segments (N_k)_w, the Kuhn segment length l_k and the polydispersity of the stiff chains can be determined. The influence of excluded volume is shown to have no effect on this set of data. The reliability of this set can be cross-checked with the mean-square radius of gyration 〈s²〉_z which can be calculated from the Benoit-Doty equation for polydisperse chains. Rigid and slightly bending rods exhibit no maximum in the BR plot, and the effect of polydispersity can no longer be distinguished from a slight flexibility if only static scattering techniques are applied.