Average Degree Of Branching Research Articles

Molecular Parameters of Hyperbranched Polymers Made by Self-Condensing Vinyl Polymerization. 2. Degree of Branching

Using a modified definition, the average degree of branching, , the fraction of branchpoints, , as well as the fractions of various structural units are calculated as a function of conversion of double bonds for hyperbranched polymers formed by self-condensing vinyl polymerization (SCVP) of monomers (or “inimers”) with the general structure AB*, where A is a vinyl group and B* is an initiating group. The results are compared to those for the polycondensation of AB2-type monomers. At full conversion, is somewhat smaller for SCVP ( ∞ ≈ 0.465) than for AB2 systems ( ∞ = 0.5). There are two kinds of linear groups in SCVP whereas there is only one kind in AB2 systems. Since there are two different active centers in SCVP, i.e., initiating B* and propagating A* centers, the effect of nonequal reactivities on is also discussed. At a reactivity ratio of the two kinds of active centers, r = kA/kB ≈ 2.59, a maximum value of ∞ = 0.5 is reached. For the limiting case r << 1, a linear polymer resembling a polycondensate will be formed whereas for r >> 1 a weakly branched vinyl polymer is expected. NMR experiments allow for the determination of reactivity ratio r.

Theoretical study on the linking process of divinyl compounds with living precursors, 1. Uniform precursor chains

AbstractThe theoretical aspect of the linking reaction between divinyl compounds and uniform living precursors has been studied by using the model of threads going through the holes of buttons. The expressions of various molecular parameters of the clusters formed during the linking process, such as the number‐ and the weight‐average molecular weights, the average degree of branching, the branch distribution function, and the molecular weight distribution function, were rigorously derived. The critical condition of gelation is given as well. The theoretical results obtained are appropriate to the core formation process for the core‐first preparation procedure of star‐shaped polymers, and to the arm‐first approach using a uniform living precursor with low or moderate molecular size.

Modell des Sprachnetzwerks: Eine genaue statistische Beschreibung natürlichsprachlicher Texte

After exact adaptation of the natural language network model of W. Hilberg to natural texts, this model is used to determine important statistical values. The correctness of these values is verified by measuring them using natural texts. The model proves to be precise and of versatile use. From the model, important findings can be gained for text processing and information compression. Among these are exact mathematical correlations for calculating the average branching degree, the size of the vocabulary, the frequency distribution of the words and their successors and even the probability of unknown links. Moreover, the characteristics of texts become easily understandable with the help of the model. Due to the hierachical application of the natural language network model on texts, a gradual information compression has already been shown.

New polymer syntheses, 79. Hyperbranched poly(ester‐amide)s based on 3‐hydroxybenzoic acid and 3,5‐diaminobenzoic acid

AbstractThe reaction of 3‐acetoxybenzoyl chloride (4) with N,N′,O‐tris(trimethylsilyl)‐3,5‐diaminobenzoic acid (5) proceeds by highly selective and almost quantitative acylation of both amino groups. The resulting 3,5‐bis(3‐acetoxybenzamido)benzoic acid (6a), or its silylated derivative (6b), was polycondensed in bulk. The silylated monomer yielded the higher molecular weights. The condensation of 3,5‐diacetoxybenzoyl chlorides with diamines containing aliphatic protons yielded acetylated tetraphenols which served as “star centers” for polycondensation. The polycondensation of silylated 3,5‐bis(3‐acetoxybenzamido)‐benzoic acid (6b), with these “star centers” yieled in turn hyperbranched star polymers. The feed ratio of monomers and “star centers” allows the control of the molecular weight. 1H NMR spectroscopy of these hyperbranched star polymers was used to determine the average degree of polymerization (DP) and the average degree of branching (DB). 1H and 13C NMR spectroscopy also revealed that all polycondensations involve a significant extent of ester‐amide interchange reactions.

Fractionation and thermal behaviour of linear low density polyethylene

An ethylene 1- octene copolymer has been fractionated by molecular weight using successive solution fractionation (s.f.f.). The fractions obtained and the original copolymer were analysed with respect to the short chain branching distribution using analytical temperature rising elution fractionation (a.t.r.e.f.). A bimodal, very wide branching distribution is observed, both for the non-fractionated polymer and for the s.s.f. fractions. A decrease of the average degree of branching with increasing average molecular weight of the fractions is observed. The melting behaviour of isothermally crystallized samples was studied using differential scanning calorimetry (d.s.c.). The low-temperature melting endotherm is caused by the melting of small crystals, composed of very strongly branched molecules. The endotherms above the isothermal crystallization temperature are caused by the melting of thicker crystals, composed of weakly branched molecules.

Equilibrium polymerization with a multifunctional initiator

AbstractThe equilibrium polymerization with a multifunctional initiator is re‐treated theoretically. The expressions for the molecular weight distribution function, the number‐ and weight‐average degrees of polymerization, the distribution of the degree of branching and the average degree of branching of the polymer formed are rigorously derived. All the formulae given are much simpler than those reported by Baur and Eisenberg. A theoretical method is established by which all the molecular parameters of the polymer can be calculated from polymerization conditions, such as the equilibrium constants, the functionality of the initiator and the initial concentrations of initiator and monomer.

Application of multimethod procedure for characterization of branched polydisperse polymers

AbstractThe multimethod procedure for characterization of branched polydisperse polymers, including gel permeation chromatography, solution viscometry, melt viscometry, and differential scanning calorimetry, is described. An equation relating the average branching degree g¯x and the average number of branch points n̄bx has been derived and compared with the theoretical Zimm–Stockmayer equation. It has been found that both equations can be consistent for theta solvent and for the branching degree exponent b=1.5. Experimental data are given for trifunctionally branched bisphenol A polycarbonate.