Intramolecular relaxation dynamics in semiflexible dendrimers

The intramolecular relaxation dynamics of semiflexible dendrimers in dilute solutions are theoretically investigated in the framework of optimized Rouse-Zimm formalism. Semiflexibility is implemented by modeling topological restrictions on the bond directions and orientations of the respective bond-vectors. Based on our recently developed approach for semiflexible dendrimers [A. Kumar and P. Biswas, Macromolecules 43, 7378 (2010)], the mechanical and dielectric relaxation moduli are studied as functions of local flexibility parameters and branching topology. It is rather interesting to observe that semiflexibility affects the local modes of G'(ω) and Δε'(ω), which have lower relaxation rate with increasing bond restrictions, while the collective modes with small relaxation rate remain almost constant. The relaxation dynamics of the flexible dendrimer is similar to that of the semiflexible dendrimer with unrestricted bond orientations (Φ = 0) and is flanked by the compressed (Φ = 30°) and expanded (Φ = 150°) conformations, respectively. The effect of semiflexibility is typically reflected in the intermediate frequency regime. The expanded conformations of semiflexible dendrimers display a power-law behavior in the intermediate frequency regime for both loss and storage modulus resembling fractal structures, while the compressed and unrestricted bond orientation conformations exhibit an approximately logarithmic dependence. The power-law exponent is found to be similar to the flexible dendrimers with excluded volume interactions. Thus, by tuning Φ, a spectrum of dynamic relaxation pattern is obtained spanning a broad range of conformations from a power-law fractal network to a non-fractal one. In certain limits, this highly generalized model captures the characteristics of flexible dendrimers and also resembles La Ferla's model semiflexible dendrimers. The influence of hydrodynamic interactions reduces the dynamical range and the width of the intermediate domain by decreasing the smaller relaxation rates and increasing the higher relaxation rates correspondingly.     

Relaxation of Copolymeric Dendrimers Built from Alternating Monomers

Summary: In this study we extend our previous work concerning the Rouse dynamics of linear alternating copolymers (Macromolecules 2003 , 36, 486) to tree‐like structures and focus on copolymeric dendrimers built from monomers of two kinds A and B; as before, we let the monomers differ in their interaction with the solvent. In the framework of generalized Gaussian structures (GGS), we consider alternating arrangements of monomers over the dendritic structures. We develop a semi‐analytical method to determine for such structures (of arbitrary functionality, f, and number of generations, g), the eigenfrequencies (relaxation times). The method allows us to compute readily the storage, [G′(ω)] and the loss, [G″(ω)] moduli. These quantities show a multitude of features which mainly depend on the difference in the mobilities, or, equivalently, in the friction coefficients ζ_A and ζ_B of the A‐ and B‐beads. These features range from the presence of large plateau‐type regions in [G′(ω)] to the appearance of double‐peaks in [G″(ω)]. In contrast to linear alternating copolymers, the behavior of the dynamic moduli of copolymeric systems with dendritic topology can shed light into their composition, i.e. into the relative numbers of A‐ and B‐beads. We discuss these aspects in view of their experimental relevance.

A system under study: a dendrimer of third generation (g = 3) with functionality f = 3, composed of alternating beads.     

Self-assembly of dendritic tris(crown ether) hexagons and their complexation with dibenzylammonium cations

The construction of a new series of dendritic tris(crown ether) hexagons via coordination-driven self-assembly is described. Combining 120° crown ether-containing diplatinum(II) acceptors with 120° dendritic dipyridyl donors in a 1:1 ratio allows for the formation of a new family of dendritic triple crown ether derivatives with a hexagonal cavity in quantitative yields. The number and the position of these pendant groups can be precisely controlled on the hexagonal metallacycle. The structures of all dendritic multiple crown ether hexgaons are confirmed by multinuclear NMR ((1)H and (31)P), ESI-MS and ESI-TOF-MS, and elemental analysis. The complexation of these dendritic trivalent receptors with dibenzylammonium cations was investigated by (1)H NMR titration experiments. The thermodynamic binding constants between the receptors and guests were established by using the nonlinear least-squares fit method based on (1)H NMR titration experiments. It was found that the association constants of each assembly decrease correspondingly upon the increase of the generation of the dendrons from [G0] to [G3], which might be caused by the steric effect of the dendrons on host-guest complexation.     

Semiflexible polymers in a random environment

We present using simple scaling arguments and one step replica symmetry breaking a theory for the localization of semiflexible polymers in a quenched random environment. In contrast to completely flexible polymers, localization of semiflexible polymers depends not only on the details of the disorder but also on the ease with which polymers can bend. The interplay of these two effects can lead to the delocalization of a localized polymer with an increase in either the disorder density or the stiffness. Our theory provides a general criterion for the delocalization of polymers with varying degrees of flexibility and allows us to propose a phase diagram for the highly folded (localized) states of semiflexible polymers as a function of the disorder strength and chain rigidity.     

Synthesis and 1H NMR studies of paramagnetic nickel(II) complexes containing bis(pyrazolyl)methane ligands with dendritic substituents

The substituted bis(pyrazolyl)methane ligands RCH(3,5-Me2pz)2(R=SiMe3, CH2Ph, G1, G2, and G3; Gn=Fréchet-type dendritic wedges of generation n) have been prepared starting from H2C(3,5-Me2pz)2. Reaction of these didentate ligands with [NiBr2(DME)] is a straightforward procedure that allows the synthesis of the nickel(II) complexes [NiBr2{RCH(3,5-Me2pz)2}]. The molecular structure of compound (R=CH2Ph) has been determined by X-ray diffraction studies. The nickel centre coordinates two bromine and two nitrogen atoms in a tetrahedral environment, and the metallacycle Ni(NN)2C adopts a boat conformation with the benzyl group in an axial position. 1H NMR studies have been carried out to characterize these paramagnetic nickel compounds in solution. Valuable information about the disposition of the ligands and dendritic wedges in solution has been obtained thanks to the influence of the paramagnetic centre on the proton resonances.     

Theoretical analysis and computer simulation of fluorescence lifetime measurements. I. Kinetic regimes and experimental time scales

The configuration-controlled regime and the diffusion-controlled regime of conformation-modulated fluorescence emission are systematically studied for Markovian and non-Markovian dynamics of the reaction coordinate. A path integral simulation is used to model fluorescence quenching processes on a semiflexible chain. First-order inhomogeneous cumulant expansion in the configuration-controlled regime defines a lower bound for the survival probability, while the Wilemski-Fixman approximation in the diffusion-controlled regime defines an upper bound. Inclusion of the experimental time window of the fluorescence measurement adds another dimension to the two kinetic regimes and provides a unified perspective for theoretical analysis and experimental investigation. We derive a rigorous generalization of the Wilemski-Fixman approximation [G. Wilemski and M. Fixman, J. Chem. Phys. 60, 866 (1974)] and recover the 1/D expansion of the average lifetime derived by Weiss [G. H. Weiss, J. Chem. Phys. 80, 2880 (1984)].     

The Effect of Incorporating Fréchet Dendrons into Rotaxanes and Molecular Shuttles Containing the 1,2‐Bis(pyridinium)ethane⊂[24]Crown‐8 Templating Motif

Fréchet‐type dendrons (G0–G3) were added as both axle stoppering units and cyclic wheel appendages in a series of [2]rotaxanes, [3]rotaxanes, and molecular shuttles that employ 1,2‐bis(pyridinium)ethane axles and 24‐membered crown ethers wheels. The addition of dendrimer wedges as stoppering units dramatically increased the solubility of simple [2]rotaxanes in nonpolar solvents. The X‐ray structure of a G1‐stoppered [2]rotaxane shows how the dendritic units affect the structure of the interlocked components. Increased solubility allows observation of how the interaction of dendritic units on separate components in interlocked molecules influences switching properties and molecular size. In a series of [2]rotaxane molecular shuttles incorporating two recognition sites, it was demonstrated that an increase in generation on either the stoppering unit or cyclic wheel could influence both the rate of shuttling and the site preference of the wheel on the axle.     

Facile synthesis of dumbbell‐shaped dendritic‐linear‐dendritic triblock copolymer via reversible addition‐fragmentation chain transfer polymerization

We report the first instance of facile synthesis of dumbbell‐shaped dendritic‐linear‐dendritic triblock copolymer, [G‐3]‐PNIPAM‐[G‐3], consisting of third generation poly(benzyl ether) monodendrons ([G‐3]) and linear poly(N‐isopropylacrylamide) (PNIPAM), via reversible addition‐fragmentation chain transfer (RAFT) polymerization. The key step was the preparation of novel [G‐3]‐based RAFT agent, [G‐3]‐CH₂SCSSCH₂‐[G‐3] (1), from third‐generation dendritic poly(benzyl ether) bromide, [G‐3]‐CH₂Br. Due to the bulky nature of [G‐3]‐CH₂Br, its transformation into trithiocarbonate 1 cannot go to completion, a mixture containing ～80 mol % of 1 and 20 mol % [G‐3]‐CH₂Br was obtained. Dumbbell‐shaped [G‐3]‐PNIPAM₃₁₀‐[G‐3] triblock copolymer was then successfully obtained by the RAFT polymerization of N‐isopropylacylamide (NIPAM) using 1 as the mediating agent, and trace amount of unreacted [G‐3]‐CH₂Br was conveniently removed during purification by precipitating the polymer into diethyl ether. The dendritic‐linear‐dendritic triblock structure was further confirmed by aminolysis, and fully characterized by gel permeation chromatography (GPC) and ¹H‐NMR. The amphiphilic dumbbell‐shaped triblock copolymer contains a thermoresponsive PNIPAM middle block, in aqueous solution it self‐assembles into spherical nanoparticles with the core consisting of hydrophobic [G‐3] dendritic block and stabilized by the PNIPAM central block, forming loops surrounding the insoluble core. The micellar properties of [G‐3]‐PNIPAM₃₁₀‐[G‐3] were then fully characterized. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1432–1445, 2007     

Assignment of the liposidomycin diazepanone stereochemistry

The liposidomycins comprise a family of complex nucleoside antibiotics that inhibit bacterial peptidoglycan synthesis. Their structures (1, 2) feature nucleoside, ribofuranoside, diazepanone, and lipid regions. Several stereogenic centers remain unassigned, including three within the diazepanone region: C-6', C-2'", and C-3'". An intramolecular reductive amination reaction has been used to prepare model diazepanones. Analysis of 40 and two of its diastereomers by NMR spectroscopy, X-ray crystallography, and molecular modeling indicates a close relative configurational and conformational match between 40 and the liposidomycin diazepanone degradation product 43 and allows the assignment of stereochemistry of the natural products as either [C-6'(R), C-2'"(R), C-3'"(R)] or [C-6'(S), C-2'"(S), C-3'"(S)].     

Diffusion and segmental dynamics of rodlike molecules by fluorescence correlation spectroscopy

The dynamics of weakly bending polymers is analyzed on the basis of a Gaussian semiflexible chain model and the fluorescence correlation spectroscopy (FCS) correlation function is determined. Particular attention is paid to the influence of the rotational motion on the decay of the FCS correlation function. An analytical expression for the correlation function is derived, from which the averaged segmental mean square displacement can be determined independent of any specific model for the polymer dynamics. The theoretical analysis exhibits a strong dependence of the correlation function on the rotational motion for semiflexible polymers with typical lengths and persistence lengths of actin filaments or fd viruses. Hence, FCS allows for a measurement of the rotational motion of such semiflexible polymers. The theoretical results agree well with experimental measurements on actin filaments and confirm the importance of large relaxation times.     

Contribution of Polymer‐Solvent Interactions to Dynamics of Linear Polymers in Dilute Solutions

In this work a theoretical approach to dynamics of linear vinyl polymers in dilute solutions of high viscosity solvents is presented. The calculations for the relaxation time spectra, polymer intrinsic viscosity [η (ω)], complex elastic modulus G*(ω), total intrinsic viscosity [η^T (ω)] and specific heat capacity C (ω) were carried out in the non‐free‐draining limits. The relaxation time spectrum calculated for dynamics of low frequency modes exhibits a Rouse‐like character. Its position and shape corresponds to the ultrasonic relaxation time spectrum observed in the system at 10⁶ Hz. On the other hand, the relaxation time spectrum associated with moderate frequency mode dynamics is narrower and typical for ultrasonic relaxation observed at 10⁷ Hz. The polymer intrinsic viscosity [η (ω)] and elastic modulus G*(ω) are shown to be represented by the model within a low‐frequency range. In turn, the specific heat capacity C (ω) is displayed as a representation of the model in the acoustic region mentioned above. In the high‐frequency range the dynamics is described by the total intrinsic viscosity [η^T (ω)] tending to a plateau where the value is equal to the sum of the single‐bead intrinsic viscosity [η_N] and effective solvent viscosity [η_eff].     

Catalytic Oxidation of Cyclohexene by Dendrimer-bond Metal Catalysts

Since Tomalia and Dovornic discussed the promising outlook of surface-functionalized dendrimer catalysts in 1994, [1] dendritic catalysts have been proposed to many kinds of catalysis.These well-defined macromolecular structures enable the construction of precisely controlled catalyst structures. The large number of the peripheral functionalities enhanced their activity in many processes. [2,3] We report herein a new method of using the dendritic catalysts in the oxidation of cyclohexene. The reactions give some interesting results.In short, the synthesis of the dendritic catalysts was initiated from the well-known PAMAM dendrimers by using their peripheral ammonia groups. The condensation reactions of these ammonia groups and salicyaldehyde (SA) offer the ligands PAMAMSA with different generation (G) numbers.dendrimer-bond PAMAMSA-Ni(Ⅱ) complexes.In the presence of the dendritic PAMAMSA-Ni(Ⅱ) catalysts, cyclohexene was fully oxidized under 1 atm of molecular oxygen at 70℃. All the oxidations give 7-oxabicyclo[4.1.0]heptane 1,2-cyclohexen-l-ol 2, 2-cyclohexen-1-one 3 and 7-oxabicyclo [4.1.0]heptan-2-one 4 as the major products. The results of the oxidation are shown in the table below (table 1):Table 1 Oxidation of cvclohexene bv PAMAMSA-Ni2+ catalysts** Reaction condition: cat. 2mg, cyclohexene 5mL, 1atm O2, 6hat 70℃.**Oxygen absorption (mL) per mol catalyst.It can be seen from table that the oxidations give a new product 7-oxabicyclo[4.1.0]heptan-2-one 4, which is the first reported product in this oxidation. Meanwhile, product 4possesses relatively high selectivity in the six oxidation processes. It will arise much more emphasison the optimizing of these reactions.     

The nucleophilicity N index in organic chemistry

The nucleophilicity N index (J. Org. Chem. 2008, 73, 4615), the inverse of the electrophilicity, 1/ω, and the recently proposed inverse of the electrodonating power, 1/ω?, (J. Org. Chem. 2010, 75, 4957) have been checked toward (i) a series of single 5-substituted indoles for which rate constants are available, (ii) a series of para-substituted phenols, and for (iii) a series of 2,5-disubstituted bicyclic[2.2.1]hepta-2,5-dienes which display concurrently electrophilic and nucleophilic behaviors. While all considered indices account well for the nucleophilic behavior of organic molecules having a single substitution, the nucleophilicity N index works better for more complex molecules. Unlike, the inverse of the electrophilicity, 1/ω, (R(2) = 0.71), and the inverse of the electrodonating power, 1/ω? (R(2) = 0.83), a very good correlation of the nucleophilicity N index of twelve 2-substituted-6-methoxy-bicyclic[2.2.1]hepta-2,5-dienes versus the activation energy associated with the nucleophilic attack on 1,1-dicyanoethylene is found (R(2) = 0.99). This comparative study allows to assert that the nucleophilicity N index is a measure of the nucleophilicity of complex organic molecules displaying concurrently electrophilic and nucleophilic behaviors.     

Electrophilic and oxidative chemistry of pyrene and its non-alternant isomers: theoretical (DFT, GIAO-NMR, NICS) study of protonation carbocations and oxidation dications from pyrene, azupyrene (dicyclopenta[ef,kl]heptalene) and dicyclohepta[ed,gh]pentalene

Mono- and diprotonated carbocations and the two-electron oxidation dications derived from parent pyrene and its nonalternant isomers "azupyrene"(dicyclopenta[ef,kl]heptalene)(DCPH) and dicyclohepta[ed,gh]pentalene (DCHP) were studied by DFT at the B3LYP/6-31G(d) level. The most likely site(s) for mono- and diprotonation were determined based on relative arenium ion energies and the structures of the energetically most favored carbocations were determined by geometry optimization. The NMR chemical shifts for the protonated mono- and dications and the oxidation dications were computed by GIAO-NMR at the B3LYP/6-31G(d)//B3LYP/6-31G(d) level and their charge delocalization paths were deduced based on magnitude of the computed [capital Delta][small delta](13)C values and the NPA-derived changes in charges. Relative aromaticity/antiaromaticity in various rings in the energetically favored mono- and dications was estimated via NICS and [capital Delta]NICS. Calculated NMR chemical shift data for and were compared with the available experimental NMR values. The available data on chemical and physical properties of DCPH and DCHP are extremely limited and biological activity data are non-existent. The present study provides the first glance into their carbocations and oxidation dications, while augmenting and reinforcing the previous stable ion data on the pyrenium cations.     

Electronic and optical properties of ZnSc2S4 and CdSc2S4 cubic spinels by the modified Becke–Johnson density functional

Structural, electronic and optical properties of the ZnSc₂S₄ and CdSc₂S₄ cubic spinels have been investigated by means of the full-potential (linearized) augmented plane wave plus local orbitals based on density functional theory. The exchange-correlation potential is treated by the GGA–PBEsol [J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, K. Burke, Phys. Rev. Lett. 100 (2008) 136406] and the recently proposed modified Becke–Johnson potential approximation (mBJ) [F. Tran, P. Blaha, Phys. Rev. Lett. 102 (2009) 226401], which successfully corrects the band-gap problem found with GGA for a wide range of materials. The obtained structural parameters are in good agreement with the available experimental data. This gives support for the predict properties for ZnSc₂S₄ and CdSc₂S₄. The band structures reveal that both compounds are semiconductor with a direct gap. The obtained gap values show that mBJ is superior for estimating band gap energy. We have calculated the electron and hole effective masses in different directions. The density of states has been analyzed. Based on our electronic structure obtained using the mBJ method we have calculated various optical properties, including the complex dielectric function ɛ(ω), complex index of refraction n(ω), reflectivity coefficient R(ω), absorption coefficient α(ω) and electron energy-loss function L(ω) as functions of the photon energy. We find that the values of zero-frequency limit ɛ₁(0) increase with decreasing the energy band gap in agreement with the Penn model. The origin of the peaks and structures in the optical spectra is determined in terms of the calculated energy band structures.     

Study of peptide dendrimers having a ferrocene core supported on mercaptoundecanoic acid

Hydrogen-bonding interactions between the carboxylic acid groups of mercaptoundecanoic acid (MUA) coated gold substrates and the ester surface of peptide dendrimers allows the formation of glutamic acid dendrimers films. Dendrimer films were prepared for generations 1-6 (G1-G6) and analyzed by spectroscopic and electrochemical techniques. Electrochemical studies using cyclic voltammetry and differential pulse voltammetry show that all films except those of G6 were electrochemically active. Lack of activity of G6 films is rationalized by the total encapsulation of the ferrocene redox probe by the dendritic sheath and lack of ion pairing, which prevents its oxidation.     

Core-shell structures in single flexible-semiflexible block copolymers: finding the free energy minimum for the folding transition

We investigate the folding transition of a single diblock copolymer consisting of a semiflexible and a flexible block. We obtain a Saturn-shaped core-shell conformation in the folded state, in which the flexible block forms a core and the semiflexible block wraps around it. We demonstrate two distinctive features of the core-shell structures: (i) The kinetics of the folding transition in the copolymer are significantly more efficient than those of a semiflexible homopolymer. (ii) The core-shell structure does not depend on the transition pathway.     

Thermodynamics of solutions of cyclic polymethylene ester oligomers in p‐dioxane and chloroform

Differential vapor pressures were measured for mixtures of two cyclic polymethylene ester oligomers in p‐dioxane and chloroform at 25, 30, 35, and 40 °C at five different concentrations ranging from 1 to 20 wt %. The Flory–Huggins interaction parameter (χ) as well as Leonard's interaction parameter (χ′) for flexible and semiflexible rings were calculated and compared to one another. A new method for the estimation of the number of segments of a cyclic polymer is proposed that allows Leonard's equations to be applied correctly to a particular cyclic compound. Consistent differences between χ and χ′ were observed for all studied mixtures, and the differences became smaller if the cyclic oligomers were considered semiflexible. Interestingly, the enthalpic parameter (κ) deduced from values of χ and χ′ did not differ within their uncertainties. This supports the prediction that mixing cyclic polymer compared to its linear counterpart is mainly due to a molecular configurational entropy difference and that this difference should become less pronounced as the cyclic compound becomes larger. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 443–455, 2000     

Maximum entropy principle applied to semiflexible ring polymers

Based on the success of the maximum entropy principle (MEP) in the study of semiflexible treelike polymers [M. Dolgushev and A. Blumen, J. Chem. Phys. 131, 044905 (2009)], it is of much interest to establish MEP's potential for general semiflexible polymers which contain loops. Here, we embark on this endeavor by considering discrete semiflexible polymer rings in a Rouse-type scheme. Now, for treelike polymers a beads-and-bonds (i.e., a discrete) picture is essential for an easy inclusion of branching points. Moreover, one may envisage (similar to our former work [M. Dolgushev and A. Blumen, J. Chem. Phys. 131, 044905 (2009)]) to impose for each angle between two bonds a distinct stiffness condition. Working in this way leads already for a polymer ring to a complicated problem. Hence, we follow a reduced variational approach as applied earlier to polymer chains, in which a single Lagrange multiplier is used for each set of identical conditions imposed on topologically equivalent bonds and bonds' orientations. In this way, we obtain for the discrete ring an analytically closed form which involves Chebyshev polynomials. This expression turns out to lead to a series of solutions: Apart from the regular solution, several other solutions appear. One may be tempted to discard the other solutions, since for them the potential energy matrix is not positive definite. A more careful analysis based on topological features suggests, however, that such solutions can be assigned to rings displaying knots. Monte Carlo simulations which take excluded volume interactions into account agree with our interpretation.