High molecular weight poly(ethylene‐2,5‐furanoate); critical aspects in synthesis and mechanical property determination

Furan‐2,5‐dicarboxylic acid (FDCA) is a widely advocated renewable substitute for terephthalic acid (TA). Preparation of high molecular weight FDCA based polyesters by an industrially common combination of melt polymerization and subsequent solid state post condensation is described. Ultimately, poly(ethylene 2,5‐furanoate) (PEF) with absolute M_n = 83,000 g mol^?1 is obtained, determined by triple detection Size Exclusion Chromatography. The bulk polymer properties of FDCA based polyesters, necessary to evaluate their industrial potential were determined the Young's modulus of PEF is determined to be 2450 ± 220 MPa and the maximum stress 35 ± 8 MPa. The influence of crystallinity on the mechanical properties as function of temperature was determined by dynamic mechanical thermal analysis. A detailed differential scanning calorimetry study on the crystallization behavior of high molecular weight PEF allowed to calculate the equilibrium melting temperature (T_m⁰) of 239.3 and 239.7 °C for the first and second melting peak, respectively. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4191–4199     

Ratios of average molecular weights and molecular weight distributions in polymers

If M_min and M_max are lower and upper bounds, respectively, to the molecular weights of different molecular weight species contained in a polymer, the weight-average to number-average molecular weight ratio M _w/M _n cannot exceed (1 + M_max/M_min)²/(4M_max/M_min). The ratio attains this maximum possible value if the masses of the two species with molecular weights M_min and M_max are equal and the masses of all the other species are negligibly small, corresponding to maximum spread in the molecular weight distribution within the specified bounds. Also for a given value of M _w/M _n = α, the M_max cannot be smaller than [2α ? 1 + 2α^1/2(α ? 1)^1/2]M_min. The minimum possible value of M_max/M_min consistent with α given is obtained in the case of maximum spread described above. If only one species is predominant, then both M _w/M _n and M_max/M_min approach unity, as is well known. Similar relations hold for the ratios of higher-order average molecular weights for which the role of the mass fractions is replaced by higher-order distribution functions.     

Thermal,viscoelastic, and mechanical properties of DCPD-containing polymers

The thermal, viscoelastic, and mechanical properties of cured dicyclopentadiene (DCPD)-containing polymers prepared from novel DCPD-modified unsaturated epoxypolyesters and styrene were evaluated. This was accomplished using thermogravimetric analysis, differential scanning calorimetry, dynamic mechanical analysis, three-point bending test, and Brinell’s hardness. The thermal, viscoelastic, and mechanical properties of DCPD-containing polymers were strongly dependent on chemical structure. The cross-linking density (υ _e) of obtained networks increased with increasing content of carbon–carbon double bonds in the poly(ester) structure. In addition, the introduction of DCPD rings into the poly(ester) structure increased the rigidity of the molecular backbone. It resulted in obtaining polymers which showed great improvement in mechanical properties including remarkably higher storage modulus ( E_{20 ^°\textC}^￠ E_{{20\,{}^{\circ}{\text{C}}}}^{'} ), flexural modulus at bending (E _mod), hardness, lower extension at maximum force (ε-F _max), as well as higher thermal stability. These good properties make these materials highly promising as potential candidates for structural applications.     

The role of magnesium in hydrolysis of triphosphates in water: Quantum mechanical/molecular mechanical modeling

The mechanism of hydrolysis of deprotonated methyl triphosphate (MTP) to methyl diphosphate (MDP) and inorganic phosphate (Pi) in water clusters in the presence and absence of magnesium cations has been modeled. Modeling has been performed by the effective fragment potential-based quantum mechanical/molecular mechanical method. The energies and energy derivatives in the quantum subsystem including MTP, reacting water molecules, and Mg²⁺ has been calculated at the density functional theory (B3LYP) level, whereas water-water interactions have been described by the TIP3P model potential. The minimum-energy path for the reaction MTP + H₂O → MDP + Pi is consistent with a two-stage dissociative process in the absence of Mg²⁺ and with a one-stage mechanism in the presence of Mg²⁺.     

Quantum mechanical approach to the chemisorption of molecular hydrogen on defect magnesium oxide surfaces

Quantum mechanical theoretical calculations have been performed on the linear atomic chain in order to simulate the interaction of molecular hydrogen with the defects present at the surface of activated MgO. The total energy of the system, the relative energy of the various molecular orbitals, and the electronic charge distribution have been computed for various lattice parameters (d _O-O = 4.0–4.8 Å) as a function of the H-H (or O-H) separation. A symmetrical motion of the hydrogen nuclei with respect to the central Mg²⁺ vacancy was assumed. It is shown that chemisorption of hydrogen on surface O^–ions sites results in the formation of pseudo-hydroxyl groups. For a small lattice parameter (4.0 Å), no stable state of molecular hydrogen has been found while an increase in the lattice parameter results in a uniform increase of the calculated activation energy for the molecular hydrogen activation process. A mechanism is proposed which is not so different from that put forward for the hydrogen activation by transition metal complexes. Molecular hydrogen is found to act as an electron donor.     

Preparation and characterization of graft terpolymers with controlled molecular structure

Segmented terpolymers, poly(alkyl methacrylate)‐g‐poly(D ‐lactide)/poly(dimethylsiloxane) (PLA/PDMS), were prepared with a combination of the “grafting through” technique (macromonomer method) and controlled/living radical polymerization (atom transfer radical polymerization or reversible addition–fragmentation transfer polymerization). Two synthetic pathways were used. The first was a single‐step approach in which a low‐molecular‐weight methacrylate monomer (methyl methacrylate or butyl methacrylate) was copolymerized with a PLA macromonomer and a PDMS macromonomer. The second strategy was a two‐step approach in which a graft copolymer containing one macromonomer was chain‐extended by a copolymerization of the second macromonomer and the low‐molecular‐weight methacrylate. The kinetics of both synthetic approaches were investigated, showing that the polymerizations exhibited a controlled/living behavior. Furthermore, the molecular structure of the terpolymers (composition, molecular weight distribution, and microstructure) was investigated by two‐dimensional liquid chromatography. Well‐defined terpolymers with controlled branch distribution, composition (F_w,PMMA/F_w,PLA/F_w,PDMS ～ 50/30/20) molecular weight (M_n ～ 50,000 g · mol^?1), and a narrow molecular weight distribution (M_w/M_n ～ 1.3) were prepared via both pathways. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1939–1952, 2004     

Molecular weight distribution and mechanical behavior of PBI fibers

Two different polybenzimidazole (PBI) samples have been investigated in order to correlate the differences in molecular weight distribution (MWD) with changes in the elastic modulus and strength of undrawn and drawn fibers. It has been found that within the weight-average molecular weight range (7,000 ≤ M_w ≤ 13,000) there was no obvious correlation with M_w and M_n. However, one sample had a narrow unimodal molecular weight distribution and the other a wide bimodal molecular weight distribution. The small percentage of high molecular weight present in the latter sample gave its fibers better mechanical properties. X-ray diffraction studies showed that the orientation in both drawn fiber samples was equal. This isolated the effects of the molecular weight distribution on mechanical properties.     

Solution properties of high molecular weight polystyrene

A series of polystyrenes with weight-average molecular weight M?_w up to 1.3 × 10⁷ was prepared by anionic polymerization in tetrahydrofuran (THF). Each sample was characterized by gel-permeation chromatography, light scattering, and viscometry. It was found that each sample had an almost symmetrical and very narrow molecular weight distribution (M?_w/M?_n < 1.07). The mean-square unperturbed radius of gyration 〈S²〉₀ was determined in trans-decalin at 20.4°C as 〈S²〉₀ = 7.8₆ × 10^?18M?_w (cm²). The particle scattering factor was well represented by the Debye equation irrespective of solvent in the range of M?_w < 4 × 10⁶, and only a small deviation was observed in benzene at higher molecular weights. The penetration function Ψ ≡ A₂M²/4π^3/2N_A〈S〉^23/2 was found to approach a relatively low asymptotic value of 0.21–0.23 at molecular weights above 2 × 10⁶ in benzene at 30°C, where A₂ is the second virial coefficient and N_A is Avogrado's number. It was also found that the theta temperature in trans-decalin was affected by the nature of polymer samples. A difference of about 3°C in the theta temperature was observed between two series of anionic polystyrenes, one prepared in THF and the other in benzene, but there was practically no difference in unperturbed chain dimension.     

Force field parameters for molecular mechanical simulation of dehydroamino acid residues

Parameters suitable to describe the conformational behavior of α – β unsaturated aminoacids and peptides in the framework of an existing force field for nucleic acids and proteins (S.J. Weiner, P.A. Kollman, D.A. Case, U. Chandra Singh, C. Ghio, G. Alagona, S. Profeta, Jr., and P. Weiner, J. Am. Chem. Soc., 106 , 765 (1984)) are proposed and tested. Attention is primarily focused on dehydrophenylalanine and dehydroalanine containing peptides. The values of the parameters needed were obtained from experimental measurements available in the literature and from ad hoc quantum mechanical calculations. The selected values have subsequently been adapted and refined through molecular mechanical simulations on model compounds, such as Ac-ΔPhe-NMe, for which it was possible to carry out STO-3G/SCF calculations to check selected points on the ?,ψ conformational map, and Ac-ΔAla-NMe, where the comparison was carried out at the 4-31G level. The newly determined force field was then applied to Ac-ΔPhe-Ala-ΔPhe-NMe, whose minimal energy structures allowed us to explain the different circular dichroism behavior observed in CH₂Cl₂ and in dioxane. Starting from two minimum energy geometries of this tripeptide, the full optimization with AM1 produced an independent guess to their structure and stability in good agreement with the molecular mechanical one.     

Behavior of molecular potential energy curves for large nuclear separations

We prove by elementary geometric methods and within the Born–Oppenheimer approximation that as the nuclei of a molecule are dissociated into spatially separated clusters, the discrete molecular energies approach sums of the energies of isolated subsystems. Our methods also show that the spectral projections associated with the discrete molecular spectrum asymptotically approach direct sums of suitable spectral projections for the isolated subsystems. These results apply to any system of particles interacting by asymptotically vanishing pair potentials. We prove that the 1/R expansion for discrete molecular potential curves is asymptotic as R → ∞, and we discuss the behavior of the coefficients of the 1/R expansion for the ground state of H₂⁺.     

Perturbative corrections to basis incompleteness in molecular SCF calculations

A unified summary is presented of the mathematical approach developed by McDowell for employing perturbation theory to correct for basis-set incompleteness in ab initio SCF calculations. Revised expressions for the corrections to the wavefunction both in terms of orbitals and spin-orbitals are presented with explicit incorporation of the spin variables. Employing H₂O as an example, we show that this approach is considerably more powerful for computing molecular energies with standard basis sets than was indicated by previous work. In particular at the higher levels of approximation it accurately reproduces the effect of polarization functions in sets such as 6-31G^* and 6-31G^**. The equilibrium molecular structure of H₂O was also computed by this approach and found to give good accuracy. In each case perturbing functions coupled to both occupied and virtual orbitals are required for acceptable results.     

Modeling of serine protease prototype reactions with the flexible effective fragment potential quantum mechanical/molecular mechanical method

A complete cycle of chemical transformations for the serine protease prototype reaction is modeled following calculations with the flexible effective fragment quantum mechanical/molecular mechanical (QM/MM) method. The initial molecular model is based on the crystal structure of the trypsin–bovine pancreatic trypsin inhibitor complex including all atoms of the enzyme within approximately 15–18 Å of the oxygen center O of the catalytic serine residue. Several selections of the QM/MM partitioning are considered. Fractions of the side chains of the residues from the catalytic triad (serine, histidine and aspartic acid) and a central part of a model substrate around the C–N bond to be cleaved are included into the QM subsystem. The remaining part, or the MM subsystem, is represented by flexible chains of small effective fragments, whose potentials explicitly contribute to the Hamiltonian of the QM part, but the corresponding fragment–fragment interactions are described by the MM force fields. The QM/MM boundaries are extended over the C–C bonds of the peptides assigned to the QM subsystem in the enzyme, C–C and C–N bonds in model substrates. Multiple geometry optimizations have been performed by using the RHF/6-31G method in the QM part and OPLSAA or AMBER sets of MM parameters, resulting in a series of stationary points on the complex potential-energy surfaces. All structures generally accepted for the serine protease catalytic cycle have been located. Energies at the stationary points found have been recomputed at the MP2/6-31+G^* level for the QM part in the protein environment. Structural changes along the reaction path are analyzed with special attention to hydrogen-bonding networks. In the case of a model substrate selected as a short peptide CH₃(NHCO-CH₂)₂ – HN–CO–(CH₂–NHCO)CH₃ the computed energy profile for the acylation step shows too high activation energy barriers. The energetics of this rate-limiting step is considerably improved, if more realistic model for the substrate is considered, following the motifs of the ThrI11–GlyI12–ProI13-–CysI14–LysI15–AlaI16–ArgI17–IleI18–IleI19 sequence of the bovine pancreatic trypsin inhibitor.     

Microhardness-structure correlation of iPP/EPR blends: influence of molecular weight and EPR particle content

The influence of molecular weight on the mechanical properties of isotactic poly(propylene) (iPP) and iPP blended with ethylene-propylene copolymers has been investigated by means of the microhardness technique. The hardness (H) of iPP is shown to slightly decrease with increasing molecular mass, within the range of molecular weights investigated. The H-decrease is correlated to a loss of crystallinity as the average molecular weight increases. On annealing, the mechanical properties are enhanced as a consequence of an increase in both, the degree of crystallinity and the crystalline lamellar thickness. A value of H ^∞ _c for iPP crystals of infinite thickness in the α-form is proposed for the first time. The inclusion of EPR particles in the iPP matrix softens the material. This result could be explained in terms of an increase in the basal surface free energy of the iPP crystals with increasing amount of rubber content. Received: 2 February 1998 Accepted: 11 May 1998     

Critical molecular weight for onset of non-newtonian flow and upper newtonian viscosity of polydimethylsiloxane

The flow curves of fractionated polydimethylsiloxanes of different molecular weights were obtained over a wide range of shear rates, from 3 × 10^?1 to 4.3 × 10⁶ sec^?1, by use of a gas-driven capillary viscometer designed to decrease the experimental error in high shear rate region. Non-Newtonian flow can occur at molecular weights below the critical molecular weight M_c for the entanglement of polymer chain. The critical molecular weight M′_c for the onset of the non-Newtonian flow is identical with that of the segment of viscous flow. For the polymer of molecular weights from M′_c to M_c, the upper Newtonian viscosity increases with an increase in molecular weight. Above M_c, the upper Newtonian viscosity is almost independent of the molecular weight.     

Exploring the quantum mechanical/molecular mechanical replica path method: a pathway optimization of the chorismate to prephenate Claisen rearrangement catalyzed by chorismate mutase

 A replica path method has been developed and extended for use in complex systems involving hybrid quantum/classical (quantum mechanical/molecular mechanical) coupled potentials. This method involves the definition of a reaction path via replication of a set of macromolecular atoms. An “important” subset of these replicated atoms is restrained with a penalty function based on weighted root-mean-square rotation/translation best-fit distances between adjacent (i±1) and next adjacent (i±2) pathway steps. An independent subset of the replicated atoms may be treated quantum mechanically using the computational engine Gamess-UK. This treatment can be performed in a highly parallel manner in which many dozens of processors can be efficiently employed. Computed forces may be projected onto a reference pathway and integrated to yield a potential of mean force (PMF). This PMF, which does not suffer from large errors associated with calculated potential-energy differences, is extremely advantageous. As an example, the QM/MM replica path method is applied to the study of the Claisen rearrangement of chorismate to prephenate which is catalyzed by the Bacillus subtilis isolated, chorismate mutase. Results of the QM/MM pathway minimizations yielded an activation enthalpy ΔH ^†† of 14.9 kcal/mol and a reaction enthalpy of −19.5 kcal/mol at the B3LYP/6-31G(d) level of theory. The resultant pathway was compared and contrasted with one obtained using a forced transition approach based on a reaction coordinate constrained repeated walk procedure (ΔH ^†† =20.1 kcal/mol, ΔH _rxn = −20.1 kcal/mol, RHF/4-31G). The optimized replica path results compare favorably to the experimental activation enthalpy of 12.7±0.4 kcal/mol. Received: 16 December 2001 / Accepted: 6 September 2002 / Published online: 8 April 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 22nd National Meeting of the American Chemical Society, 2001. Correspondence to: H.L. Woodcock e-mail: hlwood@ccqc.uga.edu Acknowledgements. The authors thank Eric Billings, Xiongwu Wu, and Stephen Bogusz for helpful discussions and related work. The authors also show grateful appreciation to The National Institutes of Health and The National Science Foundation for support of the current research.     

Tunable microstructures and mechanical deformation in transparent poly(urethane urea)s

Transparent poly(urethane urea) (TPUU) materials offer an avenue to enable material designs with potential to achieve simultaneous enhancements in both physical and mechanical properties. To optimize the performance required for each application, the molecular features that influence the microstructure, the glass transition temperature (T_g), the deformation mechanisms, and the mechanical deformation behavior must be understood and exploited. In this work, a comprehensive materials characterization of select model PUUs with tunable microstructures is addressed. Increasing the hard segment (HS) content increases the stiffness and flow stress levels, whereas altering the soft segment (SS) molecular weight from 2000 to 1000 g/mol leads to an enhanced phase mixing with a SS T_g shifted ～17 °K toward higher temperatures as well as broadening of the SS relaxation closer to room temperature. As a result, the 1K TPUU materials display greater rate‐dependent stiffening and strain hardening on mechanical deformation over the broad range of strain rates covered in this work (10^?3 to 10⁴ s^?1). In such case of similar urea‐based HS content, the molar content of the urethane linkages, per stoichiometric requirements, is much higher in the 1K TPUUs than the 2K TPUUs. These additional urethane moieties lead to an increase in the extent of intermolecular interactions, via hydrogen bonding between the HS and the SS, providing not only further phase mixing and stronger rate sensitivity but also provide 1K TPUUs with drastically improved barrier properties. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Theoretical calculation of the low laying electronic states of the molecular ion KH

Using an ab initio method the potential energy has been calculated for the 25 lowest molecular states of symmetries ²Σ⁺, ²Π, ²Δ for the molecular ion KH⁺. The calculation is based on nonempirical pseudopotentials and parameterized ℓ-dependent polarization potentials. Gaussian basis sets have been used for both atoms. The spectroscopic constants for 18 electronic sates have been calculated by fitting the calculated energy values to a polynomial in terms of the internuclear distance R. Through the canonical functions approach the eigenvalue E_v, the abscissas of the corresponding turning points (R_min and R_max) and the rotational constants B_v have been calculated up to 24 vibrational levels for the considered bound states. The comparison of the present results with those available in literature shows a very good agreement.     

Theoretical calculation of the low laying electronic states of the molecular ion RbH+

Using an ab initio method, the potential energy has been calculated for the 29 lowest molecular states of symmetries ²Σ⁺, ²Π, ²Δ for the molecular ion RbH⁺. The calculation is based on nonempirical pseudopotentials and parameterized ?‐dependent polarization potentials. Gaussian basis sets have been used for both atoms. The spectroscopic constants for 18 electronic sates have been calculated by fitting the calculated energy values to a polynomial in terms of the internuclear distance R. Through the canonical functions approach the eigenvalue E_v, the abscissas of the corresponding turning points (R_min and R_max) and the rotational constants B_v have been calculated up to 24 vibrational levels for the considered bound states. The comparison of the present results with those available in literature shows a very good agreement. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Combined molecular mechanical and quantum mechanical potential study of a nucleophilic addition reaction in solution

The procedure of combined semiempirical quantum mechanical (AM1) and molecular mechanical potential⁷ was used to study the nucleophilic addition of hydroxide to formaldehyde in solution. The gas phase AM1 potential surface is approximately 26 kcal/mol more exothermic than the corresponding ab initio 6-31 + G* calculation results. The free energy profile for the reaction in solution was determined by means of molecular dynamic simulations. The resulting free energy of activation is approximately 5 kcal/mol. The difference of the free energy of solvation between the reactant and the product states is about 38 kcal/mol. As the reaction goes on, the number of hydrogen bonds formed by the hydroxide oxygen with the surrounding water molecules decreases, whereas the number of hydrogen bonds formed by the carbonyl oxygen increases. There is no significant change in the total number of hydrogen bonds between the solute and the solvent molecules, and the average number of these hydrogen bonds is between five and six during the entire reaction process. These results are consistent with previous studies using a model based on ad initio 6-31 + G* calculations in the gas phase. The reaction path in solution is different from the gas phase minimum energy reaction path. When the two reactants are at a large distance, the attack route of the hydroxide anion in solution is close to perpendicular to the formaldehyde plane, whereas in the gas phase the route is collinear with the carbonyl group. These results suggests that although AM1 does not yield accurate energies in the gas phase, valuable insights into the solvent effects can be obtained through computer simulations with this combined potential. This combined procedure could be applied to chemical reactions within macromolecules, in which a quantitative estimation of the effects of the environment would not be easily attainable by another technique. © 1994 by John Wiley & Sons, Inc.