Universal behavior of flexible and wormlike polymers using relations derived from the blob theory and the statistical mechanical theory

The variation of the viscometric expansion factor of macromolecular chains, α_η, as a function of the number of blobs of which these chains consist, N/N_c, obeys a universal law, both for wormlike and for flexible polymers. Using also wormlike and flexible polymers, we show that the factor relating the excluded volume parameter, z, to the static expansion factor, α_G, varies with the number of statistical chain segments, in a universal manner. The universalities appear to be valid below chain lengths required for the appearance of a power law, and they do not seem to have an upper limit in molecular weight. For these two universalities concerning flexible and wormlike polymers we use relations derived from the blob theory [Polymer 20 (1979) 1083] and statistical mechanical theory [J. Chem. Phys. 57 (1972) 2843].     

Brownian dynamics simulations with stiff finitely extensible nonlinear elastic-Fraenkel springs as approximations to rods in bead-rod models

A very stiff finitely extensible nonlinear elastic (FENE)-Fraenkel spring is proposed to replace the rigid rod in the bead-rod model. This allows the adoption of a fast predictor-corrector method so that large time steps can be taken in Brownian dynamics (BD) simulations without over- or understretching the stiff springs. In contrast to the simple bead-rod model, BD simulations with beads and FENE-Fraenkel (FF) springs yield a random-walk configuration at equilibrium. We compare the simulation results of the free-draining bead-FF-spring model with those for the bead-rod model in relaxation, start-up of uniaxial extensional, and simple shear flows, and find that both methods generate nearly identical results. The computational cost per time step for a free-draining BD simulation with the proposed bead-FF-spring model is about twice as high as the traditional bead-rod model with the midpoint algorithm of Liu [J. Chem. Phys. 90, 5826 (1989)]. Nevertheless, computations with the bead-FF-spring model are as efficient as those with the bead-rod model in extensional flow because the former allows larger time steps. Moreover, the Brownian contribution to the stress for the bead-FF-spring model is isotropic and therefore simplifies the calculation of the polymer stresses. In addition, hydrodynamic interaction can more easily be incorporated into the bead-FF-spring model than into the bead-rod model since the metric force arising from the non-Cartesian coordinates used in bead-rod simulations is absent from bead-spring simulations. Finally, with our newly developed bead-FF-spring model, existing computer codes for the bead-spring models can trivially be converted to ones for effective bead-rod simulations merely by replacing the usual FENE or Cohen spring law with a FENE-Fraenkel law, and this convertibility provides a very convenient way to perform multiscale BD simulations.     

Monte Carlo simulation of micelle formation in block copolymer solutions

Short block copolymers in selective solvents (bad for A-block, good for B-block) are modeled by flexible bead-spring chains, where beads interact with short range Morse potentials of variable strength. It is shown that already very short chains (N_A = N_B = 2) exhibit a rather well-defined critical micelle concentration (cmc). The mass distribution of the micelles and their gyration tensor components as well as their internal structure are studied. It is shown that the relaxation time increases exponentially with the strength E_AA of the attractive energy between the A-monomers, and thus frozen-in micelles of medium size are obtained when E_AA is chosen too large. Our results are compared to studies of related but somewhat different models.     

Numerical evaluation of second and third virial coefficients of some inert gases via classical cluster expansion

In this project we evaluate second virial coefficient of some inert gases via classical cluster expansion, assuming each atomic pair interaction is of Lennard-Jones type. We also try to numerically evaluate the third virial coefficient of Argon gas based on bipolar-coordinate integration (Mas et?al. in J Chem Phys 10:6694, 1999), assuming the same Lennard-Jones potential as before. The second virial coefficient (Vega et?al. in Phys Chem Chem Phys 4:3000–3007, 2002) calculated from our model are compatible to the experimental data [19] The temperature at which B ₂(T) → 0 is called the Boyle’s temperature T _B (Vega et?al. in Phys Chem Chem Phys 4:3000–3007, 2002) for the Lennard-Jines (12-6) potential. For the second virial coefficient of He, we obtain the Boyle’s temperature as follow: T _B ?=?34.9312438964844 (K) B ₂(T) = 9.82958 × 10^?6 (cm³/mol).     

Numerical calculations of the viscoelastic properties of solutions of branched polymers based on the Zimm-Kilb theory

Numerical calculations were performed for the viscoelastic properties of dilute solutions of branched star polymers with equal branch lengths as formulated in terms of a bead-spring model by Zimm and Kilb without using the integrodifferential equation approximation method to calculate the eigenvalues. The complex modulus and complex viscosity were calculated as functions of frequency for various combinations of the number of branches f (4, 8, and 13), the number of beads in one branch N_b (= N/f; 20 to 100, where N + 1 is the total number of beads, N the number of springs in the molecule) and the reduced hydrodynamic interaction parameter h^* (= h/N^1/2 0.05 to 0.3, where h is the hydrodynamic interaction parameter of Zimm and Kilb). The frequency dependence of the complex modulus in the low-frequency range depends mainly on h^* and not on N_b if N_b is large enough, and it is very close to that calculated from the eigenvalues for h→∞ obtained by Zimm and Kilb, if h^* is about 0.25. As h^* decreases from 0.25, the frequency dependence gradually approaches that of the free-draining cash (h→0). Calculations may be carried out for h^* values somewhat larger than 0.25 and result in a frequency dependence that is not intermediate to the h → 0 and h → ∞ cases as evaluated by Zimm and Kilb. The physical meaning of such “super-non-free-draining” values of h^* is uncertain, however. The intrinsic viscosity ratio g′ = [η]_f/[η]_lin is an increasing function of h^* and changes very slowly with N. For h^* = 0.25, g′ is close to the non-free-draining limit for any value of N.     

Mercury(II) cyanide complexes with alkyldiamines: solid-state/solution NMR,computational, and antimicrobial studies

Mercury cyanide complexes of alkyldiamines (1–6), [Hg(L)(CN)₂] (where L?=?en (1,2-diaminoethane), pn (1,3-diaminopropane), N-Me-en, N, N′-Me₂-en, N, N′-Et₂-en, and N, N′-ipr₂-en), have been synthesized and characterized by elemental analysis, IR, ¹³C, and ¹⁵N solution NMR in DMSO-d₆, as well as ¹³C, ¹⁵N, and ¹⁹⁹Hg solid-state NMR spectroscopy. Complexes 1 and 2 have been studied computationally, built and optimized by GAUSSIAN03 using DFT at B3LYP level with LanL2DZ basis set. Binding modes of en and bn (where bn?=?1,4-diaminobutane) toward Hg(CN)₂ are completely different. Complexes with en and pn show chelating binding to Hg(II), while bn behaves as a bridging ligand to form a polymeric structure, [Hg(CN)₂-bn]_∞ [B.A. Al-Maythalony, M. Fettouhi, M.I.M. Wazeer, A.A. Isab. Inorg. Chem. Commun., 12, 540 (2009).]. The solution ¹³C NMR of the complexes demonstrates a slight shift of the ?C≡N (0.9 to 2?ppm) and ?C–NH₂ (0.25 to 6?ppm) carbon resonances, while the other resonances are relatively unaffected. ¹⁵N labeling studies have shown involvement of alkyldiamine ligands in coordination to the metal. The principal components of the ¹³C, ¹⁵N, and ¹⁹⁹Hg shielding tensors have been determined from solid-state NMR data. Antimicrobial activity studies show that the complexes exhibit higher antibacterial activities toward various microorganisms than Hg(CN)₂.     

The influence of variant PE‐b‐PEO segments on physical properties of LLDPE graft copolymers

A method was adopted to fix a series of polymers of PE‐b‐PEO with different PEO/PE segments on the chains of LLDPE. Maleic anhydride (MA) reacting with hydroxyl group of PE‐b‐PEO (mPE‐b‐PEO) was used as the intermediate. The structures of intermediates and graft copolymers were approved by ¹H NMR and FTIR. XPS analysis revealed a great amount of oxygen on the surface of grafted copolymers although the end group of PEO was fixed on the LLDPE chains through MA. Thermal properties of the graft copolymers as determined by differential scanning calorimetry (DSC) showed that PE segments in the grafted monomers could promote the heterogeneous nucleation of the polymer, increase T_c, and crystal growth rate. While the amorphous PEO segments which attached to the crystalline PE segments in LLDPE, impaired their ability to fit the crystal lattice, and depressed the crystallization of LLDPE backbones. In this study, it was also verified through the dynamic rheological data that increasing M_n of grafted monomers significantly increased the complex viscosity and enhanced the shear‐thinning behavior. Long‐branched chains formed by grafted monomers enhanced the complex moduli (G′ and G″) value and retarded relaxation rate. However, there were little influence on the rheological properties when increasing the amounts of PEO segments (or decreasing PE segments) of grafted monomers with similar molecular weight. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 506–515, 2008     

Aggregation behavior of poly(γ‐benzyl‐L‐glutamate)‐b‐polyisoprene‐b‐poly(γ‐benzyl‐L‐glutamate) rod‐coil‐rod triblock copolymer in N,N‐dimethylformamide

Solution property of poly(γ‐benzyl‐L ‐glutamate)‐b‐polyisoprene‐b‐poly(γ‐benzyl‐L ‐glutamate) (GIG copolymer) was studied by using dynamic light scattering and static light scattering for N,N‐dimethylformamide (DMF) solution and DMF/toluene mixed solutions. GIG copolymer proved to aggregate in DMF and under DMF‐rich condition, that is, high‐polar region. The aggregate decreased in size, and completely disappeared under toluene‐rich condition, that is, low‐polar region. The correlation between solubility parameter and aggregate size of GIG copolymer in the DMF/toluene solution systems quantitatively demonstrated how strongly polarity caused by hydrogen bond made an impact on the aggregation behavior. Because the main driving force to the aggregation under DMF‐rich condition originates with polyisoprene (PIP) blocks, the aggregate in DMF is considered to be a core‐shell micelle consisting of flexible PIP core surrounded by rigid poly(γ‐benzyl‐L ‐glutamate) (PBLG) shell. The values of dimensionless parameter ρ, defined as the ratio of radius of gyration 〈S²〉^1/2 to hydrodynamic radius R_H, revealed that a single chain of GIG copolymer had the form of rigid rod with flexibility, that is, once‐broken rod, caused by the incorporation of a flexible PIP chain between two rigid PBLG rods in the DMF/toluene solution system. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1740–1748, 2010     

Aggregation behavior of polystyrene‐b‐poly(ethylene/butylene)‐b‐polystyrene triblock copolymer in N‐methylpyrrolidone

Solution property of hydrogenated polystyrene‐b‐poly(ethylene/butylene)‐b‐polystyrene triblock copolymer (SEBS copolymer) was studied by using static light scattering and dynamic light scattering for cyclohexane and N‐methylpyrrolidone (NMP) solutions. From the values of dimensionless parameters ρ, defined as the ratio of radius of gyration 〈S²〉^1/2 to hydrodynamic radius R_H, and solubility parameters, SEBS copolymer proved to exist as single chain close to random coil in nonpolar cyclohexane, whereas aggregate into the core‐shell micelle consisting of poly(ethylene/butylene) (PEB) core surrounded by PS shell in polar NMP. The core‐shell micelle formed in NMP is composed of 65 polymer chains, having three times larger average chain density (d = 0.12 g cm^?3) than a single polymer chain (d = 0.04 g cm^?3) in cyclohexane. The comparison with the aggregation behaviors in other solvents demonstrated that the aggregate compactness of the copolymer depended largely on solvent polarity, resulting in formation of the highly dense PEB core (R_c = 4.5 nm) and the thick PS shell (ΔR = 22.9 nm) in high‐polar NMP. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 588–594, 2010     

Colloidal dynamics: influence of diffusion, inertia and colloidal forces on cluster formation

Computer simulations of colloidal suspensions are discussed. The simulations are based on the Langevin equations, pairwise interaction between colloidal particles and take into account Brownian, hydrodynamic and colloidal forces. Comparison of two models, one taking into account inertial term in Langevin equation and another based on diffusional approximation proposed in [D.L. Ermak, J.A. McCammon, J. Chem. Phys. 69 (1978) 1352], has shown that both models enable the prediction of the correct values of the diffusion coefficient and residence time of particle in a doublet and are therefore suitable to study the dynamics of formation and breakage of clusters in colloidal suspensions. It is shown that the appropriate selection of the time step and taking into account inertia of particles provides also the correct value of the average kinetic energy of each particle during the simulations, what allows to use the model based on full Langevin equations as a reference model to verify the validity of the numerical scheme for simulation using diffusion approximation.     

Computer-aided simulation of the influence of collective effects on polymer-melt dynamics in a straight cylindrical tube: Observation of the onset stage of the corset effect

The results of the computer-aided simulation of the dynamics of a polymer melt consisting of Fraenkel chains in straight cylindrical tubes and in bulk are discussed. Two different models are studied. In the first model, the dynamics of the polymer melt is simulated via the molecular dynamics simulation. The interaction of unbound polymer segments is described by the Lennard-Jones potential, which excludes any chain crossing of macromolecules and generates collective acoustic waves. In the second model, which serves as a reference, the system is studied via the Brownian dynamics method, in which intermolecular interactions are allowed for phenomenologically via friction and stochastic Langevin forces. In this case, cooperative effects are absent and the effect of spatial confinements makes itself evident only in a narrow near-wall layer. For the two models under consideration, there is a significant difference in the decay of dynamic correlation functions C _????(t) = ??b _??(t)b _??(t)b _??(0)b _??(0)????b _?? ² b _?? ² ??^?1, where averaging is performed over all macromolecular segments and b _?? (t) is the component of the end-to-end-segment vector (?? ?? ?? = x,y, and the cylindrical axis of the tube is directed along the z axis). For the first model allowing for collective effects, the dynamics of decay of C _???? (t)functions is much slower than that for the melt in bulk, and for the second model, in which the presence of the tube leads only to spatial confinements for the polymer segments in the direct vicinity of walls. This difference indicates the fundamental significance of the collective effects in the dynamics of polymer melts confined in porous media. This phenomenon is the first computer-simulated evidence of the onset stage of the so-called corset effect, which was first observed experimentally with the use of NMR relaxometry.     

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.     

Rare configuration of tautomeric benzimidazolecarboxylate ligands in cadmium(II) and copper(II) coordination polymers

Two Cd(HBimc)-based isomers, [Cd(HBimc^N)(HBimc^T)(H₂O)]·3.5H₂O·EtOH (1a·3.5H₂O·EtOH, H₂Bimc=1H-benzimidazole-5-carboxylic acid) and [Cd(HBimc^N)(HBimc^T)(H₂O)] (1b), and two Cu(HMBimc)-based coordination polymers, [Cu(HMBimc^N)₂(H₂O)]·1/2H₂O (2·1/2H₂O, H₂MBimc=2-methyl-1H-benzimidazole-5-carboxylic acid) and [Cu(HMBimc^T)₂]·2THF·H₂O (3·2THF·H₂O), were self-assembled from Cd(ClO₄)₂·6H₂O/H₂Bimc and Cu(ClO₄)₂·6H₂O/H₂MBimc systems, respectively. Compound 1a adopts a ladder-like chain structure, comprised of a hydrogen-bond-stabilized Cd₂(HBimc^N)₂-metallocyclic stair and a 1D straight -(Cd-HBimc^T)_n- edge, whereas compound 1b exhibits a 2D (4,4)-rhombus layered structure, intercrossed by 1D -(Cd-HBimc^N)_n- chains and -(Cd-HBimc^T)_n- chains. Compound 2 shows a 1D double-stranded wave-like chain from two single-stranded wave-like -(Cu-HMBimc^N)_n- chains and compound 3 adopts a 2D (4,4)-topological layer structure, intercrossed by subunits of 1D -(Cu-HMBimc^T)_n- chains. Interestingly, a pair of tautomeric HBimc building blocks—normal (N or HBimc^N) and tautomer (T or HBimc^T)—is simultaneously included in the structures of 1a and 1b, whilst the N- and T-configured HMBimc building blocks are present as separate entities in Cu species, 2 and 3, respectively. The existence of only a tautomer (T) mode of the benzimidazolecarboxylate-based ligand in a Cu(II) network is observed for the first time.     

Three component tandem reactions involving protected 2-amino indoles, disubstituted propargyl alcohols, and I2/ICl: iodo-reactant controlled synthesis of dihydro-α-carbolines and α-carbolines via iodo-cyclization/iodo-cycloelimination

Two simple, highly efficient three component tandem reactions for the synthesis of diversified N^aN^b di-carbamate-4,9-dihydro-3-iodo-α-carbolines and N^a-carbamate-3-iodo-α-carbolines have been described. The strategy involves one-pot condensation of bis-carbamate protected 2-amino indoles with disubstituted propargyl alcohols and I₂/ICl. The salient feature of the reaction involves iodocyclo-elimination of N^b-linked carbamate under mild condition in the final step.     

Surface diffusion and relaxation of partially adsorbed polymers

We studied by lattice simulation the surface diffusion and relaxation of isolated, self‐avoiding polymers partially adsorbed onto a flat surface. The key parameters describing the system are the number of segments in the chain, N, the adsorption energy of a segment, expressed as a dimensionless surface temperature T_s, and the segmental friction factor on the surface relative to that in the bulk, ζ_s/ζ_b. The simulation data indicate Rouse scaling of the surface diffusion coefficient, D_∥, and in‐plane relaxation time, τ, versus N for all values of T_s and ζ_s/ζ_b studied. A simple application of the Rouse model to a partially adsorbed chain, which ignores fluctuations in adsorbed trains, yields a formula for D_∥ with the correct N‐scaling. It can account for the effects of T_s when ζ_s/ζ_b is finite (≲10), but it fails when ζ_s/ζ_b diverges, predicting no surface diffusion at all, whereas simulations indicate finite surface mobilities facilitated by a caterpillar‐like motion. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1146–1154, 2000     

Synthesis and structure of [C3N2H5][Cu(H2PO4)2Cl]·H2O with a chain structure: the first example of an organically templated copper (II) phosphate

A new one-dimensional copper (II) phosphate, [C₃N₂H₅][Cu(H₂PO₄)₂Cl]·H₂O, I, with pseudo-10-membered channels along the b-axis formed by the hydrogen bonded chains, containing imidazolium ions has been synthesized and characterized by single-crystal X-ray diffraction. The compound being the first example of an organically templated copper (II) phosphate, crystallizes in the monoclinic space group P2₁/n (No. 14) with a=8.9998(14) Å, b=7.0189(11) Å, c=18.986(3) Å; β=102.964(3)°; V=1168.8(3) ų; Z=4. The copper chlorophosphate chains in I are topologically similar to those observed in fornacite and vauquelinite.     

Stereospecific sequential block copolymerizations of styrene and 1,3‐butadiene with a C5Me5TiMe3/B(C6F5)3/Al(oct)3 catalyst

This article reports a new methodology for preparing highly stereoregular styrene (ST)/1,3‐butadiene (BD) block copolymers, composed of syndiotactic polystyrene (syn‐PS) segments chemically bonded with cis‐polybutadiene (cis‐PB) segments, through a stereospecific sequential block copolymerization of ST with BD in the presence of a C₅Me₅TiMe₃/B(C₆F₅)₃/Al(oct)₃ catalyst. The first polymerization step, conducted in toluene at ?25 °C, was attributed to the syndiospecific living polymerization of ST. The second step, conducted at ?40 °C, was attributed to the cis‐specific living polymerization of BD. The livingness of the whole polymerization system was confirmed through a linear increase in the weight‐average molecular weights of the copolymers versus the polymer yields in both steps, whereas the molar mass distributions remained constant. The profound cross reactivity of the styrenic‐end‐group active species with BD toward ST led to the production of syn‐PS‐b‐cis‐PB copolymers with extremely high block efficiencies. Because of the presence of crystallizable syn‐PS segments, this copolymer exhibited high melting temperatures (up to 270 °C), which were remarkably different from those of the corresponding anionic ST–BD copolymers, for which no melting temperatures were observed. Scanning electron microscopy pictures of a binary syn‐PS/cis‐PB blend with or without the addition of the syn‐PS‐b‐cis‐PB copolymers proved that it could be used as an effective compatibilizer for noncompatibilized syn‐PS/cis‐PB binary blends. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1188–1195, 2005     

Synthesis,crystalline morphologies,self‐assembly,and properties of H‐shaped amphiphilic dually responsive terpolymers

Novel and well‐defined amphiphilic H‐shaped terpolymers poly(L‐lactide)‐block‐(poly(2‐(N,N‐dimethylamino)ethyl methacrylate) ‐block‐)poly(ε‐caprolactone)(‐block‐poly(2‐(N,N‐dimethylamino)ethyl methacrylate)) ‐b‐poly(L‐lactide) (PLLA‐b‐(PDMAEMA‐b‐)PCL(‐b‐PDMAEMA)‐b‐PLLA) were synthesized by the combination of ring‐opening polymerization, atom transfer radical polymerization, and click chemistry. The H‐shaped amphiphilic terpolymers can self‐assemble into spherical nano‐micelles in water. Because of the dually responsive (temperature and pH) properties of PDMAEMA segments, the hydrodynamic radius of the micelles of the H‐shaped terpolymer solution can be adjusted by altering the environmental temperature or pH values. The thermal properties investigation and the crystalline morphology analysis indicate that the branched structure of the H‐shaped terpolymers and the presence of amorphous PDMAEMA segments together led to the obvious decrease of PCL segments and the complete destruction of crystallinity of the PLLA segments in the H‐shaped terpolymers. In addition, the H‐shaped terpolymer film has better hydrophilicity than linear PCL or triblock polymer of PLLA‐b‐(N₃? )PCL(? N₃)‐b‐PLLA, due to the decrease or destruction of the crystallizability of the PCL or PLLA in the H‐shaped terpolymer and the presence of hydrophilic PDMAEMA segments. These unique H‐shaped amphiphilic terpolymers composed of biodegradable and biocompatible PCL and PLLA components and intelligent and biocompatible PDMAEMA component will have the potential applications in biomedical fields. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Synthesis of protected derivatives and short peptides of antAib, a novel C-tetrasubstituted α-amino acid of the Ac5c type possessing a fused anthracene fluorophore

The N^α-Boc and N^α-Fmoc protected derivatives of 2-amino-2,3-dihydro-1H-cyclopenta[b]anthracene-2-carboxylic acid (antAib), a novel fluorescent, achiral, α-amino acid, rigid analogue of the known 9-antAla and 2-antAla residues, and belonging to the class of C_i^α→C_i^α cyclized, C^α,α-disubstituted glycines (strong β-turn and helix inducers in peptides), were synthesized in seven steps from 1,2,4-trimethylbenzene. The UV absorption and fluorescence properties of Boc-antAib-OEt and Boc-antAib-OH are also described. Solution syntheses of the short peptides Boc-antAib-l-Ala-OMe, Fmoc-l-Ala-antAib-l-Ala-OMe, as well as Boc-Aib-antAib-l-Ala-OMe and the side product 2,5-dioxopiperazine cyclo-[antAib-l-Ala], are presented as examples of the coupling ability at both C- and N-termini of the antAib residue.     

A reply to “magic numbers in Cn+ and Cn− abundance distribution” based on experimental observations

The C_n⁻ abundance distributions for laser vaporization into a pulsed He stream reported by Hahn et al. (Chem. Phys. Letters 130 (1986) 12) in which C₆₀⁻ was not special are here contradicted by observation of a C_n⁻ distribution by laser vaporization where C₆₀⁻ is prominent.