The effect of molecular weight heterogeneity on the second virial coefficient of linear polymers in good solvents

The effect of molecular weight heterogeneity on the second virial coefficient A₂ in good solvents is studied for binary mixtures of monodisperse poly(α-methylstyrenes). It is concluded that A₂ for polymer mixtures passes through a maximum with variation of the mixing ration. From comparison with the data, it is concluded that no available theory quantitatively explains both the molecular weight dependence of A₂ of monodisperse polymer and the variation of A₂ of mixtures with the mixing ratio. The interpenetration function for two polymer coils with different molecular weights is discussed on the assumption that the thermodynamic interaction between two polymer coils in good solvents can be approximated by a hard-sphere model.     

Investigation of the formation of M 2 + -molecular ions in sputtering processes

The formation process of M₂⁺ molecular ions sputtered from elementary target materials is investigated. In a previous article it was shown that these molecules can be used to quantitate major elements [1]. The quantitation method was based on the assumption that the M₂⁺ molecular ions are formed by the atomic combination of independently sputtered M and M ⁺ particles above the surface. In this paper this assumption will be investigated using a Monte Carlo model to simulate the formation mechanism. The model is used to calculate the velocity distribution of the M₂⁺ dimers sputtered from three different elementary target materials (Fe, Ge, and Ni). The results are compared with experimental data. Good agreement exists between theory and experiment that supports the Monte Carlo model and hence also the assumed formation mechanism.     

A MODEL FOR THE MOLECULAR STRUCTURE AND ORIENTATION OF THE CHROMOPHORE IN A DIMERIC PHYTOCHROME MOLECULE*

A model for the molecular structure and orientation of red-light absorbing form of phytochrome (P,) chromophores in a dimeric molecular model of P_r is proposed. A chromophore model with probable molecular structures was generated to reproduce the absorption spectrum produced by its π-electron conjugating system. The model has C₅-Z, syn, C₁₀-E, anti and C₁₅-Z, syn configurations and a protonation at a C-ring nitrogen. Orientation of the chromophore model in the dimeric phytochrome molecular was analyzed by displaying the atoms of the chromophore, the coordinates of which were converted into those with respect to the molecular axes to the dimeric molecule, on a 3-D graphic workstation. The conversions were performed by using the azimuthal angles between the Z axis of the dimeric molecule (axis of 2-fold rotational symmetry) and the dipole moments of the electronic transition at the blue- (384 nm) and red- (667 nm) absorbing bands of the chromophore, which were calculated as 55.5° and 59.3°, respectively, based on linear dichroism of the oriented phytochrome molecules. The result demonstrates that the long axis of the P, chromophore lies almost parallel to the Y axis of the molecular model, and that the tetrapyrrolic chromophore is well contained within the flat chromophoric domain without protruding from it, a configuration that assures that the chromophore is protected against aqueous environments. The model may explain the rotation angle of the transition moment of the red-absorbing band, induced by the phototransformation from P_r to P_rr which we measured as smaller than that measured in nonoriented preparations by a photoselection technique. The model also suggests a molecular basis for the polarotropic response of phytochrome.     

Effects of chain length distribution on viscoelastic properties of entangled linear polymers: Blending laws for binary blends

The reptation idea of de Gennes and the tube model theory of Doi and Edwards are extended to explain the terminal viscoelastic properties of binary blends in the highly entangled state of two linear monodisperse polymers with different molecular weights M₁ and M₂. A modified tube model is proposed that considers the significance of the constraint release by local tube renewal in accounting for the relaxation process of the higher molecular weight chain. Its relaxation by both reptation and the constraint release is remodeled as the disengagement by pure reptation of an equivalent primitive chain. From knowledge of the longest relaxation times of the blend components, the stress equation is formulated from which blending laws of viscoelastic properties for the binary blends are derived. To force better agreement between theory and experiment at the pure monodisperse limits of the blends, a crude treatment to include the effect of contour-length fluctuation in the equivalent-chain model is also discussed. Theoretical predictions of the zero-shear viscosity and steady-state shear compliance are shown to be in good agreement with literature data on undiluted polystyrenes and polybutadienes over a wide range of the blend composition and M₂/M₁ ratio. The asymptotic of the laws for blends with M₂/M₁ → 1 and 0 are comparable to those from the relaxation spectrum proposed by others earlier on the basis of the tube model.     

Core distortions in metal atoms and the use of effective core potentials

The recent experimental determination of the geometry of Ti(CH₃)₂Cl₂ shows it to be inconsistent with the VSEPR model, a result not uncommon for molecules containing transition metal atoms. The valence shell charge concentrations (CCs) that appear as maxima in L(r)=−²ρ(r), provide a physical basis for the VSEPR model of molecular geometry for main group molecules. The same model accounts for the geometry of transition metal molecules with the proviso that the CCs are formed within the outer shell of the core of the metal atom, as defined by the shell structure of L(r). This observation appears to be in conflict with calculations for Ti(CH₃)₂Cl₂ showing that its geometry can be predicted using an effective core potential for the metal atom, a procedure that would appear to preclude the presence of core distortions. The apparent contradiction is resolved by distinguishing between the definition of the core using L(r) and one based on the orbital model.     

Modeling of Superacid Catalyzed Step‐Growth Polymerization of Isatin and Biphenyl or Terphenyl Monomers

A mathematical model for the kinetics and molecular weight development of superacid catalyzed step‐growth polymerization of isatin and biphenyl or terphenyl monomers is developed. By considering different reactivities among the several types of polymer molecules present in an otherwise conventional A₂ + B₂ step‐growth polymerization system, ultrahigh molecular weights are predicted by the model for superacid catalyzed polyhydroxyalkylation reactions, a result that remains unclear in the literature since it seems to be in disagreement with the classical A₂ + B₂ theory. Three polymerization systems are addressed in this study: (a) polymerization of isatin and biphenyl, (b) modified isatin and biphenyl, and (c) modified isatin and terphenyl. Overall good agreement between calculated and experimental results of polymerization rate, and evolution of number‐ and weight‐average molecular weights (M _n and M _w, respectively) is observed. However, some discrepancies for molar mass dispersity (Ð ) are observed.     

Holographic quantitative structure-activity relationship for prediction of the toxicity of polybrominated diphenyl ether congeners

Polybrominated diphenyl ether congeners (PBDEs) might activate the AhR (aromatic hydrocarbon receptor) signal transduction, and thus might have an adverse effect on the health of humans and wildlife. Because of the limited experimental data, it is important and necessary to develop structure-based models for prediction of the toxicity of the compounds. In this study, a new molecular structure representation, molecular hologram, was employed to investigate the quantitative relationship between toxicity and molecular structures for 18 PBDEs. The model with the significant correlation and robustness (r ² = 0.991, q ² _LOO = 0.917) was developed. To verify the robustness and prediction capacity of the derived model, 14 PBDEs were randomly selected from the database as the training set, while the rest were used as the test set. The results generated under the same modeling conditions as the optimal model are as follows: r ² = 0.988, q ² _LOO = 0.598, r ² _pred = 0.955, and RMSE (root-mean-square of errors) = 0.155, suggesting the excellent ability of the derived model to predict the toxicity of PBDEs. Furthermore, the structural features and molecular mechanism related to the toxicity of PBDEs were explored using HQSAR color coding.     

The structures of low molecular weight glycerin propoxylates: An experimental,semi-empirical,and Monte Carlo study

A simple Monte Carlo model has been developed for calculating the structural features and properties of low molecular weight triols produced by the base-catalyzed propoxylation of glycerin. The model computes the probability of a reaction to a specific oligomer from the local site reactivities of model compounds with an adjustment for the molecular weight of the reacting oligomer. The resulting product array is then used to calculate typical polymer properties such as average molecular weight, polydispersity, and average chain length. Trial rate constants were estimated from the activation energies of MNDO-PM3 semi-empirical molecular orbital theory. For the compounds used to model the oligomer chain end groups, the activation enthalpies were found to be within the ranges reported for experimental values. Although the predicted enthalpies of activation were significantly higher for the alkoxylation directly at glycerin, this was found to be attributable to intramolecular hydrogen bonding in the reactants that was disrupted in the transition states. Although the hydrogen bonding energies were higher than what are normally considered typical, comparison tests showed that the calculated energies agreed well with experimental values of alkoxide anion–alcohol systems. The PM3 rate constants, when used to calculate Monte Carlo probabilities, predicted the isomer distribution of the four isomeric monopropoxylates with a error of 4%. Optimization of the model reduced this to 0.5%. However, to accurately predict the oligomer distribution of higher molecular weight adducts and other properties, the correction term (M₀/M_i)^b had to be included, where M₀/M_i is the ratio of the molecular weight of glycerin to the molecular weight of the oligomer undergoing alkoxylation, and b is assigned the value 0.7. Although b is empirical, it is consistent with a simple molecular mechanics (MM2) conformational study of the relative availability of the reactive end groups. When the final model was used to simulate the propoxylation of glycerin for a variety of PO/glycerin ratios, it was found to accurately reproduce properties such as primary hydroxyl content, polydispersity, oligomer distribution, and change in the monopropoxylate isomer ratio as a function of bulk PO/glycerin ratio. © 1995 John Wiley & Sons, Inc.     

Stochastic model for gel permeation separation of polymers

The stochastic theory of chromatography developed by Giddings and Eyring and by McQuarrie is applied to gel permeation chromatography (GPC) by first recasting their assumptions to fit the GPC process and secondly by making specific assumptions about the molecular size dependence of the rate constants λ₁ and λ₂ for entrapment and elution of a polymer molecule, respectively. The model assumes that: (1) a monodisperse sample is injected; (2) molecules behave independently within the column; (3) no molecular diffusion occurs; (4) the polymer molecules are unperturbed random coils; (5) entrapment sites in the bed are identical; (6) λ₁ is proportional to the probability P_e that the square of the polymer end-to-end distance is less than the square of the average pore radius in the bed; (7) λ₂ is constant. The calculated difference in retention times, t_R-t_o (where t_R is the retention time for a molecule of arbitrary molecular size and t_o is the retention time for a molecule whose size totally precludes entrance into the pores of the bed), is shown to be proportional to P_e. The model as thus applied is based on only one parameter. The theory is tested by examining the ratio P_e/(t_R ? t_o)exp, predicted to be constant, for narrow polystyrene fractions in the molecular weight range 1.1 × 10⁴ – 8.9 × 10⁵. Chromatographs were obtained by Moore and Arrington by using a θ solvent and a single column packed with a porous glass bed having a sharp distribution of pore sizes. Ratio values ranged from 0.046 to 0.073 with an average value of 0.058 ± 0.009. This relative constancy demonstrates semiquantitative utility of the model for gaining insight into the GPC process.     

Frequency and molecular-mass-dependent nonexponential proton NMR relaxation in polymer melts

A theoretical treatment of the nonexponential relaxation behavior of the different proton nuclear magnetic resonance (NMR) relaxation processes in polymer melts is presented. Formulas are derived for a three-component model given by two versions and a homogeneous distribution of correlation times. The theoretical results were tested with measurements of T₁, T_2e, and T₂ as functions of frequency and molecular mass in linear fractionated polyethylene samples. While the T₁ relaxation always yields exponential magnetization decays, the T_2e and T₂ measurements show biexponential relaxation behavior. From the calculations it was found that the correlation time of the local motion is independent of the molecular mass, whereas the correlation time of the slowest motional process increases with M^2.8_w for the three-component model and with M^2.2_w for the distribution of correlation times, respectively. © 1992 John Wiley & Sons, Inc.     

Nonstoichiometric polycondensation I. synthesis of polythioether from dibromomethane and 4,4′-thiobisbenzenethiol

High molecular weight poly(phenylene thioether) ( 3 ) was successfully obtained by the polycondensation of 4,4′-thiobisbenzenethiol ( 1 ) and dibromomethane ( 2 ) with a variety of feed ratios in the presence of 1,8-diazabicyclo[5,4,0]undec-7-ene (DBU) in 1-methyl-2-pyrrolidinone (NMP) at 75°C. The resulting polymer showed the maximum inherent viscosity (η_inh) of 0.50 dL/g in 4 h when 1.5 equivalents excess of 2 was used. The model reaction using benzenethiol ( 4 ) and dichloromethane ( 5 ) in the presence of DBU in deuterated dimethylsulfoxide (DMSO-d₆) at 25°C indicated that the rate of the second nucleophilic displacement reaction (k₂) is 61 times faster than that of the first one (k₁). The maximum of theoretical molecular weights calculated at various stoichiometric imbalance (S) under the condition of k₂/k₁ = 61 showed a good agreement with the experimental molecular weights at specific polymerization times.     

Ethylene/hexene copolymerization with the heterogeneous catalyst system SiO2/MAO/rac‐Me2Si[2‐Me‐4‐Ph‐Ind]2ZrCl2: The filter effect

The main focus of this study is the ethylene/hexene copolymerization with the silica supported metallocene SiO₂/MAO/rac‐Me₂Si[2‐Me‐4‐Ph‐Ind]₂ZrCl₂. Polymerizations were carried out in toluene at a reaction temperature of 40°C–60°C and the cocatalyst used was triisobutylaluminium (TIBA). The kinetics of the copolymerization reactions (reactivity ratios r_E/H, monomer consumption during reaction) were investigated and molecular weights M_w, molecular weight distributions MWD and melting points T_m were determined. A schematic model for the blend formation observed was developed that based on a filtration effect of monomers by the copolymer shell around the catalyst pellet.     

Three-dimensional Quantitative Structure-Activity Relationship Analyses of a Series of Butenolide ETA Antagonists

Two kinds of Three-dimensional Quantitative Structure-activity Relationship(3D-QSAR) methods,comparative molecular filed analysis(CoMFA) and comparative molecular similarity indices analysis (CoMSIA) ,were applied to analyze the structure-activity relationship of a series of 63 butenolide ETA selective antagonists with respect to their inhibition against human ETA receptor,The CoMFA and CoMSIA models were developed for the conceivable alignment of the molecules based on a template structure from the crystallized data.The statistical results from the initial orientation of the aligned molecules show that the 3D-QSAR model from CoMFA(q^2=0.543) is obviously superior to that from the conventional CoMSIA(q^2=0.407).In order to refine the model,all-space search (ASS) was applied to minimize the field sampling process.By rotating and translating the molecular aggregate within the grid systematically,all the possible samplings of the molecular fields were tested and subsequently the one with the highest q^2 was picked out .The comparison of the sensitivity of CoMFA and CoMSIA to different space orientation shows that the CoMFA q^2 values are more sensitive to the translations and rotations of the aligned molecules with respect to the lattice than those of CoMSIA.The best CoMFA model from ASS was further refined by the region focused technique.The high quality of the best model is indicated by the high corss-validated correlation and the prediction on the external test set.The CoMFA coefficient contour plots identify several key features that explain the wide range of activities,which may help us to design new effective ETA selective antagonists.     

The low‐temperature phase of 1,3‐di­bromo‐2,4,6‐tri­methyl­benzene: a single‐crystal neutron diffraction study at 120 and 14 K

In the low‐temperature phase of di­bromo­mesityl­ene (1,3‐di­bromo‐2,4,6‐tri­methyl­benzene), C₉H₁₀Br₂, the mol­ecule deviates significantly from the C_3h molecular symmetry encountered in tri­bromo­mesityl­ene (1,3,5‐tri­bromo‐2,4,6‐tri­methyl­benzene), even for the endocyclic bond angles. An apparent C_2v molecular symmetry is observed. The angle between the normal to the molecular plane and the normal to the (100) plane is ∼20°. The overall displacement was analysed at 120 K with rigid‐body‐motion tensor analysis. The methyl group located intermediate between the two Br atoms is rotationally disordered at both temperatures. This disorder was treated using two different approaches at 14 K, viz. the conventional split‐atom model and a model using the special annular shapes of the atomic displacement parameters that are available in CRYSTALS [Watkin, Prout, Carruthers & Betteridge (1999). Issue 11. Chemical Crystallography Laboratory, Oxford, England], but only through the latter approach at 120 K. The disorder locally breaks the C_2v molecular symmetry at 14 K only. Intra‐ and intermolecular contacts are described and discussed in relation to this methyl‐group disorder. The bidimensional pseudo‐hexagonal structural topology of tri­halogeno­mesityl­enes is altered in di­bromo­mesityl­ene insofar as the (100) molecular layers are undulated and are not coplanar as a result of an alternating tilt angle of ∼34° propagating along the [011] and [01] directions between successive antiferroelectric molecular columns oriented roughly along the a axis.     

A model for dynamic relaxations in amorphous polymers. I. Conceptual framework,formal implementation of simplest version,and application to poly(ester carbonates)

A new model for the dynamic relaxations occurring below the glass transition temperature in amorphous polymers is introduced. This model combines ideas from theoretical solidstate physics, thermodynamics, and statistical mechanics. Formal analogies are made between the dynamic relaxations and phase transitions. The concepts of percolation theory are briefly discussed. The molecular level motions which might be giving rise to each dynamic relaxation are incorporated within this framework. The simplest version of the model is then formally implemented within the context of bisphenol-A polycarbonate (BPAPC) and its poly (ester carbonates) (PEC). The following results are calculated: (1) Characteristic temperatures (T_c) for BPAPC, similar to γ₁, and γ₂ relaxation temperatures observed by dynamic mechanical spectroscopy (DMS) at commonly used measurement frequencies. (2) T_c for the β₂ relaxation in tetrabromo-BPAPC much higher than the T_c in BPAPC. (3) A slow and monotonic increase in both the intensity and the T_cof the γ₂ relaxation with an increasing fraction of terephthalate comonomer in PEC copolymers. It is hoped that this model, which is admittedly tentative at this time, will be useful as a working hypothesis. The next paper of this series will provide extensions and generalizations of the model, and its application to the poly (alkyl methacrylates).     

The application of the perrin–agishev model for calculation of the translational diffusion coefficients of liquid dichloroalkanes

The article presents the translational diffusion coefficients calculated for dichloroalkanes series C _n H_{2 n} Cl₂ (where n =?6, 8, 10, 12) in the liquid state, with the use of the Perrin and Agishev model. It has been shown that the molecules of dichloroalkanes assume a mutually parallel arrangement in three possible coordinations. The model of arrangement, orientations and packing of the molecules has been presented. The activation parameters of the compounds studied have been discussed. The physical and structural properties of the liquids studied (macroscopic density, electron density and molecular weight) are correctly described within the van der Waals model predicting their orientations and packing. The formulae linking the diffusion, viscosity and temperature for the liquids have been presented. The assumption that each molecule can be approximated by an ellipsoid of the semiaxes lengths a, b and c has been justified. The translations become slower with increasing volume and weight of the molecule. The diffusion coefficients decrease with increasing molecular weight.     

Cluster analysis of periodic distributions; application to conformational analysis

A method is described to analyze observed conformations for molecular fragments with more than three torsional degrees of freedom. The method is an adaption of statistical cluster analysis to multidimensional, symmetric, periodic distributions of data points. Application to the molecular fragment M(PPh₃)₂ with eight torsional degrees of freedom reveals a model of conformational interconversion. The model implies gearing motion of the two PC₃ fragments alternating with stepwise inversions of the helicities of the PPh₃-propellers.     

Kinetic model for tensile deformation of polymers. Part IV: Effect of polydispersity

A previously introduced molecular model for tensile deformation of solid, flexible chain polymers is used to study the effect of the molecular weight distribution on the strain at break, or maximum draw ratio. The parameters in the model are chosen to represent melt-crystallized linear polyethylene. We focus, in particular, on the relation between the maximum draw ratio and two distribution characteristics: theM _t molecular weight average, first introduced by Graessley, and the polydispersity ratioM _z /M _w . For a log-normal molecular weight distribution, an increase in polydispersity at constantM _t leads to a broadening of the optimum rate (or temperature) window for achieving maximum elongation, but is accompanied, however, by a substantial decrease in the maximum attainable draw ratio. Studies on the deformation of systems having a bimodal molecular weight distribution indicate that blends made ofequal weight fractions of long and short chains exhibit an unexpectedly high elongation at break. These results are explained in terms of the model and possible technological implications are discussed.Dedicated to Professor Hans-Henning Kausch on the occasion of his 60th birthday.