ISSN:0007-1641    

DOI:10.1002/pi.4980090202

出版商:John Wiley&Sons, Ltd    

年代:1977

数据来源: WILEY

摘要:

AbstractA simple (2, 2) Padé approximant based on the first three terms in the asymptotic cluster series for the expansion factor α2(z) is shown to give fairly good values over the entire positive range of the interaction parameter z. In a separate discussion it is shown by a specific example that extrapolations of viscosity data in good solvents and based on excluded‐volume relations for flexible chains must be used only with great caut

ISSN:0007-1641    

DOI:10.1002/pi.4980090203

出版商:John Wiley&Sons, Ltd    

年代:1977

数据来源: WILEY

摘要:

AbstractConfigurational properties, viz mean squares of the end‐to‐end distance (〈R2〉) and the radius of gyration (〈S2〉), probability distribution ofRand the ratio between mean squares of the principal axes of equivalent ellipsoid (〈XX2〉: 〈YY2〉:〈ZZ2〉), have been calculated for model polymer molecules under differing solvent conditions. The present study follows a computational statistical approach which is based on the Metropolis sampling technique. The molecules are represented by tetrahedral chains withtrans/gauchebond conformational energy difference equal to 1.0 kT. The solvent condition is characterised by the intersegmental interactions which are assumed to be given by a square‐well potential. The depth of the potential well, Δεs, serves to define the solvent parameter.It is shown that in the region Δεs∼−0.4 kT the configurational criteria for the existence of the theta condition are fulfilled (the chains assumed 〈R2〉 and 〈S2〉 values that correspond to the random‐walk state and the limiting probability function governing the end‐to‐end distance distribution is gaussian). The calculated values of 〈R2〉,〈S2〉 and 〈XX2〉 〈YY2〉:〈ZZ2〉 indicate that the chains in “good” solvents (Δεs<−0.4 kT) exist in highly extended configurations. As the system assumes the below‐theta conditions (Δεs<−0.4 kT) the extended configurations collapse into compact ones. Such compact configurations are not spherical but retain an appreciable degree of elongation. The probability distribution ofRin the limit of infinite chain length deviates significantly from the gaussian behaviour in both the above and below‐theta conditions. The present calculations suggest that the introduction of thetrans/gaucheconformational energ

ISSN:0007-1641    

DOI:10.1002/pi.4980090204

出版商:John Wiley&Sons, Ltd    

年代:1977

数据来源: WILEY

摘要:

AbstractNumber and weight average molecular weights and scattering behaviour of star molecules with extended branched nuclei are calculated by application of cascade theory. The nuclei considered arise from random polycondensation of monomers of the A3or of the A—B/C type. Nuclei of the first type are characterised by very large molecular polydispersities (Mw/Mnα Mw), while nuclei of the second type have less broad molecular weight distributions (Mw/Mnα Mn). The rays of the stars are assumed to be either monodisperse or to obey the Schulz—Flory “most probable” length distribution. Analytic expressions are given forMw, Mn, 〈S2〉zand the particle scattering factorPz(h)which was averaged over the ensemble. The results are compared with stars of spherical and uniform nuclei whose molecular weights and mean square radii of gyration equalMwNand 〈S2〉zNfrom the other two types of nuclei. In the limit of very large ray lengths the scattering behaviour is determined solely by the number of branchesz. At shorter chain length of the rays structure and polydispersity of the nuclei have marked influence. This influence is still easily noticed from the angular dependence of scattered light at chain lengths where no differences in the 〈S2〉zversusMwplot are detectable. The mean square radius of gyration depends only weakly on the number of rays and eventually becomes independent of it ifz15. In that limit 〈S2〉zdepends virtually on the length of the rays alone and its distribution. Stars whose rays have a most probable length distribution exhibit 〈S2〉zvalues twice as large as stars with monodisperse rays. A procedure is suggested and discussed for the determination of the number and length of the rays if the scattering behaviour of the isolated nucleus and the is

ISSN:0007-1641    

DOI:10.1002/pi.4980090205

出版商:John Wiley&Sons, Ltd    

年代:1977

数据来源: WILEY

摘要:

AbstractThe spanning tree model' (utilising Gaussian‐flight statistics) for the kinetics of simultaneous ring‐chain competition in linear and branched polycondensation reactions has been extended by the use of the path weighting method of cascade statistics to the system glycerol/adipic acid.In this system there is no single fixed increment in ring sizes as more units are added to the ring‐closing path, since a glycerol unit incorporated through the reaction of its two primary hydroxyls contributes a longer increment to the path length than when one primary and one secondary hydroxyl are involved. A computational method has been developed to count, as the reaction proceeds, the mean number of paths of all lengths available for forming a cycle back to a given root functionality, with each path receiving the correct Gaussian weight according to its l

ISSN:0007-1641    

DOI:10.1002/pi.4980090206

出版商:John Wiley&Sons, Ltd    

年代:1977

数据来源: WILEY

摘要:

AbstractIntramolecular reaction and gelation in reactions of a poly (propylene oxide) triol and hexamethylene di‐isocyanate in benzene at 70° have been investigated. The numbers of ring structures formed in the pre‐gelation region have been evaluated from cryoscopic measurements ofMnand overall extents of reaction of isocyanate groups. It is found that intramolecular reaction increases with initial dilution, and at a given dilution is a maximum for equimolar concentrations of reactive groups. Again, at a given initial dilution, more intramolecular reaction occurs than for linear polymerisations. Various ways of presenting the results are discussed, and one of them in particular, the extent of intermolecular reaction,pch, as a function of overall extent of reaction of the minority group,p, gives useful linear relationships. Also, by combining gelation and intramolecular reaction in terms of plots ofpchvs. p, a distinction can be drawn between what may be termed the chemical and physical gel points. Finally, values of the Flory‐Huggins interaction parameter,X, have been determined from the cryoscopic data. These show fairly normal behaviour ‐ they are generally less than 0.5 — with some dependence on the density of hydroxyl groups and the proportion of polyoxypropylene units present. Such behaviour is in sharp contrast with that found previously for poly (ethylene‐oxide)/hexamethylene di‐isoc

ISSN:0007-1641    

DOI:10.1002/pi.4980090207

出版商:John Wiley&Sons, Ltd    

年代:1977

数据来源: WILEY

摘要:

AbstractIn gel permeation chromatography on long‐chain branched polymers, calibration with linear samples leads to incorrect results. There are, however, several ways in which the data can be treated correctly. All of them call for the use of extra experimental information, such as viscosity or light scattering data of the whole polymer or the GPC eluent. The Drott—Mendelson method, using [η] of the whole polymer and GPC data, has been employed for analysing three low density polyethylene samples. The potentialities of viscometry and light‐scattering measurements in the GPC effluent have also been examined.From [η], Mwand GPC data the long‐chain branching index g′ can be derived in three ways, although it should be stated that the average g′‐values so found for polydisperse sample

ISSN:0007-1641    

DOI:10.1002/pi.4980090208

出版商:John Wiley&Sons, Ltd    

年代:1977

数据来源: WILEY

摘要:

AbstractIt is argued that one can envisage two extreme regimes in rubber. The first is a dilute regime, where crosslinks are the only significant interaction between chains, and is the conventional model. The other extreme is one in which a very entangled situation exists where the chain statistics under deformation are remote from free Gaussian statistics. This latter case is studied and it is argued that the entropy per crosslink takes the form\documentclass{article}\pagestyle{empty}\begin{document}$$ S = \frac{k}{2}\left\{{J^2 } \right.\left. {\left({{\textstyle{{1 - a} \over {1 - aj}}}} \right) + \log \left({{\textstyle{{1 - aj} \over {1 - a}}}} \right)} \right\} - k\left\{ {\left. {J^2 + \beta (J - 1)} \right\}} \right. $$\end{document}where α and β are independent of deformation but depend on temperature and density, andJ2is the usual first invariant. The dilute regime is α = β

ISSN:0007-1641    

DOI:10.1002/pi.4980090209

出版商:John Wiley&Sons, Ltd    

年代:1977

数据来源: WILEY

摘要:

AbstractCrosslinked polyacrylamide gels formed by copolymerisation of acrylamide andN,N′‐methylenebisacrylamide in aqueous solution have been characterised by viscoelastic measurements in the frequency range 0.05–150 Hz. These data are consistent with the model, derived from permeability data, of a non‐draining central core surrounded by a rather dilute freely draining zone. Rotary diffusional relaxation of the non‐draining cores is the major mechanism which contributes to relaxation at times below the experimental frequency scale. The results are in quantitative agreement with the data derived from the permeability studies. Though more than two‐thirds of the gel substance is packed into non‐draining zones, macromolecular probes of radii up to 4 nm find access to all the network strands, as determined by a new analysis of liter

ISSN:0007-1641    

DOI:10.1002/pi.4980090210

出版商:John Wiley&Sons, Ltd    

年代:1977

数据来源: WILEY

摘要:

AbstractModel‐networks designed for neutron scattering experiments were synthesised anionically. Each of the crosslinkages is surrounded by deuterated segments. The well defined correlation distancedbetween neighbouring crosslinkages is shown by the unique peak in the scattering diagrams. The productd Q−1/3‐Qbeing the swelling ratio of the network ‐ is a constant, which demonstrates the affine character of the deformation introduced by swelling. Taking into account the modulusG* of uniaxial deformation, the swelling intoQand the distancedbetween crosslinkages it was possible to estimate the memory‐termhmore a

ISSN:0007-1641    

DOI:10.1002/pi.4980090211

出版商:John Wiley&Sons, Ltd    

年代:1977

数据来源: WILEY