Average Degree Of Branching Research Articles

Assessment of starch branching and lamellar structure in rice flours

Apparent amylose content is used to describe milled rice flour composition. This spectrophotometric method is often the only direct measurement of starch structure in routine quality analysis. However, starch exhibits 6 levels of structure. The (supra)molecular starch structure in rice flours was measured: average degree of branching by 1H NMR spectroscopy and semi-crystalline lamellar structure by small angle X-ray scattering (SAXS). The suitability of these methods in routine quality analysis for breeding programs or the food industry was assessed in terms of precision and accuracy. Determination of apparent amylose content exhibits high precision (ca 5 % error) but low accuracy. Determination of average degree of branching exhibits a similar precision but good accuracy. Sample preparation (dissolution) is the first source of error in 1H NMR spectroscopy and presumably also in spectrophotometry. Within narrow ranges of apparent amylose content (less than 2.5 % absolute difference) differences in average degree of branching and lamellar structure could be observed. The difference between chemical structures of different amyloses/amylopectins within a given sample is not negligible. This opens a way to explore how finer details of molecular and supramolecular starch structure can play a role in understanding rice quality.

Preparation of branched polystyrene by free radical emulsion polymerization in the presence of functional monomer

ABSTRACTSeveral branched polystyrenes were prepared by free radical emulsion polymerization in the presence of α-mercaptohexyl methacrylate (MHM) as the chain transfer monomers, potassium peroxodisulfate as the initiator and sodium dodecyl benzene sulfate as the emulsifier. Branched polystyrenes of high molecular weight and high branching degree were obtained. The obtained polymers were characterized by using three detection size exclusion chromatography (TD-SEC). The branched polystyrenes showed considerably higher molecular weights and higher branching degrees using this reaction system. The higher the mole ratio of MHM to monomer or the higher mole ratio of MHM to initiator, the higher were the obtained absolute weight average molecular weight and the branching degree of the obtained polystyrenes. In addition, low temperature of polymerization reaction also contributed to the high average molecular weight and the high average branching degree of branched polystyrene. The higher average molecular weight of branched polystyrene obtained in this system was accompanied by the higher average branching degree of the branched polystyrene. It was also shown that the nature of branched structures was not affected by the amount of initiator and reaction temperature of the polymer.

The effect of baking and enzymatic treatment on the structural properties of wheat starch

In this study, bread was baked with and without the addition of α-amylase. Starch was extracted from the baked bread and its molecular properties were characterized using 1H NMR and asymmetric flow field-flow fractionation (AF4) connected to multi-angle light scattering (MALS) and other detectors. The approach allows determination of molar mass, root- mean-square radius and apparent density as well as the average degree of branching of amylopectin. The results show that starch size and structure is affected as a result of the baking process. The effect is larger when α-amylase is added. The changes include both a decrease molar mass and size as well as an increase in apparent density. Moreover, an increase in average degree of branching and the number of reducing ends H-1(β-r) and H-1(α-r) can be observed.

Cloud point pressure in the system polyethylene + ethylene – Impact of branching

We propose here a simple theory for polydisperse, branched polyethylene dissolved in ethylene based on a cubic equation, namely the Sako-Wu-Prausnitz-equation of state, in combination with the Lattice Cluster Theory in the incompressible version, which is predictive concerning the branching, while using continuous thermodynamics to account for polydispersity with respect to the molecular mass. The new theory considers polymers to follow the Schulz-Flory distribution and to adopt an average degree of branching. It does not require different parameters for different molar masses, polydispersities or degrees of branching and hence, the number and mass average molar mass as well as average branch content are sufficient. We parameterize this theory for ethylene based on critical data and for polyethylene based on simple arguments and some experimental data of n-alkanes. The binary parameter describing the dispersion energy and its temperature dependence stemming from Lattice Cluster Theory is fit to experimental cloud point data from literature of one specific sample of polyethylene in ethylene. The theory is then used to predict the cloud point curves and critical properties of nine other polyethylene samples in ethylene. The fit and predicted cloud point curves show quantitatively correct temperature dependence. For high polydispersities, the concentration dependence is only qualitatively correct, which is most probably due to the oversimplified Schulz-Flory distribution. The influence of branching on cloud point pressures and critical pressures at constant temperature is predicted quantitatively correct.

"To measure is to know": how advances in image analysis are supporting neural repair strategies

Neuronal regeneration in the peripheral nervous system arises via a synergistic interplay of neurotrophic factors, integrins, cytoskeletal proteins, mechanical cues, cytokines, stem cells, glial cells and astrocytes. A plethora of additional potential factors are yet to be discovered (Yiu and He, 2006). In spite of encouraging progress, axonal repair in the central nervous system (CNS) remains elusive. There is a growing consensus that in order to capture such a moving target, a systematic approach has to eclipse the “trial and error” methodology that has proven so effective in many other instances. The role of large scale automation is critical in such an undertaking. This philosophy has in fact been championed for many years already by Big-Pharma together with larger academic laboratories under the heading: “High Content Analysis” (HCA). Neuronal cells in 2D microplate cultures are generally used (see Figure 1A). They are exposed to libraries of test compounds and variable environmental conditions as their response is being measured (e.g., axonal length, nucleus size, number of branching points…). More complex model systems are gaining traction, including cell co-cultures, neural explants, 3D cell cultures, organotypic slices, or whole organisms such as zebrafish. But traditional neuronal cell cultures remain a workhorse of research against neurodegenerative diseases.

Synthesis and characterization of novel hydroxyl-terminated hyperbranched polyurethanes

Abstract A series of novel hydroxyl-terminated hyperbranched polyurethanes (HBPUs) were synthesized via stepwise polymerization by diethanolamine (DEOA), isophorone diisocyanate (IPDI) and trimethylolpropane (TMP). It is interesting to note that the HBPUs can be purified by water. The HBPUs were characterized with 1H nuclear magnetic resonance (NMR), 13C NMR, Fourier transform infrared spectroscopy (FT-IR) and elemental analysis. The average degree of branching (DB) of HBPUs was calculated from the first generation to the fourth generation to be 1.00, 0.74, 0.59 and 0.57 by quantitative 13C NMR, respectively. The branching model and molecular structure of HBPUs were deduced by the 13C NMR and the value of DB. To investigate the changes of hydrogen bonding interaction in HBPUs with a variation in structure of different generations, the deconvolution of FT-IR spectra was carried out using Origin 7.0 software through the Gaussian curve-fitting method. The ratio of hydrogen-bonded -NH and -OH groups of HBPUs was calculated to be 80.8%, 85.1%, 84.8% and 85.4% from the first generation to the fourth generation by deconvoluted -NH and -OH zone, respectively. The interaction of hydrogen bonding and glass transition temperature (Tg) of HBPUs increased with the increase of generation. The trend of thermal stability and Tg coincide with the change of hydrogen-bonded interactions.

Multi-Objective Optimization of Bulk Vinyl Acetate Polymerization with Branching

Inclusion of long chain branching (LCB) in polymers is a challenging and important task in any free radical polymerization as LCB influences polymer product quality. In the present case, batch optimization study for the bulk polymerization of vinyl acetate has been considered to find optimal process conditions for imparting LCB in polymer architecture. A theoretical study has been conducted with a validated model to observe the effect of live radical concentration on LCB as this is an important factor for branching in polymer via chain transfer to polymer route. In order to obtain better polymer product in less time at various temperatures, a need was observed to perform a multi-objective optimization study as the selected objectives were conflicting in nature. Owing to the complex nature of moment-based species balance equations and molecular weight distribution function, elitist non-dominated sorting genetic algorithm II (NSGA II), a well-established multi-objective evolutionary algorithm, has been employed as an evolutionary computation method to find out the Pareto optimal solutions. Minimization of polymerization time, maximization of molecular weight and maximization of number average degree of branching (Bn) can be simultaneously achieved, while the solutions were obtained within the experimental range of polydispersity index and weight average molecular weight (Mw) given in the open literature. Results show a wide range of process choices satisfying process objectives and constraints, both in low as well as high temperature regions.

Degree of branching of the hyperbranched polymers resulted from ab2 polycondensation with substitution effect

The analytical expressions of the various structural units and the average degree of branching for the hyperbranched polymers resulted from AB2 polycondensation with substitution effect were derived by the kinetic mechanism. The reactivity difference between the B group in linear unit and that in terminal group has great effect on the molecular parameters of the products obtained. The concentration of terminal units has a maximum with the increase of the conversion of A groups (x). The higher the reactivity ratio (r) of linear B group to branched one is, the later the maximum appears and the larger it is. The degree of branching of the hyperbranched polymers obtained is controllable by adjusting the parameters of r and x, which increases with increasing both x and r.

Emulsion polymerization of isoprene. Estimation of the branching exponent with the help of a mathematical model

AbstractThis work investigates a batch and unseeded emulsion polymerization of isoprene at 10°C with n‐dodecylmercaptan as chain transfer agent (CTA). The obtained polyisoprene (PI) was analyzed by size exclusion chromatography (SEC) with on‐line viscometry. A global polymerization model was adjusted to the measurements of conversion, average particle size, and average molecular weights. The CTA concentration strongly affects the average molecular weights but has a negligible effect on conversion, average particle diameter, and average branching. Due to the combined effects of chain transfers to the polymer and to the CTA, the final molar mass distributions exhibited dispersity indexes higher than 10. The polymerization model predictions on the average degree of branching was combined with an ideal SEC model for adjusting the branching exponent of PI in tetrahydrofuran at 25°C that resulted ε = 2.5. A sensitivity analysis showed that +20% errors in $\overline{M}$w induced variations in ε lower than −10%. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010

Preparation of branched polyacrylonitrile through self‐condensing vinyl copolymerization

AbstractBranched polyacrylonitrile (PAN) was prepared through a self‐condensing vinyl copolymerization of acrylonitrile and 2‐(2‐bromopropionyloxy)ethyl acrylate (BPEA). The branched architecture of the product was confirmed by NMR spectra and the average degree of branching (DB) was estimated. Through a comparison of the intrinsic viscosity of the product with that of its linear analogue, the contraction factor g′ was calculated. It was found that the viscosity of the branched PAN was obviously lower that that of linear PAN. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008

Mathematical modeling of the bivariate molecular weight—Long chain branching distribution of highly branched polymers.: A population balance approach

In the present study a population balance approach is described to follow the time evolution of molecular polymer properties in free-radical polymerizations. The model formulation is based on the fixed pivot technique (FPT) which was properly adapted in two dimensions in order to calculate the bivariate molecular weight–long chain branching distribution (MW–LCBD) for highly branched polymers like poly(vinyl acetate) (PVAc) and low-density poly(ethylene) (LDPE) produced in chemically initiated free-radical polymerization systems. The method assumes that the overall polymer population can be assigned to selected discrete points which are also called ‘grid points’. Accordingly, dynamic bivariate population balance equations (PBEs) are derived for the ‘live’ and ‘dead’ polymer chains, which are solved at the specified grid points. Thus, the infinite size of differential molar balance equations is reduced to a smaller and feasible system of differential equations. The validity of the numerical calculations is examined via a direct comparison of simulation results obtained by the 2-D FPT with available experimental data of the molecular weight distribution (MWD), number and weight average molecular weights ( M n , M w ) and number average degree of branching ( B n ) of highly branched polymerization systems (i.e., Vac and LDPE). In general, the 2-D FPT can provide very accurate predictions of the molecular and branching characteristics of highly branched polymers in a relatively short time. It is important to point out that, to our knowledge, this is the first time that the joint MW–LCBD for branched polymers has been calculated by a sectional grid method via the direct solution of the governing PBEs for both ‘live’ and ‘dead’ polymer chains.

Formation of Short and Long Chain Branches during the Free Radical Functionalization of Polyamide 6 in the Melt

Polyamide 6 (PA6) was treated in the melt at 230 °C in a discontinuous mixer with diethyl maleate (DEM) and dicumyl peroxide (DCP). The grafting of DEM to PA6 chains was investigated by 1H NMR analysis, and it reached easily up to 4.5 mol %. The grafted diethyl succinate groups (DES) can successively react with terminal amino groups of different polyamide macromolecules, thus yielding branched polyamide macromolecules. The average degree of branching, determined by titration analysis, is about one per macromolecule under the used experimental conditions and can be improved by further blending with PA6. Thermal analysis of branched PA6 showed lower melting and crystallization temperatures than those of simply processed linear PA6. Blends of unmodified and functionalized polyamide showed a higher viscosity and a more effective shear thinning behavior than the simply processed linear PA6. Experimental evidence was discussed, and a possible reaction mechanism was proposed.

Preparation of linear low‐density polyethylene by the in situ copolymerization of ethylene with an iron oligomerization catalyst and rac‐ethylene bis(indenyl) zirconium (IV) dichloride

AbstractAn iron oligomerization catalyst, [(2‐ArNC(Me))2C5H3N]FeCl2 [Ar = 2,6‐C6H3(F)2], was combined with rac‐ethylene bis(indenyl)zirconium (IV) dichloride [rac‐Et(Ind)2ZrCl2] to prepare linear low‐density polyethylene (LLDPE) by the in situ copolymerization of ethylene. A series of LLDPEs with different properties were prepared by the alteration of the reaction temperature, Fe/Zr molar ratio, Al/(Fe + Zr) molar ratio, and reaction time. The structures of the polymers were characterized with differential scanning calorimetry, 13C NMR, gel permeation chromatography (GPC), and so forth. The melting points, crystallizations, and densities of the resulting products increased, and the average branching degree decreased, as the reaction temperature, Al/(Fe + Zr) ratio, and reaction time increased. The melting points, crystallizations, and densities of the polymers decreased, and the average branching degree increased, when the Fe/Zr ratio increased. The 13C NMR and GPC results showed that there were no unreacted α‐olefins remaining in the resulting polymers because the percentage of low‐molar‐mass sections (C4–C10) of the oligomers obtained with this catalyst was very high (>70%). In addition, the formation of polymers with two melting points under different reaction conditions was examined in detail, and the results indicated that the two melting points of the polymers could be attributed to polyethylene with different branches. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 984–993, 2005

Model of Hyperbranched Polymerization Involving AB2 Monomer and B3 Core Molecules both Reacting with Substitution Effect

A kinetic model of hyperbranched polymerization is presented where an AB2 monomer reacts with up to 10% of a B3 one (A and B are functional groups) to yield a hyperbranched polymer. The model consists of two compact rate equations for entire distributions of two kinds of molecules that are formed in the system. Changes in reactivity of B groups in the form of the so-called first shell substitution effect are taken into account. Molecular parameters, namely the number and weight averages of polymerization degree as well as the average degree of branching of hyperbranched molecules, are extracted out from the rate equations and plotted against conversion.

EMULSION COPOLYMERIZATION OF ACRYLONITRILE AND BUTADIENE. SEMIBATCH STRATEGIES FOR CONTROLLING MOLECULAR STRUCTURE ON THE BASIS OF CALORIMETRIC MEASUREMENTS

Fil: Vega, Jorge Ruben. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Santa Fe. Instituto de Desarrollo Tecnologico para la Industria Quimica. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnologico para la Industria Quimica; Argentina

Theoretical consideration of the molecular mass distribution of starlike polymers formed by attachment of linear polymers to dendritic cores

AbstractStar‐shaped polymers can be synthesized by condensation of linear polymers to dendritic cores. The distribution of molecular masses of such hybrid star polymers and the factors influencing it have been investigated by calculations based on population balance equations and Laplace transformations. Moreover, the expressions for numerical calculations of molecular mass distributions have been derived for both Poisson and Schultz–Zimm types of initial molecular mass distributions. According to the calculation results, the molecular mass distribution of the star polymers is strongly dependent on the distribution of the length of linear polymers. Beyond this, the molecular mass development is affected by several parameters that describe the reaction degree of dendritic cores, thus, by the fraction of all functional groups of dendritic cores involved in grafting, denoted by p; the average branching degree of one starlike molecule, represented by ρ; or the fraction of dendritic molecules becoming the cores of star polymers, expressed by p/ρ, provided the star molecule contains only one core. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2751–2758, 2001

Molecular Parameters of Hyperbranched Copolymers Obtained by Self-Condensing Vinyl Copolymerization, 2. Non-Equal Rate Constants

The kinetics, molecular weight averages, and the average degree of branching, DB, are calculated for the self-condensing vinyl copolymerization (SCVCP) of a vinyl monomer M with an inimer AB* in the case of different reactivities of active species. Emphasis is given to two limiting cases: formation of macroinimers occurs if the monomer M is more reactive than the vinyl groups of inimers or polymer, and hyperstars are formed in the opposite case. It is shown that the kinetics, the molecular weight averages, and the average degree of branching strongly depend on the relative reactivities of monomer and inimer. Comparison with experimental data shows that consistent fits of the reactivity ratios can be obtained.

Monte Carlo Simulation of Hyperbranched Copolymerizations in the Presence of a Multifunctional Initiator

The Monte Carlo method is applied to simulate the copolymerization of a self-condensing vinyl monomer and a conventional vinyl monomer in the presence of a multifunctional initiator at equal rate constants. With the increase of the molar ratio of self-condensing vinyl monomer in the monomer composition, the number average degree of polymerization decreases and the weight average degree of polymerization decreases at a lower conversion of double bonds but increases at a higher conversion of double bonds. The molecular weight distribution, PI, changes from 1.01 to 12.0 and the average degree of branching, DB, increases from 0 to 0.456. We discovered that the addition of conventional vinyl monomer can modify the ratio of multi-arm hyperbranched macromolecules in the product, i. e., the content of macromolecules with core moiety will increase with the increase of the ratio of conventional vinyl monomer. The possibility of controlling PI and DB by changing the conversion and monomer compositions is demonstrated.

Substituent distribution in highly branched dextrins from methylated starches

Granular potato starch and amylopectin potato starch were methylated to molar substitutions (MS) up to 0.29. Extensive alpha-amylase digestion gave mixtures of partially methylated oligomers. Precipitation of larger fragments by methanol yielded mainly α-limit dextrins (84–99%). Methanol precipitates were extensively digested with beta-amylase yielding α,β-limit dextrins. The average substitution level of branched glucose residues in the dextrins thus obtained was determined after per deuteriomethylation by using FAB mass spectrometry, and compared with that of the linearly linked glucose residues. The present work demonstrates that methylation does not show any preference for substitution at either branched or linearly linked glucose residues, taking into account the inherently lower amount of substitution sites at branched residues. The results corroborate earlier studies wherein it was found that substituents in branched regions are distributed almost randomly. In addition, the data enable the determination of the average degree of branching of partially methylated dextrins.

Molecular Parameters of Hyperbranched Copolymers Obtained by Self-Condensing Vinyl Copolymerization. 1. Equal Rate Constants

The kinetics, molecular weight averages and the average degree of branching, DB, are calculated analytically for the self-condensing vinyl copolymerization (SCVCP) of a vinyl monomer M with an “inimer” AB*, i.e., a molecule having a vinyl group A and an initiating group B*. MWD and DB strongly depend on the monomer/inimer ratio γ = M0/I0 (or the “dilution factor”, γ + 1 = (M0 + I0)/I0). At low conversions, the process resembles a living polymerization of M, where the AB* inimers act as initiators only; at high conversions, the process resembles a self-condensing vinyl homopolymerization (SCVP) of AB* inimers. For a high monomer/inimer ratio (γ ≫ 1), the number-average molecular weight, M̄n, is given by the product of the values for the SCVP of inimer and the living polymerization of monomer initiated by inimer. For a given M̄n value, the polydispersity index decreases with γ. For γ > 1, DB decreases with γ, however, the DB values are 4 times higher than expected from the “dilution” of AB* molecules by M molecules. For low values of γ, DB even exceeds the values for a homo-SCVP; a maximum of DB = 0.5 is reached at γ ≈ 0.6. These effects can be explained by the addition of monomer molecules to in-chain active centers (i.e., in linear segments) leading to very short branches. The trends predicted by our calculations are confirmed by preliminary experimental data.