Large Chain Length Research Articles

Self-consistent polymer integral equation theory: Comparisons with Monte Carlo simulations and alternative closure approximations

Recently, Schweizer, Honnell, and Curro reported a self-consistent formulation of the polymer reference interaction site model (PRISM) theory for polymer melts. The purpose of this paper is to compare the predictions of this theory to Monte Carlo simulations of hard chains thereby allowing an independent test of the various approximations in the PRISM theory. We find that the self-consistent PRISM theory with the Percus–Yevick (PY) closure is very accurate for both the intramolecular and intermolecular correlations in hard 20-mers for a wide range of densities. The accuracy of the theory for longer chains is somewhat diminished. We also compare the PRISM theory predictions using the PY, hypernetted chain (HNC), and Martynov–Sarkisov (MS) atomiclike closures. All the closures give equally good predictions at high densities, but the HNC and MS closures exhibit unphysical features, and ultimately fail to converge, at lower densities and/or large chain lengths.

Photocrosslinking of polymers containing cationically polymerizable groups in the side‐chain by sulfonium salts

The photochemically induced crosslinking of polymers having vinyloxy moieties in the side chain. Sulfonium salts used as photocatalysts initiated a cationic polymerization with high efficiency owing to a large kinetic chain length of the cationic polymerization of the vinylether moieties. The photoinduced crosslinking of polymers having epoxide side chains initiated by sulfoniumsalts was also reported.

Preparation and properties of UV‐autocurable BTDA‐based polyester multiacrylates. I. Effects of acrylic functionality and polyol molecular weight

AbstractA series of UV‐autocurable benzophenone tetracarboxylic dianhydride (BTDA)‐based polyester multiacrylate oligomers was synthesized and the effects of acrylic functionality and molecular weight on their physical properties were investigated. The multiacrylate oligomers were prepared by the ring‐opening reaction of glycidyl methacrylate and diacrylate oligomers containing pendant acid groups. The latter was prepared from BTDA, PEG, and hydroxyethyl acrylate (HEA). The obtained autocurable oligomers are cured rapidly when exposed to ultraviolet (UV) without the addition of photoinitiator or photosensitizer. Increasing the mole percentage of GMA in oligomer led to higher acrylic functionality and photocuring rate. The increasing in the functionality of acrylic oligomer was reflected in higher crosslinking density of the cured film which resulted in an increase in Young's modulus and breaking strength, while elongation at break decreased. On the other hand, increasing PEG molecular weight led to a decrease in Young's modulus and breaking strength due to existence of a small amount of acrylate phase and a larger chain length between crosslinks. The dynamic mechanical analysis results showed that storage modulus (E') and glass transition temperature (Tg) were affected by the mol % of GMA and the molecular weight of PEG in the cured oligomers. With increasing mol % of GMA in the oligomers, the storage modulus and Tg shifted to higher temperatures; however, storage modulus and Tg decreased with increasing PEG molecular weight.

Strong-stretching and Scheutjens–Fleer descriptions of grafted polymer brushes

The analytical theory of the conformations of end-grafted polymer ‘brushes’ is compared to direct numerical solutions of the mean-field equations developed by Scheutjens and Fleer. For moderately large chain length N, the predicted distribution of chain free ends and parabolic monomer density profile are confirmed in detail. The size (≈N1/3) and shape of corrections to the monomer density profile for finite N have been determined theoretically and are compared to numerical profiles. The fluctuations of chain conformations about the most probable paths are analysed in terms of an analogy to motion in a quantum-mechanical harmonic oscillator, in good agreement with numerical results.

Finite-size corrections and numerical calculations for long spin 1/2 Heisenberg chains in the critical region

Leading and next-to-leading-order finite-size corrections to the ground and first excited states are calculated for the spin-1/2 anisotropic Heisenberg model in the critical region. The analytic results are compared to numerical data obtained for chains up to a length of N=1024. It is found that, near the isotropic point, the asymptotic region where the results obtained for N to infinity are applicable sets in at very large N values, and for obtaining good accuracy in fitting the numerical data one has to take into account several correction terms, even at large (N>100) chain lengths.

A stochastic theory of community food webs. III. Predicted and observed lengths of food chains

This paper offers a quantitative theory of the length of food chains. The theory derives from a mathematical model of community food webs called the cascade model. The paper tests the predictions against data from real webs. An exact formula for the expected number of chains of each length in a model web with any given finite number, S , of species is, to our knowledge, the first exactly derived theory of the length of food chains. Since the numbers of chains of different lengths are dependent in the cascade model, we evaluate the goodness of fit between the observed and predicted numbers of chains by a Monte Carlo method. Without fitting any free parameters, and using no direct information about chain lengths other than that implied by the total number of species and the total number of links in a web, we find that the cascade model describes acceptably the observed numbers of chains of each length in all but 16 or 17 of 113 webs. Of 62 webs previously used to test the cascade model, the cascade model describes acceptably the chain lengths in all but 11 or 12. With a fresh batch of 51 webs, we establish first that (apart from two outlying webs) the numbers of links are very nearly proportional to the numbers of species and that the constant of proportionality is consistent with that in the original 62 webs. This finding verifies the so-called species–link scaling law with new data. The cascade model describes acceptably the chain lengths of all but 5 of the 51 new webs. Most of the 16 or 17 webs with chain lengths described poorly by the cascade model have unusually large average chain lengths (greater than 4 links) or unusually small average chain lengths (fewer than 2 links).

PROPERTIES OF UV-CURED POLYURETHANE ACRYLATES: EFFECT OF POLYOL TYPE AND MOLECULAR WEIGHT

Several families of UV-cured polyurethane acrylates were synthesized and the effects of polyol type and molecular weight on their physical properties were investigated. Increasing polyol molecular weight led to a lower polyol glass transition temperature, a smaller amount of a separate urethane acrylate phase, and a larger chain length between crosslinks. The first two effects were reflected in lower modulus and strength at room temperature while the larger chain length between crosslinks led to higher elongation at break (room temperature) and lower modulus at high temperatures. The use of different polyols (polycarbonate, polytetramethylene oxide, polypropylene oxide, and polycaprolactone) primarily affected the room temperature modulus due to differences in the position and breadth of the polyol glass transition. The properties of materials based on isocyanatoethyl methacrylate (IEM) and toluene diisocyanate-2-hydroxyethyl melhacrylate (TDI-HEMA) were also compared.

Excess functions for ( n-alkanenitrile + n-alkane) liquid mixtures 2. Excess enthalpies at 298.15 K for propanenitrile and n-butanenitrile with some C 5 to C 14n-alkanes

The excess enthalpy H E at 298.15 K has been measured for 7 ( n-alkanenitrile + n-alkane) mixtures: (1 − x)C 2H 5CN + xn-C 5H 12, + xn-C 6H 14, and + xn-C 7H 16; and (1 − x) n-C 3H 7CN + xn-C 6H 14, + xn-C 8H 16, + xn-C 12H 26, and + xn-C 14H 30. H E is positive, symmetrical in mole fraction, and between 1.2 and 1.7 kJ·mol −1 for x = 0.5. The dependence of H E on chain length resembles that of V E for the same mixtures, i.e. its magnitude increases with increasing alkane size and decreasing nitrile size in a fashion consistent with the diminished role of polarity in nitriles of large chain length.

Excess functions for ( n-alkanenitrile + n-alkane) liquid mixtures I. Excess volumes at 303.15 K for propanenitrile, n-butanenitrile, and n-hexanenitrile with some C 5 to C 14n-alkanes

The excess volume V E at 303.15 K has been measured for 11 ( n-alkanenitrile + n-alkane) mixtures: C 2H 5CN + n-C 5H 12, + n-C 6H 14, + n-C 7H 16, and + n-C 8H 18; n-C 3H 7CN + n-C 5H 12, + n-C 6H 14, + n-C 8H 18, + n-C 10H 22, + n-C 12H 26, and + n-C 14H 30; and n-C 5H 11CN + n-C 6H 14. Three of the mixtures, (C 2H 5CN + n-C 5H 12), ( n-C 3H 7CN + n-C 5H 12), and ( n-C 5H 11CN + n-C 6H 14), exhibit sign inversion with the negative portion of the V E isotherm occurring in nitrile-rich mixtures. For the remaining mixtures, V E is positive with a magnitude which increases with increasing alkane size and decreasing nitrile size in a fashion consistent with the diminished role of polarity in nitriles of large chain length.

'Single addition' and 'transnucleotidation' reactions catalyzed by polynucleotide phosphorylase. Effect of enzymatic removal of inorganic phosphate during reaction.

The reaction of the tetranucleotide, pA-A(2)-A, with 2'(3')-0-(alpha-methoxyethyl)uridine 5'-diphosphate, Mg(2+) ions, and M. luteus polynucleotide phosphorylase followed by mild acid treatment to remove the blocking groups results in a 49% yield of the desired single addition product, pA-A(3)-U, together with smaller amounts of pA-A-U, pA-A-A, pA-A(2)-U, pA-A(2)-A, pA-A(3)-A, pA-A(4)-U, and pA-A(4)-A. The side products are thought to arise from the phosphorolysis of the acceptor molecule by the inorganic phosphate formed in the reaction mixture and from subsequent additions to the various oligonucleotide species by the resulting adenosine 5'-diphosphate. A system developed for the removal of inorganic phosphate as it is formed in the synthesis involves the addition to the reaction mixture of calf spleen nucleoside phosphorylase and nicotinamide riboside and, under these conditions, pA-A(3)-U can be prepared in 90% yield with essentially no side products. Under similar conditions, pA-A(3)-A, pA-A(3)-G, and pA-A(3)-C may be prepared from pA-A(2)-A and the appropriate blocked nucleoside diphosphate in yields of 85-94%. The incubation of pA-A(2)-A alone with polynucleotide phosphorylase exhibits the phenomenon of "transnucleotidation" in that the molecule is partially converted to oligonucleotides of smaller and larger chain lengths. In the presence of the phosphate removal system, however, the tetranucleotide is not attacked by the enzyme, and thus, "transnucleotidation" appears to be simply a combination of phosphorolytic and addition reactions catalyzed by trace amounts of inorganic phosphate contaminating the enzyme and/or the substrate.

The Melting Temperatures of the n-Paraffins and the Convergence Temperature for Polyethylene.

The extrapolation of the melting points, T m , of the n-paraffins to large chain lengths (n → ∞) is reexamined in order to resolve the differences in the proposed values of the convergence temperature . Experimental liquid entropies can be made consistant with a term, R In n, proposed by Flory and Vrij. This term effectively replaces the well-known expression T m = T 0 (n + a)/(n + b) with an expression T m = T 0 (n + a)/(n + ln n + 6); thus, slowing the convergence rate and increasing T 0 from 141.1 °C to 144.7 °C. Independent estimates of the parameters in the melting relationship were obtained from thermodynamic data and the least squares estimate of T 0 = 144.7 °C (calculated from 33 melting points with a standard deviation of T m = 0.3 °C) could not be altered by more than ± 0.5 °C by any reasonable variation of the parameters. A simplified melting expression is obtained for polyethylene which includes both the chain end and fold surface energies, and it is shown that chain end effects partly account for the discrepancy between the 144.7 °C convergence temperature and experimental melting temperatures (~ 139 °C) of extended chain polyethylene crystals.

The long chain approximation in free radical reaction systems

A long chain approximation is presented for the analysis of free radical mechanisms. This permits the calculation of relative concentrations on the basis of the chain propagation reactions alone and is valid for large chain lengths. An application is given to the calculation of product distributions in the high-pressure thermal cracking n-hexadecane and comparisons are made with existing experimental data. Due to the meager information on rate constants and to the limited accuracy of the data these comparisons indicated the plausibility of the approximation but do not provide a measure of its accuracy.

Application of Cell Theory to Liquid Hydrocarbons

The cell theory in the formulation of Prigogine, Trappeniers, and Mathot and their assumptions are examined. The molecular volumes of n-paraffins of high molecular weight are well represented in terms of an energy and volume parameter characteristic of the repeating unit. Fairly good agreement for branched systems is also found on making the proper modifications in the equation of state. The resulting low temperature heats of vaporization seem reasonable. One can show that the theory leads to the Kurtz-Lipkin-Sankin relations and interprets, so far, for paraffins their K1 and K5. Isotherms up to about 1000 bars can be represented fairly satisfactorily, 80–90% of the total compression observed being accounted for. This applies to n-paraffins as well as polyethylene and, in a semiempirical manner, to polystyrene. The physical significance of the constants in the empirical Tait equation is explored. For large chain lengths C is a pure numeric and independent of structure and molecular weight, in qualitative conformity with experimental results. B is related to the ratio of characteristic energy and volume of the submolecule, or to the above parameter K1. These results argue in favor of extending the theory, so as to permit handling of a wider range of variables, and other types of molecules.