Quantification Of Branching Research Articles

Quantification of branching within high molecular weight polymers with polyester backbones formed by transfer-dominated branching radical telomerisation (TBRT).

New branched polymerisations offer previously inaccessible macromolecules and architectural understanding is important as it provides insight into the branching mechanism and enables the determination of structure–property relationships. Here we present a detailed inverse gated 13C NMR characterisation of materials derived from the very recently reported Transfer-dominated Branching Radical Telomerisation (TBRT) approach to quantify branching and provide an insight into cyclisation.

A combined photoionization time-of-flight mass spectrometry and laser absorption spectrometry flash photolysis apparatus for simultaneous determination of reaction rates and product branching.

In recent years, predictions of product branching for reactions of consequence to both combustion and atmospheric chemistry have outpaced validating experiments. An apparatus is described that aims to fill this void by combining several well-known experimental techniques into one: flash photolysis for radical generation, multiple-pass laser absorption spectrometry (LAS) for overall kinetics measurements, and time-resolved photoionization time-of-flight mass spectrometry (PI TOF-MS) for product branching quantification. The sensitivity of both the LAS and PI TOF-MS detection techniques is shown to be suitable for experiments with initial photolytically generated radical concentrations of ∼1 × 1012 molecules cm-3. As it is fast (μs time resolution) and non-intrusive, LAS is preferred for accurate kinetics (time-dependence) measurements. By contrast, PI TOF-MS is preferred for product quantification because it provides a near-complete picture of the reactor composition in a single mass spectrum. The value of simultaneous LAS and PI TOF-MS detection is demonstrated for the chemically interesting phenyl radical + propene system.

Effects of Chain Transfer Agent and Temperature on Branching and β‐Scission in Radical Polymerization of 2‐Ethylhexyl Acrylate

AbstractPoly(2‐ethylhexyl acrylate) is synthesized by conventional radical bulk polymerization both with and without 1‐dodecane thiol as chain transfer agent (CTA) at temperatures from 4 to 140 °C. Electrospray‐ionization mass spectrometry is used to analyze the polymer. This reveals the occurrence of significant β‐scission at high temperature and confirms the presence of CTA‐capped polymers at all temperatures, as well as combination products from 4 to 65 °C. Subsequent 13C melt‐state NMR analysis allows quantification of branching and β‐scission. Both are reduced when CTA is present, consistent with a “patching” effect. As expected, the amounts of β‐scission and branching increase with synthesis temperature, although β‐scission dominates at the highest temperature. The backbiting rate coefficient of 2‐ethylhexyl acrylate is determined from NMR results, taking β‐scission into account for the first time. Remarkable agreement with literature kbb values is obtained, especially for activation energy. This strongly suggests family‐type behavior for acrylate kbb.

In situ study of aggregate topology during growth of pyrolytic silica

Ramified aggregates are formed in many kinetically-limited growth processes such as in sooting flames. The structures are disordered and present a challenge to quantification. The topology of such nanomaterials is important in understanding their formation and properties. Recently, a method has been developed for the quantification of branching in aggregates using small-angle scattering. The method allows for determination of the average number of branches, branch length, short circuit path through an aggregate, aggregate total mass, aggregate polydispersity, primary particle coordination number, Sauter mean diameter, primary particle polydispersity, particle size distribution, and surface to volume ratio. In this report the new topological method is applied to in situ measurements previously published from a flame aerosol as a function of height above the burner. The topological evolution of primary and fractal structures is observed. This facilitates the understanding of growth dynamics and the structural rearrangements that occur during flame synthesis.

Assessment of the Branching Quantification in Poly(acrylic acid): Is It as Easy as It Seems?

Branching in polymers is an important feature that plays a role in their applications. The degree of branching (DB) has been quantified in several polymers using NMR spectroscopy. In this work, the DB of poly(acrylic acid), PAA, was quantified. The precision and accuracy of DB quantification in this polymer has been assessed for the first time. Incomplete dissolution lowers the accuracy of DB. Moisture content, chain end, and impurities have to be taken into account to assess the solubility correctly. The incomplete solubility may be partially due to some clustering and it might for example explain the notable inaccuracy of the molecular weights determined by SEC for PAA. The error introduced during data treatment in NMR spectroscopy affects the precision of DB. This study enables the design of the best approach for a precise and accurate DB quantification not only for PAA but also for other branched polymers. An accurate DB increases the knowledge of the polymer structure, enhancing the capacity to tailo...

Quantification of branching in fumed silica

The fractal structure of ceramic aggregates has been widely studied in terms of the mass fractal dimension and primary particle size. However, there has not yet been a quantitative description of the branched topology in these structures. In this work, the highly ramified aggregate structure in six commercial grades of hydrophilic fumed silica is investigated. Ultra-small angle X-ray scattering was coupled to a hierarchical scattering model, the unified scattering function, to obtain topological parameters. These generic topological parameters were used to quantify branching and were then compared with simple aggregation simulations. Surprisingly, a single parameter, the sticking probability, can empirically account for complex topological differences in the materials studied. It is found that samples of higher specific surface area display a higher branch fraction. For grades of highest specific surface area, a hyper-branched structure is observed with extensive branch on branch aggregation. This approach can be used to quantify complex morphological differences in ceramic oxide and carbon black aggregates.

Three-dimensional reconstruction of Haversian systems in human cortical bone using synchrotron radiation-based micro-CT: morphology and quantification of branching and transverse connections across age.

This study uses synchrotron radiation-based micro-computed tomography (CT) scans to reconstruct three-dimensional networks of Haversian systems in human cortical bone in order to observe and analyse interconnectivity of Haversian systems and the development of total Haversian networks across different ages. A better knowledge of how Haversian systems interact with each other is essential to improve understanding of remodeling mechanisms and bone maintenance; however, previous methodological approaches (e.g. serial sections) did not reveal enough detail to follow the specific morphology of Haversian branching, for example. Accordingly, the aim of the present study was to identify the morphological diversity of branching patterns and transverse connections, and to understand how they change with age. Two types of branching morphologies were identified: lateral branching, resulting in small osteon branches bifurcating off of larger Haversian canals; and dichotomous branching, the formation of two new osteonal branches from one. The reconstructions in this study also suggest that Haversian systems frequently target previously existing systems as a path for their course, resulting in a cross-sectional morphology frequently referred to as 'type II osteons'. Transverse connections were diverse in their course from linear to oblique to curvy. Quantitative assessment of age-related trends indicates that while in younger human individuals transverse connections were most common, in older individuals more evidence of connections resulting from Haversian systems growing inside previously existing systems was found. Despite these changes in morphological characteristics, a relatively constant degree of overall interconnectivity is maintained throughout life. Altogether, the present study reveals important details about Haversian systems and their relation to each other that can be used towards a better understanding of cortical bone remodeling as well as a more accurate interpretation of morphological variants of osteons in cross-sectional microscopy. Permitting visibility of reversal lines, synchrotron radiation-based micro-CT is a valuable tool for the reconstruction of Haversian systems, and future analyses have the potential to further improve understanding of various important aspects of bone growth, maintenance and health.

Scattering Function for Branched Wormlike Chains.

Wormlike or threadlike structures with local cylindrical geometry are abundantly found in nature and technical products. A thorough structural characterization in the bulk for a whole ensemble, however, is difficult. The inherent semiordered nature of the tortuous large-scale structure and especially the quantification of branching renders an assessment difficult. In the present work we introduce a hybrid function expressing the scattering intensities for X-rays, neutrons, or light in the small-angle regime for this system. The function is termed "hybrid" because it employs terms from different approaches. The large-scale structure is described via a Guinier term as well as a concomitant power-law expression in momentum transfer q taken from the so-called unified function. The local cylindrical shape, however, is taken into account through a form factor for cylinders from rigid-body modeling. In principle, the latter form factor can be replaced by an expression for any other regular body so that the new hybrid function is a versatile tool for studying hierarchical structures assembled from uniform subunits. The appropriateness and capability of the new function for cylindrical structures is exemplified using the example of a wormlike micellar system.

Quantification of Branching in Model Three-Arm Star Polyethylene

The versatility of a novel scaling approach in quantifying the structure of model well-defined 3-arm star polyethylene molecules is presented. Many commercial polyethylenes have long side branches, and the nature and quantity of these branches varies widely among the various forms. For instance, low-density polyethylene (LDPE) is typically a highly branched structure with broad distributions in branch content, branch lengths and branch generation (in hyperbranched structures). This makes it difficult to accurately quantify the structure and the inherent structure–property relationships. To overcome this drawback, model well-defined hydrogenated polybutadiene (HPB) structures have been synthesized via anionic polymerization and hydrogenation to serve as model analogues to long-chain branched polyethylene. In this article, model 3-arm star polyethylene molecules are quantified using the scaling approach. Along with the long-chain branch content in polyethylene, the approach also provides unique measurements...

Generalized fuzzy quantifiers and the modeling of fuzzy branching quantification

Lindstrm (Theoria, 1966; 32:186195) introduced a very powerful notion of quantifiers, which permits multiplace quantification and the simultaneous binding of several variables. Branching quantifica...

Detection and quantification of branching in polyacrylates by size-exclusion chromatography (SEC) and melt-state 13C NMR spectroscopy

Chain branching has been investigated in a homologous series of poly( n-alkyl acrylates) (methyl, ethyl, n-butyl, n-hexyl) obtained by radical polymerization. The total amount of chain branching was quantified using melt-state 13C nuclear magnetic resonance (NMR) spectroscopy. It gave access to low degrees of branching in both soluble and insoluble polyacrylates, homopolymers and copolymers. The lowest degree of branching was found for the ethyl member of the series with quantification by conventional solution-state NMR found to take a prohibitively long time. The method proposed here is compared to the ones published previously, and previous literature results are critically reviewed. The presence of long-chain branching (LCB) was selectively detected using multiple-detection size-exclusion chromatography (SEC), with LCB being found for all soluble homopolymers but the poly( n-butyl acrylate). This finding was confirmed by close examination of the Mark–Houwink parameters for the various polyacrylates studied in this work or those previously published.

029 Novel Parameters for Computer-Assisted Image Analysis to Study Angiogenesis

Angiogenesis is a dynamic process that requires interaction of proangiogenic and antiangiogenic factors. Several methodologies have been used to evaluate this process. The quail chorioallantoic membrane (CAM) is a suitable model to explore angiogenesis in vivo. Recently, the morphometric parameters of fractal dimension (Df) and grid intersection (ρ) are used to quantify angiogenesis in CAM. However, more information is necessary to understand angiogenic mechanisms. New methods to measure additional parameters such as the average blood vessel thickness, tortuousity, total branch length and complexity (junction node number), are described herein. For the analysis, CAM images were obtained from ex ovo culture of E8-E9 quail embryos. MatLab®(The MathWorks, Natick, MA) software was used for the analyses of branches nodes, thickness and length of the forming branches. Conventional morphometry was done using IPLab (Scanalytics, Fairfax, VA). To validate the new parameters, leptin, VEGF and neutralizing antibodies were evaluated. Leptin and VEGF treated CAM had increased complexity and vascular densities (Df = 1.5 ± 0.005; ρ = 12.3 ± 0.689) and (Df = 1.6 ± 0.006; ρ = 14.3 ± 0.465), respectively, compared to PBS control (Df = 1.3 ± 0.035; ρ = 8.6 ± 0.439). There was a corresponding decrease antileptin and anti-VEGF antibodies. The node-structural map applied to CAM images reveled 53% increase in the number of one-branch nodes and 50% increase in three-branch nodes with leptin compared to controls. Additionally, the total branch length was 30% greater with leptin along with a decrease in vessel thickness, The analyses allowed quantification of branching, tortuousity, thickness, and length of the new blood vessels. Together with the conventional morphometric parameters, these new analyses will help understand the mechanisms exerted by angiogenesis-modulating molecule.

Quantification of branching in disordered materials

AbstractThe phenomenon of structural branching is ubiquitous in a wide array of materials: polymers, ceramic aggregates, polymeric networks, and gels. Branching has a strong influence on the structure–property relationships of these materials. Despite the interdisciplinary importance and decades of effort, the analytical description and quantification of branching are weak. Existing techniques for polymers based on size exclusion chromatography and rheology are, at best, qualitative, and quantitative characterization techniques such as nuclear magnetic resonance spectroscopy and transmission electron microscopy (for ceramic aggregates) have limitations in providing routine quantification. For ceramic aggregates, theoretical work has dominated, and only a few publications on analytical studies exist to support the theory. Small‐angle scattering of X‐rays and neutrons can be used to quantify the branch content through application of concepts native to fractal geometry. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1395–1405, 2006

A defense of branching quantification

Adding branching quantification to a first-order language increases the expressive power of the language,without adding to its ontology. The present paper is a defense of this claim against Quine (1970) and Patton (1991).

Quantification of branching in polyethylene by 13C-NMR using paramagnetic relaxation agents

The role of paramagnetic relaxation agents Cr(acac) 3 and Fe(acac) 3 and the effect of 13C-NMR instrumental conditions have been studied in quantification of branching in polyethylene. The addition of relaxation agent, with spectrometer set for gated decoupling mode and a pulse delay of 8.5 sec, has considerably shortened the experimentation time. Various grades of polyethylene have been analyzed for branching through computerized 13C-NMR under these conditions.

On branching quantifiers in English

One of Hintikka's aims, in the paper Hintikka (1974),3 was to show that there are simple sentences of English which contain essential uses of branching quantification. If he is correct, it is a discovery with significant implications for linguistics, for the philosophy of natural language, and perhaps even for mathematical logic. Philosophically, it would influence our views of the ontological commitment inherent in specific natural language constructions, since branching quantification is a way of hiding quantification over various kinds of abstract abstract objects (functions from individuals to individuals, sets of individuals, etc.). Linguistically, the discovery of branching quantification would force us to re-examine, and perhaps re-interpret, Frege's principle of compositionality according to which the meaning of a given expression is determined by the meanings of its constituent phrases. For example, the meaning of a branching quantifier expression of logic like: