Scattering properties of a single semiflexible polyelectrolyte

The structure factor of a single semiflexible polyelectrolyte has been calculated as a function of chain length, intrinsic backbone stiffness, and salt concentration. Because of the insignificant coupling of the intrinsic stiffness and electrostatic persistence length, we carry out our calculations in the flexible limit. Within the variational scheme adopted here, we obtain fractal dimensions consistent with our earlier calculations of the configurational properties. As the chain length is increased, the electrostatic interaction is progressively screened, leading to the crossover regions. In the first crossover, the effective fractal dimension, D_eff, is as low as 1, and in the second crossover D_eff is 5/3, although the radius of gyration exponent is 2/5. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2644–2652, 2001     

Chain dynamics in entangled polymers: Diffusion versus rheology and their comparison

This review article scrutinizes and reanalyzes the extensively available literature data on the tracer and self chain diffusion coefficients D_tr and D_s along with the corresponding zero‐shear viscosity η₀ to show that D_s ∝ M^?ν starts with ν > 2.0 and converges to the asymptotic scaling exhibited by D_tr ∝ M^?2.0 as the molecular weight M increases beyond M/M_e = 10–20, in contrast to the onset of the asymptotic scaling M³ for η₀ taking place typically for M/M_e ? 10–20. A coherent analysis of these observations leads to the suggestion that the observed crossover in D_s is due to the constraint release effect, which diminishes around M/M_e = 10–20 and is negligible in measurements of D_tr when the matrix molecular weight P is much greater than M. The contour length fluctuation (CLF) effect, which is believed to cause the molecular weight scaling of η₀ to deviate significantly from its limiting behavior of M³, has little direct influence on the chain diffusion. The absence of the CLF effect on D_s leads to a much stronger than linear dependence of the product η₀D_s on M, which has been observed previously. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1589–1604, 2003     

Mean‐Field Calculation of MZ for Randomly Branched Condensation Polymers

The mean‐field theory of Flory–Stockmayer for randomly branched polymers in the regime of strong chain overlap is extended to a calculation of M_Z via the recursive method of Miller and Macosko. The formalism includes condensation polymers, copolymers, chain stoppers, bifunctional diluents to control the chain length between branch points, multiple branching agents, and arbitrary stoichiometries. M_Z closely approximates the largest branched polymer in the system and is therefore a key parameter describing static scaling behavior near the gel point. Nonuniversal static scaling of M_Z is illustrated with examples from the literature. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1415–1422     

A novel approach toward the prediction of the glass transition temperature: Application of the EVM model,a designer QSPR equation for the prediction of acrylate and methacrylate polymers

We describe an original QSPR model called the EVM model (Energy, Volume, Mass) to calculate the glass transition temperature (T_g) of aliphatic acrylate and methacrylate homopolymers using classical molecular mechanics and dynamics. The latter was used to calculate an energy density function related to the cylindrical volume of a 20 monomer unit polymer segment (TSSV, Total Space around a Standard deviation Volume). We then calculated the T_g as a function of this density function and the repeat unit molecular weight, although no interchain interactions were taken into account. For linear and branched aliphatic acrylate and methacrylate polymers, the standard deviation from linear regression was 12 K, and the r² was 0.96. The model allows calculation of the T_g with an average absolute error of error of 10% for linear and branched derivatives not included in the original linear regression analysis. The results obtained with the EVM model are compared with those obtained with Bicerano's model. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 2579–2590, 1997     

Effect of the directionality of the ester group on the formation of hairpins in polyesters containing naphthalene and a flexible spacer

Steady-state fluorescence measurements and molecular dynamics simulations have been used to study the intramolecular formation of excimers in five model compounds for polyesters containing naphthalene groups separated by flexible spacers. The model compounds are derived from 2-hydroxynaphthalene and HOOC (CH₂)_n COOH, n = 2–6. The ratio of the intensity of excimer and monomer emissions, I_D/I_M, is nearly independent of the viscosity of the medium, η, over the range covered in dilute solution. Although I_D/I_M is always very small, it shows an odd–even effect for the first four members of the series, with maxima when n is odd. Molecular dynamics simulations provide an explanation for the small values of I_D/I_M, their weak dependence on η, and the trend of I_D/I_M with n. The results for the present series of model compounds are compared with previous work, which reported larger values of I_D/I_M, and a stronger dependence of I_D/I_M on η, for bichromophoric compounds derived from 2-naphthoic acid and aliphatic glycols, where the direction of the ester groups is reversed. The origin of the difference in the behavior of I_D/I_M in the two series is identified. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1127–1133, 1997     

Identifying the primitive path mesh in entangled polymer liquids

Similar to entangled ropes, polymer chains cannot slide through each other. These topological constraints, the so-called entanglements, dominate the viscoelastic behavior of high-molecular-weight polymeric liquids. Tube models of polymer dynamics and rheology are based on the idea that entanglements confine a chain to small fluctuations around a primitive path which follows the coarse-grained chain contour. To establish the microscopic foundation for these highly successful phenomenological models, we have recently introduced a method for identifying the primitive path mesh that characterizes the microscopic topological state of computer-generated conformations of long-chain polymer melts and solutions. Here we give a more detailed account of the algorithm and discuss several key aspects of the analysis that are pertinent for its successful use in analyzing the topology of the polymer configurations. We also present a slight modification of the algorithm that preserves the previously neglected self-entanglements and allows us to distinguish between local self-knots and entanglements between distant sections of the same chain. Our results indicate that the latter make a negligible contribution to the tube and that the contour length between local self-knots, N_lk is significantly larger than the entanglement length N_e. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 917–933, 2005     

Brushes formed by self-similarly branched polymers and random manifolds

When randomly branched polymers are grafted to a surface, polymer brushes are the result, similarly as well known in the case of linear grafted polymer chains. These brushes behave, however, special, as severe restrictions in the conformation of individual polymers are present. These restrictions are firstly due to the high degree of branching and secondly to the natural maximum stretching ratio of the branched molecules, that is given by H_max = aM^1/D. a is the typical size of a monomeric unit, D is the spectral dimension and M the total mass of the branched polymer. Brushes cannot exceed this height, and limits on the grafting density as functions of the spectral dimension are investigated. For all thermodynamic situations the minimum area per chain scales as σ_min = aM^{(D − 1)/D}.     

Computer simulation of three‐arm star polymers

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

Synthesis and characterization of multiarm star-branched polyisobutylenes: Effect of arm molecular weight

A series of star-branched polyisobutylenes with varying arm molecular weights was synthesized using the 2-chloro-2,4,4-trimethylpentane/TiCl₄/pyridine initiating system and divinylbenzene (DVB) as a core-forming comonomer (linking agent). The resulting star-branched polymers were characterized with regard to the weight-average number of arms per star molecule (N̄_w) and dilute solution viscosity behavior. As the molecular weight of the arm (M̄_{w, arm}) was increased, dramatically longer star-forming reaction times were needed to produce fully developed star polymers. It was calculated that N̄_w varied from 50 to 5 as the M̄_{w, arm} was increased from 13,000 to 54,000 g/mol. The radius of gyration, R_g, of the star polymers was observed to increase as M̄_{w, arm} was increased. The solution properties of the star polymers were evaluated in heptane using dilute solution viscometry. It was determined that the stars had a much higher [η] compared to the respective linear PIB arms, but a much lower [η] compared to a hypothetical linear analog of an equivalent molecular weight. The dependence of [η] on temperature for the stars and linear arms was very small over the temperature range 25 to 75°C, with only a very slight decrease with increasing temperature. [η]_star was also determined to increase with increasing M̄_{w, arm}, but decrease with increasing M̄_{w, star}. The branching coefficient, g′, calculated for the stars at 25°C, increased as N̄_w decreased and agre ed well with literature values for other star polymer systems. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 3767–3778, 1997     

Influence of long‐chain branching on the miscibility of poly(ethylene‐r‐ethylethylene) blends with different microstructures

The melt miscibility of two series of poly(ethylene‐r‐ethylethylene) (PE_Exx) polymers with different percentages (xx) of ethylethylene (EE) repeat units was examined with small‐angle neutron scattering (SANS). The first series consisted of comb/linear blends in which the first component is a heavily branched comb polymer (B90) containing 90% EE and an average of 62 long branches with a weight‐average molecular weight (M_W) of 5.5 kg/mol attached to a backbone with M_W = 10.0 kg/mol. The comb polymer was blended with six linear PE_Exx copolymers, all of which had M_W ≈ 60 kg/mol and EE percentages ranging from 55 to 90%; they were denoted L55 to L90, with the number referring to the percentage of EE repeat units. The second series consisted of linear/linear blends; the first component, with M_W = 220 kg/mol and 90% EE, was denoted L90A, and the second components were the same series of linear polymers, with M_W ≈ 60 kg/mol and various EE compositions. The concentrations investigated were 50/50 w/w, except for the blend of branched B90 and linear L90 (both components were 90% EE), for which 25/75 and 75/25 concentrations were also examined. The SANS results indicated that for the comb/linear blends, only the dB90/L90 blends were miscible, whereas the other five blends phase‐separated; for the linear/linear blends, dL90A/L83 and dL90A/L78 were miscible, whereas the other three blends were immiscible. These results indicate that long‐chain branching significantly narrowed the miscibility window of these polyolefin blends. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 466–477, 2002; DOI 10.1002/polb.10102     

Novel Reaction Route Including Enzymic Reaction For A Synthesis Of A Branched Polysaccharide

Abstract

Stereoselective synthesis of α-D-glucosyl-branching polysaccharide by chemical and enzymic reactions was investigated. Ring-opening polymerization of 1,6-anhydro-3-O-benzoyl-2,4-di-O-benzyl-β-D-glucopyranose (1) with PF₅ as catalyst at low temperature gave a highly stereoregular polymer, which was converted to 2,4-diO-benzyl-(1→6)-α-D-glucopyranan by debenzoylation with sodium methoxide. The polymer was glucosylated according to the glycosyl imidate method. Deprotection of the branched polysaccharide was carried out with sodium in liquid ammonia at -78 °C to give a (1→6)-α-D-glucopyranan having α-D-glucopyranosyl and β-D-glucopyranosyl branches. Only the β-D-glucopyranosyl branch of the polymer was completely removed by enzymatic hydrolysis by the use of cellulase to provide stereoregular (1→6)-α-D-glucopyranan having an α-D-glucopyranosyl branch at the C-3 position. Polymers were characterized by optical rotation, NMR spectroscopy, GPC, and X-ray diffractometry.     

Correlating backbone‐to‐backbone distance to ionic conductivity in amorphous polymerized ionic liquids

The morphology and ionic conductivity of poly(1‐n‐alkyl‐3‐vinylimidazolium)‐based homopolymers polymerized from ionic liquids were investigated as a function of the alkyl chain length and counterion type. In general, X‐ray scattering showed three features: (i) backbone‐to‐backbone, (ii) anion‐to‐anion, and (iii) pendant‐to‐pendant characteristic distances. As the alkyl chain length increases, the backbone‐to‐backbone separation increases. As the size of counterion increases, the anion‐to‐anion scattering peak becomes apparent and its correlation length increases. The X‐ray scattering features shift to lower angles as the temperature increases due to thermal expansion. The ionic conductivity results show that the glass transition temperature (T_g) is a dominant, but not exclusive, parameter in determining ion transport. The T_g‐independent ionic conductivity decreases as the backbone‐to‐backbone spacing increases. Further interpretation of the ionic conductivity using the Vogel–Fulcher–Tammann equation enabled the correlation between polymer morphology and ionic conductivity, which highlights the importance of anion hoping between adjacent polymer backbones. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Synthesis and swelling behavior of amphiphilic comb‐like branched polymer (AA‐co‐CMS)‐g‐PMMA

Copolymerization of acrylic acid and p‐chloromethylstyrene (p‐CMS) in dioxane initiated with α,α′‐azobisisobutyronitrile was carried out to produce macroinitiator P(AA‐co‐CMS) containing PhCH₂Cl group at 65°C. Then methyl methacrylate was grafted onto P(AA‐co‐CMS) backbone using PhCH₂Cl group as an initiation site and FeCl₂/triphenyl phosphine complex as a catalyst. The resulted copolymer (AA‐co‐CMS)‐g‐PMMA with a comb‐like branched structure has a hydrophilic backbone (PAA) and hydrophobic side chains (PMMA). Compositions and structures of macroinitiator and the grafted product of P(AA‐co‐CMS)‐g‐PMMA were determined by ¹H‐NMR, infrared (IR), and gel permeation chromatography (GPC). The average graft number, the average length of branch chains, the graft ratio, and the graft efficiency were investigated. The swelling behavior of the comb‐like branched polymer was also investigated. The gradual increase of swelling ratios was accompanied by an increase of pH and temperature. The kinetic exponents indicated that the swelling transport mechanisms transformed from Fickian diffusion to non‐Fickian transport as the decreasing pH. Copyright © 2009 John Wiley & Sons, Ltd.     

Poly(oxanorbornenedicarboximide)s dendronized with amphiphilic poly(alkyl ether) dendrons

Attaching dendritically branched side chains to each repeat unit of a linear polymer produces molecular building blocks of nanometer‐sized dimensions called dendronized polymers. The structure of these complex molecular architectures is highly tunable and, therefore, of interest for a wide range of potential applications. The first examples of dendronized polymers prepared by living ring‐opening metathesis polymerization of oxanorbornenedicarboximide macromonomers with poly(alkyl ether) dendrons are reported. Small‐angle X‐ray scattering experiments on bulk samples confirm that the diameter of the individual cylindrical polymers can be tailored by the choice of dendron generation or the length of the hydrocarbon peripheral group. Analysis of the SAXS data based on a core‐shell model indicates that although the diameter of the cylinder increases with generation, the size of the core does not change; this suggests that these dendrons only loosely encapsulate the polymer backbone. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 3221–3239     

Effect of diluents on the melt viscosity of branched polybutadienes

The enchanced low-shear melt viscosity of branched polybutadienes is shown to be sensitive to dilution with low molecular compounds. The viscosity of branched polymers falls more rapidly with dilution than that of linear polymers, i.e., branched polymers show increased response to plasticization. At least one instance is demonstrated in which the viscosity ratio η_br/η_lin reverses from a value greater than unity to less than one in passing from dry polymer to rubber extended with relatively large quantities of oil.     

The linear rheological responses of wedge‐type polymers

The linear rheological responses of a series of specially designed wedge‐type polymers synthesized by the polymerization of large molecular weight monomers have been measured. These wedge polymers contained large side groups which contained three flexible branch chains per polymer chain unit. The master curves for these polymers were obtained by time temperature superposition of dynamic data at different temperatures from the terminal flow regime to well below the glass transition temperature, T_g. While these polymers maintained a behavior similar to that of linear polymers, the influence of the large side group structure lead to low entanglement densities and extremely low rubbery plateau modulus values, being near to 13 kPa. The viscosity molecular weight dependence was also somewhat higher than that normally observed for linear polymers, tending toward a power law near to 4.2 rather than the typical 3.4 found in entangled linear chains. The glassy modulus of these branched polymers is also found to be extremely low, being less than 100 MPa at T_g ?60 °C. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 899–906     

Effects of hydroxyl‐group end capping and branching on the physical properties of tailored polyethylene terephthalates

Polyethylene terephthalates (PETs) with well‐defined chemical structures were prepared by molecular design, and the effect of the chemical structure on the physical properties of PET was investigated. Hydroxyl‐group end‐capped PETs with η_inh = 0.4–0.6 dL/g exhibited a viscosity behavior similar to Bingham fluids, although other PETs with similar molecular weights (MWs) showed Newtonian flow behavior. This rheological feature was more noticeable for hydroxyl‐group end‐capped branched PETs. In addition, hydroxyl‐group end‐capped branched PETs became solidlike from 80 rad/s as the frequency was increased. On the other hand, hydroxyl end‐capped linear PETs showed a noticeable viscoelastic transition peak around 20 rad/s. High MW linear and branched PETs with η_inh ≥ 0.9 prepared by multistep synthesis showed non‐Newtonian fluid behavior. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 1027–1035, 2001     

Internal plasticization of poly(vinyl) chloride using glutamic acid as a branched linker to incorporate four plasticizers per anchor point

Internal plasticization of polyvinyl chloride (PVC) using thermal azide‐alkyne Huisgen dipolar cycloaddition between azidized PVC and electron‐poor acetylenediamides incorporating a branched glutamic acid linker resulted in incorporation of four plasticizing moieties per attachment point on the polymer chain. A systematic study incorporating either alkyl or polyethylene glycol esters provided materials with varying degrees of plasticization, with depressed T_g values ranging from ?1 °C to 62 °C. Three interesting trends were observed. First, T_g values of PVC bearing various internal plasticizers were shown to decrease with increasing chain length of the plasticizing ester. Second, branched internal plasticizers bearing triethylene glycol chains had lower T_g values compared to those with similar length long‐chain alkyl groups. Finally, thermogravimetric analysis of these internally plasticized PVC samples revealed that these branched internal plasticizers bearing alkyl chains are more thermally stable than similarity branched plasticizers bearing triethylene glycol units. These internal tetra‐plasticizers were synthesized and attached to PVC‐azide in three simple synthetic steps. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 1821–1835     

Polycondensations of dicarboxylic acids and diols derived from optically active amino alcohols

Polycondensations of dicarboxylic acids with diols having amide moieties derived from optically active amino alcohols were carried out. Polymers with M _ns 8,700–17,400 were obtained by the polycondensations using 1.2 eq. of 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide hydrochloride (EDC·HCl) in DMF at room temperature for 8 h in satisfactory yields. The T_g of the polymer rose with decrease of the methylene chain length of the dicarboxylic acid. In the T_gs of the polymers from L-leucinol, even-odd effect was observed with increase of the methylene chain length of the dicarboxylic acid. The molecular rotation values of the polymers were constant except for the polymer from succinic acid, which showed the negatively largest one. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 2925–2934, 1997     

Wear and friction in glassy polymers: Microscratch on blends of polystyrene and poly (2,6-dimethyl-1,4-phenylene oxide)

The microscopic process of abrasive wear and friction in glassy polymers was studied by using a special microscratch technique. A miscible blend of polystyrene (PS) and poly(phenylene oxide) (PPO) was used. It was found that as the composition varies there seems to exist two wear regimes in the blends controlled by different breakdown mechanisms corresponding to the brittle—ductile transition. Detailed study of the contact loads and SEM micrographs indicate that abrasive wear in the glassy polymers is controlled by microcracking under the asperity contacts. The critical load τ_c for initiating microscopic cracks can be linked to the macroscopic wear via a statistical Weibull model where τ_c is taken to be the mean of a strength distribution function. On the other hand, the friction coefficient was found to be independent of the composition but to vary strongly with the contact load. It approaches zero at the extrapolated zero load, but increases rapidly and eventually levels off with contact load. This behavior can be understood by a simple frictional adhesion model in which the polymer deformation during a frictional contact is analyzed by considering the compressive plastic ploughing and shearing yielding around the asperity contact. The shear strength S_o of the polymer/asperity contacts was found to vary with the normal load. The vertical scratch hardness H_v, which characterizes the spontaneous indentation yielding on the polymer surface, was found to be independent of scratch length and depth, and indeed can be regarded as a material constant. Although both S_o and H_v can accurately describe the frictional behavior of the glassy polymers, they bear no correlation to abrasive wear in the same materials. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1295–1309, 1997