摘要:

AbstractThis paper describes a computer program that is useful in the elucidation and visualization of particular stereoregular polymer chains. The input is the fractions of isotactic, syndiotactic, and heterotactic triplets in a real polymer as determined by some technique such as NMR. The program calculates a matrix of conditional transition probabilities from these fractions. This matrix in conjunction with a random‐number generator is used with Monte Carlo techniques to calculate a specific sequence of 0's and 1's. The sequence contains 101 elements. This is the generated polymer chain. The number of various kinds of doublet, triplet, etc., is then counted for this particular generated chain, and compared with that calculated from the matrix for the chain of infinite length. Comparisons among these sets of figures show that the generated polymer chains are usually quite typical of the infinite chain.The application of NMR techniques to the determination of the relative numbers of isotactic, heterotactic, and syndiotactic triplets in synthetic polymers was pioneered by Bovey (1) several years ago. The data thus obtained can be used in a straightforward manner to calculate various average properties of the polymer chain. Although these average properties may be used to describe the polymer, frequently it is difficult to visualize exactly what a typical polymer chain might look like from a stereoregularity point of view. This paper describes a computer program that calculates various sequence averages for aninfinitepolymer chain and that generates by Monte Carlo techniques a polymer chain typical of the NMR data. In addition the program, by calculating various sequence averages for the generated polymer chain, permits evaluation of just how representative the generated polymer i

ISSN:0449-2994    

DOI:10.1002/polc.5070250103

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1968

数据来源: WILEY

摘要:

AbstractComputer programs in use in our laboratory for the calculation of binary and ternary copolymerization behavior are reviewed. In the case of binary copolymerization an analytical equation is available, allowing rapid and precise calculations of various parameters of interest. In the case of ternary and higher component systems numerical methods of integration are required. The application of the Runge‐Kutta method to ternary copolymerization systems is outlined. Examples and some of the difficulties encountered with both systems are presente

ISSN:0449-2994    

DOI:10.1002/polc.5070250104

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1968

数据来源: WILEY

摘要:

AbstractComputer programs we have developed during the course of studies on copolymerization, on terpolymerization, and on the chemical reactions of polymers are described. The programs are useful for (a) evaluating monomer reactivity ratios from either copolymerization or terpolymerization data, (b) for predicting the compositions of copolymers and terpolymers from monomer reactivity ratios and monomer feed composition data, (c) for calculating the extents of cyclization to be expected when inter‐sequence cyclizations occur in copolymers and terpolymers, and (d) for calculating the yields of products obtained when copolymers are degraded selectivel

ISSN:0449-2994    

DOI:10.1002/polc.5070250105

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1968

数据来源: WILEY

摘要:

AbstractA FORTRAN II program for calculating copolymer compositions, run numbers, diad, triad, tetrad, and pentad distributions, and sequence number distributions and sequence weight distributions for addition type copolymers is described. The program is applicable to both instantaneous and high‐conversion copolymer

ISSN:0449-2994    

DOI:10.1002/polc.5070250106

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1968

数据来源: WILEY

摘要:

AbstractA program has been written and used to compute vinyl terpolymer compositions as a function of monomer feed. The results are presented as a set of triangular contour maps. Six hypothetical monomers of typical reactivity have been investigated in their 20 possible terpolymerizations. With respect to composition it is concluded that variation in electronegativity is less important than the variation in resonance stabilization commonly encountered in vinyl monomers. The approach of these terpolymer systems to azeotropic behavior is graphically derived from the contour maps. Loci of partial azeotropy are drawn for a number of systems. No true ternary azeotropes have been observed.

ISSN:0449-2994    

DOI:10.1002/polc.5070250107

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1968

数据来源: WILEY

摘要:

AbstractThe classical methods of determining relative reactivities of monomers to free‐radical polymerization, namely polymerization to low conversion of several initial monomer compositions, purification of the polymers formed, compositional analysis, and fitting of the data to the differential form of the copolymer equation by any of several techniques, suffer from several problems. In particular, the various methods of treating the data assume no change in monomer composition at low conversion. This is a reasonable approximation when the reactivities are similar, but when they are grossly different (e.g., r1/r2>100), even 2 to 3% conversion can cause highly significant shifts in the monomer composition, particularly for those points where the more reactive monomer is present in relatively small amounts. Illustrations of the potential magnitude of these errors are provided. A computer program has been written that utilizes one of the integrated forms of the copolymer equation and thereby includes the conversion corrections in the treatment of the data. This procedure should yield more precise r1and r2values than the classical techniques, with less direct computational effort on the part of the investigato

ISSN:0449-2994    

DOI:10.1002/polc.5070250108

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1968

数据来源: WILEY

摘要:

AbstractExact functions expressing the distribution of the end‐to‐end vector for real chains of finite length are unknown. Moments of the distribution can be calculated, however, for linear chains unperturbed by excluded‐volume effects. Thus, second and fourth moments for real chains with interdependent bond rotational potentials, in the rotational isomeric state approximation, can be computed as a function of chain length by methods developed recently. These moments are here compared with those calculated for hypothetical models, e.g., for the Gaussian distribution (to which all distributions converge in the limit of infinite chain length), for the freely jointed chain, for the distribution involving the inverted Langevin function, for the freely rotating chain, for the Porod “wormlike” chain, and for the chain with independent bond rotations that have a symmetrical hindrance potential. The convergence of the series expansion for the distribution function in terms of its even moments obtained by Nagai is investigated for the freely jointed chain (for which any number of moments may be readily calculated). Application of this series to the model with interdependent bond rotations is also c

ISSN:0449-2994    

DOI:10.1002/polc.5070250109

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1968

数据来源: WILEY

摘要:

AbstractPrevious work has shown that it is possible to calculate the translational and rotational frictional coefficients of complex structures by modeling them by a surface shell of spherical elements. The basic equations of this shell model method and its application to spheres, prolate ellipsoids of revolution, proteins, and viruses, are reviewed here. Several new results are also presented. It is demonstrated analytically that the rotational frictional coefficient for a sphere, calculated according to the shell model, agrees with the Stokes‐Kirchoff law. The rotational frictional coefficients of right circular cylinders have been calculated by digital computation; end effects are less marked than they are according to a theory of Broersma. Finally, the sedimentation behavior of various geometrical arrays of oligomeric aggregates of spherical subunits has been tabulated, to facilitate application to multichain protein system

ISSN:0449-2994    

DOI:10.1002/polc.5070250110

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1968

数据来源: WILEY

摘要:

AbstractThe method of Flory was used to calculate unperturbed mean‐square dimensions of linear alkanes at 25°C by utilizing the assumption of three‐fold rotational isomerism and allowing, but giving small statistical weight to, configurations involving successive gauche rotations of opposite sign. The necessary 15 × 15 matrix multiplications were made with an IBM 1620 computer. The reciprocal square root of these calculated dimensions were assumed equal toAv, and diffusion coefficients of pentane through dotriacontane were then computed by means of the Kirkwood‐Stokes equation. These coefficients were then compared with experimental values from four different solvents and with self‐diffusion measurements. In general, it may be said that theory and experiment agree well for solvents of low viscosity. For more viscous solvents (tetralin and decalin) experimental diffusion coefficients are about 80% larger than those calculated for pentane. As chain length increases, however, better agreement is

ISSN:0449-2994    

DOI:10.1002/polc.5070250111

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1968

数据来源: WILEY

摘要:

AbstractAngular light scattering by polymer latex dispersions is used for determining the particle size distribution. The analysis consists of calculating the experimental Rayleigh ratios Vθ,vand Hθ,hfor vertically and horizontally polarized components of scattered light. Corrections for solvent scattering and reflection effects are also applied. The polarization ratios are calculated for each concentration and extrapolated to infinite dilution, thereby correcting for multiple scattering at finite concentrations. The polarization ratios at infinite dilution are converted to polarizations and compared with theoretical values corresponding to anticipated possible size distributions. A topographical map of the root‐mean‐square deviations on a plot of the size parameter versus the distribution parameter is obtained. This map gives an indication of the uniqueness of the fit over the range of theoretical values searched. Data obtained on a Dow polystyrene latex are used for an example analysis. Details of the computer routine are discussed. Similar programs exist for the size distribution analysis and determination of number concentration of spherical particles utilizing the angular absolute specific intens

ISSN:0449-2994    

DOI:10.1002/polc.5070250112

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1968

数据来源: WILEY