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  • 1970-1974  (562)
  • 1971  (562)
  • Physics  (500)
  • Engineering General  (62)
  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 575-586 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A quadratic thick shell element derived from a three-dimensional isoparametric element was first introduced by Ahmad and co-workers in 1968. This element was noted, however, to be relatively inefficient in representing bending deformations in thin shell or thin plate applications. The present paper outlines a selective integration scheme for evaluating the stiffness matrix of the element, in which each component of the strain energy is evaluated separately using a different Gaussian integration grid for each contribution. By this procedure, the excessive bending stiffness of the element, which results from the use of me quadratic interpolation functions, is avoided.The improved performance of this element, as compared with the original thick shell element, is demonstrated by analyses of a variety of thin and thick shell problems. Editors' note: A similar development was outlined by O. C. Zienkiewicz and co-workers in lnt. J. num. Meth. Engng, 3, 275-290 (1971). Some important details differ between the two papers which are thus complementary.
    Additional Material: 14 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 591-591 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 591-592 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 1-2 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 3-3 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 5-11 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It has long been recognized that permeability, compressibility and viscosity vary during the consolidation of soil. However, the introduction of these variations into consolidation theory leads to formidable difficulties due to their rendering the equations highly non-linear. Numerical methods are given herein which enable the governing equation to be solved for a variety of different non-linear laws.
    Additional Material: 3 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 13-24 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The simultaneous iteration method of obtaining eigenvalues and eigenvectors is employed for the solution of undamped vibration problems. This method is of significance when a few of the dominant eigenvalues and eigenvectors are required from a large matrix, and hence is particularly suitable for vibration problems involving a large number of degrees of freedom. It is shown that advantage may be taken of both the symmetry and the band form of the mass and stiffness matrices, thus making it feasible to process on a computer larger order vibration problems than can be processed using transformation methods. A method of allowing for body freedom is given and some numerical tests are discussed.
    Additional Material: 2 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 25-33 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The general eigenvalue problem Ax = λBx as arising from vibration problems tackled by the finite element method is often solved by the economization method in which the two matrices are reduced to a more manageable size and approximate answers are obtained.This paper analyses the method in a more mathematical way than previous accounts and leads to a definition of the optimum set of variables to be retained during the reduction. An extension to the method is suggested which allows the approximate eigenvalue to be improved and bounds are obtained on the eigenvalues of the full problem before reduction.An estimate is made of the calculation involved in the method and it is concluded, by reference to examples, that the extended method leads to a more efficient algorithm.
    Additional Material: 3 Tab.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 35-43 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A technique is described for solving the compressible flow equations in subsonic flow. The general quasi-linear equation ∇.g∇v = 0 is considered with g a function of ∇v. ∇v, and iterations of the form ∇.gn∇vn+1 = 0 are analysed, where g0 is suitably chosen and gn defined from vn for n≥1. This approach is applied to the compressible flow equations in terms of a velocity potential ø: monotonic convergence is predicted and at each iteration the error is multiplied by a factor less than the square of the greatest Mach number in the solution.Reliable convergence has been obtained in practice solving the linear equation for øn+1 by a finite difference method. The alternative of working in terms of the stream function ψ is discussed, and also discretization by the finite element method.
    Type of Medium: Electronic Resource
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 53-61 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A solution is presented for the computation of the transient thermoelastic stresses in a hollow cylinder with temperature boundary conditions given as a circumferential variation of surface heat transfer coefficient. The temperature distribution is solved explicitly. The problem is set up using the Airy stress function which leads to the biharmonic equation. This approach requires the satisfaction of three Michell integrals at the inner boundary in order to ensure single-valued displacements and rotation. An iterative method is described in which these integrals are all simultaneously satisfied and thus provide the necessary non-zero boundary conditions for the solution of the biharmonic equation which is rapidly solved by Gaussian elimination. Results are presented for the general case where the temperature is a function of r and θ. The computer program is checked by assuming a constant value of the surface heat transfer coefficients. In this case a closed form solution is obtained.
    Additional Material: 6 Ill.
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  • 12
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 103-117 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of the finite element rank force method for the dynamic analysis of redundant structures is presented. The applied loading consists of discrete and distributed loads. Both forced and free vibrations are considered, the latter yielding latent vectors corresponding to dynamic redundancies.It is shown that the dynamic properties of an element are given by a static flexibility matrix, an inverse mass matrix, a damping parameter and a displacement vector representing the effect of the applied distributed loading.
    Additional Material: 5 Ill.
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 119-129 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A stiffness matrix for a finite element having the planform of an annular segment is derived using the displacement approach. Numerical problems involved in the derivation are discussed and rapid convergence to exact solutions is demonstrated on three sample problems. It is concluded that the new element will be of great value to engineers concerned with the analysis of slabs of bridge decks curved in plan.
    Additional Material: 8 Ill.
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 145-147 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Dynamic Relaxation (DR) method of solving a set of simultaneous linear equations requires an estimate of the spectral radius of the matrix. Dividing each equation by the corresponding row sum of moduli of the elements of the matrix gives a convenient upper bound of unity to this. This note shows that the DR method then gives a faster asymptotic rate of the convergence than the degenerate Chebyshev method which it closely resembles.
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  • 15
    Electronic Resource
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 149-149 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 16
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 151-151 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 17
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 155-160 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The conventional central finite difference equations for the plane stress extension of flat plates are derived as a localized Ritz process. A dual differential-variational discretization of this type enables common classification of the finite difference and finite element methods. Also, it provides alternative methods of establishing sufficiency conditions and relative rates of convergence for discrete systems derived from a localized Ritz process, and the existence of solution bounds for discrete systems derived using difference procedures.
    Additional Material: 7 Ill.
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  • 18
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 161-179 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the development of consistent discrete models, via the concept of finite elements, of linear and non-linear electrothermomechanical behaviour of continuous bodies. In the development, general energy balances are utilized to derive equations governing electromagnetic fields over an element and coupled equations of motion and heat conduction of a typical element of the continuum. These equations make it possible to study a general class of field problems involving arbitrary geometries and boundary conditions. Sample problems are included.
    Additional Material: 9 Ill.
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  • 19
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 199-213 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical solution of the biharmonic equation in a rectangular domain is presented in the context of continuous dynamic programming techniques. The equations are specialized to the solution of elastic rectangular plates. A suitable approximate expression of a certain functional equation containing derivatives only in one direction is used to derive equations for the stiffness and flexibility matrices of the plate. It is shown that those matrices satisfy matrix Riccati equations subject to suitable initial conditions. It is also shown that the condition of optimality in the Hamilton-Jacobi-Bellman equation directly expresses a classical variational principle, i.e. the principle of complementary energy. Some numerical examples are finally presented.
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  • 20
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 181-198 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dynamic finite element technique, which is referred to in the literature as ‘computer-analysis’, is applied to wave propagation problems occurring in finite and semi-infinite linearly elastic membranes of revolution. Both semi-infinite and finite versions of cylindrical and conical membranes are considered, and a finite membrane having a meridional curve which is parabolic is solved. The source of excitation is generally a constant velocity motion of one end of the membranes, but the results for a stress-pulse input at one end of a semi-infinite cylindrical membrane are also given. The results for the finite membranes are new, and the results for the semi-infinite problems are discussed with respect to previously published results. The two-dimensional state of stress in the membrane requires careful ordering of the calculations, and the boundary conditions for finite membranes are shown to follow logically from this ordering of the calculations. The difference in the solutions resulting from prescribing an axial or a tangential velocity excitation at the end of a conical membrane is presented, and the mesh size necessary for convergence to the solution is indicated. The graphs of the results clearly indicate regions in space and time where the membrane model should be replaced by the shell formulation to represent a realistic structure. The technique is shown to be self-contained and independent of any formal method such as the method of characteristics.
    Additional Material: 18 Ill.
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  • 21
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 215-232 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents an analysis of the response of plastic spherical and cylindrical shells subjected to loads applied through a rigid boss. Special emphasis is placed on following the load-deflection behaviour of these structures after the application of the yield-point load in order to predict the appearance of any snapping action.The method of analysis assumes that upper bound calculations are applicable and that the associated velocity fields can be represented by a series of piecewise continuous polynomials. The internal dissipation of energy for the structures are then written in terms of the coefficients of these polynomials and the values appropriate to the solution are found by using a non-linear programming routine.The results of this analysis are correlated with a non-dimensional boss size parameter p and compared with the results of experimental investigations. Mention is also made of the possible effects of initial imperfections.
    Additional Material: 12 Ill.
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  • 22
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 233-248 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element technique is used to determine the natural frequencies and the mode shapes of a cantilever plate mounted on the periphery of a rotating disc. The plane of the plate is assumed to make any arbitrary angle with the plane of rotation of the disc. The distributed centrifugal force is resolved into two components - one acting in the plane of the plate and the other normal to the plate. The stresses produced in the middle surface of the plate due to the in-plane forces are first determined. The increase in the bending stiffness of the plate elements due to these in-plane stresses is obtained in a manner similar to that used in the stability analysis of plates. The component of the distributed centrifugal force normal to the plate surface is added to the inertia force.From the results of computations carried out for various values of the aspect ratio, the speed of rotation, the disc radius and the setting angle, empirical formulae are derived giving the effect of these parameters on the natural frequencies. These empirical formulae are observed to be in agreement with the corresponding known formulae for rotating cantilever beams, when the aspect ratio is high.
    Additional Material: 8 Ill.
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  • 23
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 249-259 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a search procedure for finding the unconstrained maximum or minimum of a function of many independent variables. If this function represents the volume, cost, stiffness, etc. of a structure and each of the independent variables is associated with a parameter governing the geometry of the structure then designs of optimum geometry may be made in certain cases with the assistance of this search procedure. The procedure consists of steepest gradient calculations used in conjunction with a reverse Fibonacci location process. A ridge-following technique is included to speed convergence in addition to localized exploration in the region of an optimum.The search procedure has been programmed for computer use and an outline of its structural design applications is presented together with an example of its efficiency in a specific case.
    Additional Material: 6 Ill.
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  • 24
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 261-273 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A study of bending of plates for small deformations by applying the finite element method is presented in this paper.A new class of displacement functions has been developed for rectangular bending elements. For the first time a method is proposed for the derivation of displacement functions in which trigonometric expressions that had apparently failed to yield satisfactory results in earlier attempts can be used along with polynomial terms.The derivation leads to conforming type of displacement functions which satisfy the convergence criterion. The approach also demonstrates how many more new displacement functions can be found.
    Additional Material: 7 Ill.
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  • 25
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 275-290 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The solution of plate and shell problems by an independent specification of slopes and middle surface displacements is attractive due to its simplicity and ability of reproducing shear deformation. Unfortunately elements of this type are much too stiff when thickness is reduced.In an earlier paper a derivation of such an element was presented1 which proved very successful in ‘thick’ situations. Here a very simple extension is made which allows the element to be economically used in all situations.The improved flexibility is achieved simply by reducing the order of numerical integration applied to certain terms without sacrificing convergence properties. The process is of very wide applicability in improvement of element properties.
    Additional Material: 10 Ill.
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  • 26
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 291-292 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 27
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 293-294 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 28
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 29
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 295-296 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 30
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 317-325 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The theory of conjugate approximations1 is used to obtain consistent approximations of stress fields in finite element approximations based on displacement assumptions. These consistent stresses are continuous across interelement boundaries and involve less mean error than those computed by the conventional approach.
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  • 31
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 299-315 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A system of finite element shell analysis codes, called SABOR/DRASTIC, is used to analyse a complex two-layered shell of revolution under static and dynamic asymmetric loads. The dynamic analysis is compared with experimentally measured response. In this linear elastic analysis, emphasis is placed on the inherent flexibility of the finite element method in modelling the complex structural geometry of a given test specimen. Static studies, which involve variations in important shell parameters, and dynamic studies, which provide a successful correlation with experiment, are used to illustrate both the detail and the generality with which shell analyses may now be performed with confidence.
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  • 32
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 327-347 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Many of the known finite elements are based on a variational procedure in a functional basis of monomials. The present paper attempts to formulate completely a finite element procedure which is non-variational on a functional basis which is left to the choice of the user.
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  • 33
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 349-360 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computer program is described for the analysis of plates in extension using the equivalent plane-framework idealization. The conjugate gradient method is adopted to solve the resulting large number of simultaneous equations. Performance figures are quoted for the program when used on an ICL KDF9 machine with a restriction of 18K on the available core store. The method is generally shown to provide a satisfactory solution to a heavy computational task and thus permits the solution of very large structural systems on a small computer.
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  • 34
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 379-388 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A very simple equation solver of very large capacity is developed. The method described here does not require a very large in-core memory; however, a fast random access device like a magnetic disk drive is required.
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  • 35
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 445-446 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 36
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 447-448 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 37
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 509-517 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper considers methods of solution of the relevant equations based on the Newton-Raphson process. Expressions are derived for calculation with both good and very poor initial guesses and for calculation of pressure, volume and temperature during an equilibrium process. A method of programming the calculations is outlined. Variations and modifications to suit specific situations are discussed.
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  • 38
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 519-528 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computer orientated method is presented which generates meshes of triangular elements in plane and curved surfaces. Depending on geometrical and material variations, the region to be discretized is divided into a number of four sided zones. By using curvi-linear co-ordinate systems, nodes within and on the boundary of each zone are automatically positioned and referenced to a global Cartesian co-ordinate system. Elements are automatically assembled from these nodes. Input data is required to specify the positions and material properties of each zone and how they are connected. Examples are given which illustrate the range of meshes that can be generated. Extension of the method to generate three-dimensional tetrahedral elements is indicated.
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  • 39
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 529-552 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The discrete element displacement method is used to analyse the finite-deflection behaviour of shallow arches. The arches are idealized as assemblies of shallow curved elements and the necessary properties of the displacement patterns in these elements are discussed. Numerical solutions of the geometrically non-linear problem are obtained by directly minimizing the total potential energy of the system.
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  • 40
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 553-563 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For a hierarchy of polynomials on the triangle there is derived an algorithm for computing the stiffness matrix of the plate bending element. The algorithm is easy to program and means a considerable saving of the computing time. The same approach can be used for any elliptic equation with constant coefficients.
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  • 41
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 565-574 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element procedures usually require more degrees of freedom for a specified accuracy than does a classical Ritz procedure if suitable coordinate functions are available. This paper develops a combined global and local dependent variable representation which couples the conventional and finite element Ritz methods. This hybrid method preserves much of the flexibility of the finite element method while increasing the solution accuracy for a specified system order. The method is illustrated by examination of a beam and a plate vibration problem.
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  • 42
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 63-87 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element method is applied to the stability analysis of structural systems subject to non-conservative forces. The development of the method is general, but the specific application considered here is the stability of thin-walled members subject to follower forces. The method predicts the type of instability, whether it be buckling or flutter. Example problems, for which exact solutions are known, illustrate the accuracy and convergence characteristic of the finite element formulation.
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  • 43
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 89-101 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The point matching numerical method and its generalization, the method of boundary point least squares, have been successfully applied to numerous boundary value and eigenvalue problems. The present paper demonstrates the application of these techniques to problems in the micromechanics of fibrous composite materials, i.e. determination of elastic moduli and stress concentrations for parallel-fibre materials which are loaded transversely with respect to the fibres. The solution technique utilizes exact solutions of the governing equations of plane elasticity for each component fibre and its surrounding matrix material in a typical repeating section of the composite material. The continuity conditions for stresses and displacements between fibre and matrix and the repeatability conditions at the boundary of the repeating section are satisfied approximately in a pointwise manner. Some special numerical techniques which were found to be particularly useful in applying the point matching method to these problems are delineated. The method is demonstrated for composite materials having circular, elliptical and square fibres in regular, staggered arrays. Numerical results are given which show the accuracy of the method as well as stress concentration and composite elastic moduli data.
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  • 44
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 131-144 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper discusses the mathematical foundations of a technique that has been used extensively in structural optimization.1-6 Two basic problems are considered. The first of these is the concave programming problem which consists of finding the global minimum of ‘piece-wise concave functions’ on ‘piece-wise concave sets’. Since any function can be approximated by a piece-wise concave function, this method could in principle be used to find the global minimum in non-convex optimization problems. The second one is the piece-wise linear programming problem in which the objective function is convex and piece-wise linear. The iterative method outlined for handling this problem is shown to be much more efficient than the standard simplex method of linear programming.
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  • 45
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    International Journal for Numerical Methods in Engineering 3 (1971) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 46
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 154-154 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 47
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 361-377 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The equations governing the axisymmetric dynamic deformation of an elastic solid are considered as a symmetric hyperbolic system of linear first-order partial differential equations. The characteristic properties of the system are determined and a numerical method for obtaining the solution of mixed initial and boundary value problems in elastodynamics is presented. Two examples are considered.
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  • 48
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 405-413 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In convection heat transfer problems, it is convenient to solve the governing differential equations by using straightforward marching techniques for numerical integration. However, the boundary layer equations in these heat transfer problems are not of the initial value type even though they are parabolic equations. Consequently marching techniques are not successful until correct initial values are known. A means of determining these initial values is presented herein. Selected optimization methods are utilized in conjunction with marching integration techniques to solve third- and fourth-order ordinary differential equations which have three unknown initial boundary conditions. Two optimization methods, one deterministic and the other non-deterministic in nature, are used both independently and in combination as determined by the particular circumstances. Two applications are used to demonstrate the technique and comparison is made with existing solutions.
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  • 49
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 443-444 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 50
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 444-445 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 51
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 485-493 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The convergence of nodal displacements obtained by the finite element method is investigated for special element patterns in plane elasticity with the aid of the differential equation derived from the equilibrium condition at each node. The convergence of strains is also discussed. It is shown that averaging is an effective tool for obtaining approximations to strain for some kinds of mesh arrangement. It is also shown that the approach becomes inaccurate along force boundaries.
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  • 52
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 495-508 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A refined axisymmetric curved finite element for the analysis of thin elastic-plastic shells of revolution is described in the paper. The improved element is obtained by employing cubic polynomials in terms of local Cartesian co-ordinates for the assumed in-plane and out-of-plane displacements. This introduces into the solution two internal degrees of freedom in the cord direction of each element. These internal degrees of freedom are removed by static condensation before assembling the individual element stiffness matrices, and are subsequently recovered after the nodal displacements are obtained. On comparison with the previous formulation, this procedure greatly improves the accuracy of the solution especially with regards to in-plane stress-resultants at discontinuities in the meridional curvature and interelement equilibrium of forces. The latter fact makes it possible to analyse shells with a discontinuous meridional slope. In using this element, improvement in the convergence of the elastic-plastic solutions has also been observed.Several examples illustrate the quality of solutions. The reported study is limited to axisymmetric loadings cum boundary conditions.
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  • 53
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1-13 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: General kinetic equations for the gelation reaction of tetrafunctional amino monomer with formaldehyde are formulated according to Case's gelation theory. The ratio of the rate constant of the condensation reaction to that of the addition reaction is evaluated by applying a theoretical kinetic equation to the experimental measurements. The ratio of the rate constant for addition of an imino group to that for an amino group is also determined by combining the kinetic equation, stoichiometric relation, and expression for the gel point. The total yield of resin, the yield of sol, and the number-average molecular weight of the sol fraction are discussed.
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  • 54
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1117-1131 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The diffusive permeability of water P, which relates to diffusive flux of water under a concentration gradient of water (measured by diffusion of tritiated water), and the hydraulic permeability of water K, which relates to the water flux under a hydraulic pressure gradient are defined. For the case of diffusive transport one has P = KRT/ν1, where ν1 is the molar volume of water. The relationship between P and K was investigated as a function of hydration H, i.e., the volume fraction of water in swollen polymer membranes. The following characteristic features of water permeability are revealed. (a) In the lowhydration region (H 〈 0.2), water permeates by diffusion even under an applied hydraulic pressure gradient and KRT/ν1 = P. (b) In the higher hydration region KRT/ν1 is greater than P, and the ratio ω = KRT/ν1P increases nearly exponentially with decrease of (1-H)/H. Water in this region moves partly by bulk flow under an applied hydraulic pressure gradient but moves only by diffusion in the absence of a pressure gradient. (c) The dependence of log P on (1-H)/H is nearly linear in regions of both high and low hydration but the slopes are different. The transition occurs in about the same H range where the discrepancy between P and KRT/ν1 becomes significant. Excellent agreement was found between the experimental data for P as a function of H and the theoretical prediction based on the free-volume concept of diffusive transport in hydrated homogeneous membranes.
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  • 55
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1133-1145 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The glass transition temperatures of a number of poly(vinyl phenyl ketones), poly-(vinyl benzoates), and poly(phenyl acrylates) have been measured by a refractometric method. The effects exerted on Tg by the nature and position of the ring substituents and by the different groups binding the pendant phenyl rings to the polyvinyl chain are discussed. The importance of knowledge of the side-group motions in the glassy state for the interpretation of glass temperature data is emphasized.
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  • 56
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1149-1151 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 57
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1153-1171 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The relation between molecular weight, chain rigidity and the length of the high-elasticity plateau is determined from frequency and temperature dependences of the storage modulus for polybutadienes and polystyrenes with Mw/Mn ≤ 1.1. Use is made of the concept of equivalence of high-elastic states characterized by equal lengths of high-elastic plateaus for linear polymers. The high-elastic states of the linear polymers studied are equivalent if the polymer chains have equal numbers of dynamic segments and if the reference temperature is T0 = 1.22Tg, where Tg is the glass transition temperature. The viscoelastic properties of the polymers in the high-elastic state are determined unambiguously by Tg and the molecular weight of the dynamic segment. The quantitative relation between thermomechanical characteristics obtained by measuring deformation versus temperature under a constant time regime and dependence of storage modulus versus frequency under isothermal conditions is discussed.
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  • 58
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1483-1494 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The sorption and diffusion constants of CH2Cl2 at room temperature in quenched polyethylene film drawn at 60°C to different draw ratios λ between 6 and 25 drop drastically between λ = 8 and λ = 9 and then remain nearly constant, dropping only slightly up to λ = 25. Also, the exponential dependence of diffusion constant on concentration of sorbent increases abruptly in the same draw interval and then remains constant at the higher draw ratios. The data may be explained well by a composite madel: a low-permeability fiber structure embedded in a high-permeability spherulitic matrix. As the draw ratio is increased, the initially spherulitic film is gradually transformed into the fiber structure with the transformation being completed between λ = 8 and λ = 9. During subsequent drawing to λ = 25 the mutual arrangement of microfibrils, the basic elements of the fiber structure, changes by longitudinal sliding. However, their transport properties remain nearly constant. The diffusion constant drops a little as a consequence of the increased fraction of tie molecules which reduces the number of unperturbed sorption sites.
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  • 59
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    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The kinetics of aminolysis of 1,2;3,4-meso-erythritol dicarbonate and 1,2;3,4;5,6-mannitol, sorbitol, and dulcitol tricarbonates by n-butylamine in dimethylformamide solution was investigated. The dicarbonate and tricarbonates are considered respectively as models of dyads and triads in the poly(vinylene carbonate) chain. The theoretical kinetic curves for the dimer and the trimers were calculated by solution of kinetic equations and close agreement with experiment was obtained. A version of the Monte-Carlo method was developed to provide a model for the reaction process by a computer calculation including the neighboring group effect in enhancing reactivity. The theoretical curve for a trimer coincides with the experimental one. These results confirm the accelerating influence of the unreacted neighboring groups. For the polymeric chain the experimental and calculated curves deviate for conversions beyond 10%. This indicates an additional polymer effect, which is as yet unexplained.
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  • 60
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 779-799 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Extensive gel-permeation chromatography (GPC) results are presented which reveal in much more detail than hitherto the effects of fractionation during the crystallization of polyethylene from solution. It is suggested how these results may be used to assess the affects of fractionation on the production of single crystals. In addition the results are compared with the fractionation which would be expected assuming the crystals to be in equilibrium with the solution. It was found that the results can be explained very well on this basis. A discussion of this rather unexpected result is included.
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  • 61
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 801-814 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The effect of temperature and strain rate on the compressive yield behavior of polystyrene is compared with the effect of the same variables on crazing in tension. The results support the conclusion of other, more extensive work, which shows that crazing involves the same types of molecular processes as those which occur during deformation under compression and shear. An improved method of measuring compressive stress-strain curves is then described, and the compressive yield stress is also compared with an extrapolated tensile yield stress. The difference between the two is in line with concepts which assume a dependence of yield stress on the state of hydrostatic tension (or compression). It can be adequately described by the Mohr-Coulomb yield criterion. Application of this criterion also enables a theoretical stress strain curve in tension to be derived from other results in compression. Comparison of the tensile stress-strain curve so obtained with those which can be directly measured with other plastics, supports the hypothesis that crazing is favored by a marked decline in engineering stress during tensile elongation (plastic instability).
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  • 62
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 815-827 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The crystallization of a series of “odd-odd” polyamides has been examined for a variety of fusion conditions and crystallization temperatures. Diverse kinds of spherulites and other crystalline structures have been formed in these nylon polymers by direct crystallization from the melt and by melt-seeding techniques. The structures formed in this way have been characterized primarily with the aid of optical microscopy. In this series of polymers, characteristic textural features yield a fairly unified pattern of crystallization behavior. Crystalline aggregates are formed near the respective melting points of these polymers. In very thin sections (ca. 0.1μ), plateletlike crystals of high crystallinity exhibit optical and diffraction behavior characteristic of single crystals.
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  • 63
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 829-839 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The mobilities of polymer chain segments in mixtures of rubber and carbon black were investigated by nuclear magnetic resonance. Spin-spin relaxation time (T2) measurements on cis-polybutadiene and ethylene-propylene-diene rubber (EPDM) bound rubbers detected at least two relaxing regions: an immobile region and a relatively free region. The molecular motions in the relatively free region are still constrained compared to those of the pure gum.
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  • 64
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 841-852 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The adsorption of a series of block and random styrene-methyl methacrylate copolymers on an animal charcoal and on Graphon has been studied. On charcoal, adsorption decreases with increase of molecular weight because of the inability of larger coils to penetrate into the adsorbent. An analysis is presented which requires that coils undergo considerable distortion on adsorption in pores. The adsorption of random copolymers on Graphon is also in reverse order of molecular weight; this effect may be due to particle bridging leading to the formation of interparticle “pores.” The relative affinity of the styrene and methyl methacrylate residues is different on charcoal and Graphon, respectively; on both surfaces, however, relatively few of the more active residues are required for adsorption. Block and random copolymers are adsorbed to different extents which depend on the nature of the adsorbent surface.
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  • 65
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1729-1745 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Atactic, isotactic, and optically active poly(propylene oxides), PPOx, were irradiated with both γ-rays and electron beams. Up to a dose of 37 Mrad no change could be detected in the optical activity. G values for hydrogen evolution decreased as compared to polypropylene in about the same ratio as G(H2) of polyoxymethylene decreased as compared to polyethylene. G values for crosslinking and scission, estimated by means of gelation theories of Saito and Inokuti, were found to be greater for isotactic than for atactic PPOx. The behavior of transient infrared and ultraviolet absorption bands is discussed. Intrinsic viscosity data indicate a rapid initial chain degradation whereas CO gas and OH group production is linear with dose. Evidence for the conversion of one type of free radical to another on heating an irradiated sample from 77°K to room temperature is based on the behavior of transient infrared and ultraviolet absorption bands.
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  • 66
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1763-1776 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: As in the case with other polymers previously reported, the values of the refractive index increment dn/dc of polyethylene and the n-alkanes change with molecular weight. Most of the variation may be understood by examination of the role of density in the Lorentz-Lorenz mixing equation for specific refractivity, R12 = p1R1 + P2R2 used to calculate dn/dc. It may also be shown that as the absolute refractive index difference between solute and solvent becomes smaller, dn/dc becomes more sensitive to density change of the solute.
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  • 67
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1747-1761 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The contribution to the disorder scattering by imperfect spherulites resulting from fluctuations in the magnitude of the anisotropy is analyzed for two-dimensional spherulites. The fluctuations are described in terms of a parameter characterizing the meansquare amplitude of the fluctuation and a correlation function describing the distance over which the correlation occurs. Cases considered are those where the correlation depends on either the radial or the angular separation of the scattering volume elements. As with the case of disorder in orientation, one finds that disorder in anisotropy may result in a nonzero value of intensity at μ = 0° and 90°, a decrease in the higher-order variation of scattered intensity with θ, and an increase in the intensity of scattering at higher values of θ over that for a perfect spherulite. In addition, disorder in the angular direction leads to an increase in the scattered intensity at small values of θ as compared with the zero intensity of scattering from a perfect spherulite at θ = 0°.
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  • 68
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1777-1791 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Ozone has been used as a selective oxidizing agent for degrading polyethylene single crystals at room temperature in order to confirm and extend results on surface structure obtained by use of fuming nitric acid at temperatures above 60°C. The surfaces of the crystals were rendered highly accessible to the ozone gas by preparing the crystalline material in a highly expanded form; the solvent in which the crystals were suspended was removed by sublimation from the solid state. The extent and nature of the reaction were studied by measuring the increase in weight and in density, by direct chemical analyses, and by making use of infrared spectroscopy and gel-permeation chromatography. It was found that the surfaces of the crystals are attacked at room temperature by ozone, with resulting chain scission, and the broad features of the chemical reaction were established. Some folded chains are found to be as long as the original thickness of the crystal, and once folds have been cut, continuing reaction shortens the chains. In the early stages of the degradation, during which most of the weight increase takes place, the density of the crystals increases, and the magnitude of the increase is that expected from the increase in weight alone, i.e., assuming no increase in effective volume.
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  • 69
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1793-1805 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Detailed critical examinations of three aspects of nitric acid treatment of polyethylene are reported. (1) The endgroups introduced by the nitric acid are examined. It is concluded that in samples degraded to a single-crystal traverse stage, carboxyl features only as endgroup, and conversely each chain-end is terminated by such a group. Consequently, the carboxyl content can be used for quantitative characterization of the cut chain length. The function and position of the nitro group remains unexplained. (2) The morphological selectivity of the nitric acid-induced degradation is scrutinized. It is concluded that the crystal core is attacked and thinned by the acid; the slowing down of the reaction is principally due to accumulation of reaction products. Accordingly, the usual distinction between a vulnerable amorphous layer and a resistant crystal core is not justified on the basis of such degradation experiments. It follows that meaningful structural information is obtained only when the relevant crystal properties are studied as a function of chain cutting, assessed from the molecular weight distribution (GPC), as opposed to that of degradation time alone. (3) The role of sample consistency and reagent strength has been examined. It is demonstrated that for the reaction to be sufficiently uniform throughout the sample for the results to be meaningful, the reaction rate has to be slow compared to the rate at which the reagent diffuses into the specimen. To realize these conditions, finely dispersed samples and weak reagents were found to be favorable
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  • 70
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1807-1837 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Previous studies on selective degradation of polyethylene single crystals with fuming nitric acid have been extended, both by using acid of lower concentration which gave better control over the degradation, and by resorting to ozone as an oxidizing agent which among others enabled the degradation temperature to be conveniently lowered. The molecular weight distribution was followed by gel-permeation chromatography in the course of degradation. Complete consistency between these different methods has been established, modifying some of the previous conclusions reached by this method. The principal feature which emerges is that we have a distribution of fold lengths. The largest straight fold stems can stretch across nearly the entire layer defined by the low-angle x-ray period, while there is a continuous distribution of shorter folds terminating deeper down in the crystals. The limiting depth at which the number of terminating folds becomes negligible can be identified and quantitatively assessed. The method of analysis is described, and individual data are discussed in detail. This picture of a fold surface layer containing essentially adjacently reentrant folds of uneven length agrees with quite recent results on other related chain-folded systems (annealed crystals, short chains, bulk structures) obtained in these laboratories and thus appears to be of general validity. The consequences of the model for our picture on polymer crystals in particular on the nature of the “amorphous” component, are discussed.
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  • 71
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1839-1850 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Steady flow and dynamic viscosities were determined for symmetrical linear and starbranched block copolymers of butadiene and styrene above their upper (polystyrene) glass transition. Block structures examined were B-S-B, (B-S-)3, S-B-S, (S-B-)3 and (S-B-)4. At constant molecular weight and total styrene content viscosities were greater for polymers terminating in styrene blocks, irrespective of branching. Branching decreased the viscosity of either polybutadiene-terminated or polystyrene-terminated block polymers, compared at equal Mw. However, comparisons at equal block lengths showed that the length of the terminal blocks, not the total molecular weight, governs the viscoelastic behavior of these polymers to a surprisingly good approximation. This unusual result is rationalized in terms of the two-phase domain structure of these polymers, which persists to a significant degree in the melt. Below the glass transition of the polystyrene blocks the effects of branching were masked by differences in the morphology of the domain structure unrelated to branching.
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  • 72
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1851-1869 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A wide-line NMR study of chain segmental motion in nylon 66 has been made on a rolled sheet having “double orientation.” In this sheet the crystallite c axis, i.e., the molecular chain axis, is oriented preferentially along the roll direction, and the crystallographic (010) plane lies predominantly parallel to the roll plane, or the plane of the sheet. The direction of the applied magnetic field with respect to the sheet is characterized by two angles, the polar angle γ subtended by the roll direction and the magnetic field, and an azimuthal angle φ. NMR spectra were taken at various values of the angles γ and φ and at three temperatures -196°C, 20°C, and 180°C. The second moments of the absorption spectra taken at 180°C were compared with theoretical predictions of second moments based on two models for the high-temperature segmental motion (called the αc process) in crystalline regions of nylon 66. One model consists of rotational oscillation with amplitudes δ of segments around their axies. The second model is denoted 60° flip-flop motion and consists of rotational 60°C jumps of the segments around their axes between two equilibrium sites with the possibility that the segments also oscillate with a general amplitudes δ around each site. The experimental results are consistent with fairly large amplitudes δ, in which case both models approach the limiting case of full segment rotation. For this reason the experiments do not allow a distinction between the two models. From the second moments at -196°C and 20°C the decrease in second moment due to the low temperature segmental motion, the γ process, is obtained. This motion occurs in noncrystalline regions of nylon 66 and is found to cause a decrease in second moment which is strongly dependent on the two angles γ and φ, implying double orientation of the noncrystalline segments. It is suggested that at low temperatures the noncrystalline segments become immobilized in sites dictated by the crystallite orientation through the extensive hydrogen bonding known to exist in nylon 66.
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  • 73
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1911-1914 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 74
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 2095-2097 
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    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 75
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 2105-2108 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 76
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 245-265 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The two essential aspects of axial dispersion in gel permeation chromatography have been studied: (1) the relationship of axial dispersion to the continuity equations of chromatographic transport, and (2) the relationship to molecular size and the system parameters of an individual column. Theoretical analyses are presented for both of these problems and are applied to an experimental study of axial dispersion by both zonal (small-zone) and frontal (large-zone) experiments with a series of macromolecular species having discrete, precisely known molecular weights. Theoretically predicted non-Gaussian elution profiles were observed for the small-zone experiments, and axial dispersion coefficients for each molecular species were determined as a function of flow rate. Resulting values were found to be in good agreement with the theoretical equation relating axial dispersion to molecular size, flow rate, and two “calibration constants” of the column. These results provide a rational basis for axial dispersion effects in terms of the fundamental processes and system parameters of gel columns. Extension of the analysis to multicomponent systems is discussed.
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  • 77
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 345-362 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Under steady shear flow, the normal stress and the shear stress in both dilute and concentrated solutions of monodisperse poly-α-methylstyrenes and their blends were measured. It was confirmed that the molecular theories of Rouse and Zimm extended to concentrated solutions can explain the relation between the zero-shear normal stress coefficient and the zero-shear steady-flow viscosity for both monodisperse and polydisperse systems. Shear-rate dependence of steady-flow viscosity can be understood fairly well by the molecular entanglement concept proposed by Graessley so long as the polymer is monodisperse or the amount of the higher molecular weight component is high. However, zero-shear viscosity of blended systems cannot be explained quantitatively by the theory of Graessley. The shear-rate dependence of steady-state compliance of blended systems was also observed, and it can well be explained by the theory of Tanaka, Yamamoto, and Takano which interpreted the shear rate-dependent steady-state compliance in terms of the relaxation time spectrum and its variation with shear rate.
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  • 78
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 363-368 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Average values for dispersion γsd and polar γsd contributions of the solid surface tension γs γsd + γsp for poly(methylene oxide) (PMO) and Na-treated polytetrafluoroethylene (PTFE) are determined by a new computational analysis of wettability data. PMO displays γsd equals; 21.8 ± 0.9 and γsp = 11.5 ± 1.5 dyn/cm while Na-treated PTFE displays γsd = 36.1 ± 3.0 and γsp = 14.5 ± 2.9 dyne/cm. These surfaces present the highest fractional surface polarity ps = γsp/γs = 0.29-0.35 yet encountered for organic polymers or oriented monolayers. These unusual surface tension properties are correlated with surface chemistry and adhesion phenomena.
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  • 79
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 369-372 
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    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 80
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 373-375 
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    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The dependence of the intrinsic viscosity of polyelectrolytes on the concentration of added salt is given satisfactorily by a formula obtained recently. A new viscosity - molecular weight relation gives satisfactory agreement with experiments.
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  • 81
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 383-384 
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    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 82
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 2081-2093 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Terephthalamide nylons with two to five carbon atoms in the aliphatic portion of the chain have been crystallized from aqueous solutions of hexafluoro-2,2-propandiol. The 3T and 4T nylons in particular form rodlike crystals. Indications are that these are bundles of cylindrical structures about 50 nm in diameter. Electron diffraction shows the symmetry to be C2v. Films of the nylons were drawn with great difficulty. The x-ray diffraction on the films is consistent with a monoclinic structure, though the crystal structure could not be positively established. There is some evidence for a polymer chain alignment perpendicular to the long axis of the rods.
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  • 83
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    Topics: Chemistry and Pharmacology , Physics
    Notes: Two linear polyethylene fractions (Mη, 11,260 and 100,000) and mixtures of these fractions have been isothermally crystallized from the melt under pressures up to 3000 atm. Characterization of individually crystallized fractions with transmission electron microscopy indicates that pressure can be used to produce a crystallite whose thickness is a measure of the chain length within it. Although the high molecular weight fraction yields spherulites containing individually varying lamellae thicknesses, the maximum thickness of each lamella is a measure of the chain length within it. Both electron micrographs and differential thermal analysis results show that crystallization of homogeneous mixtures of the high and low molecular weight fractions under high pressure results in a distinct fractionation and segregation according to molecular weight.
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  • 84
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 2099-2103 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 85
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 2119-2130 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A general theory of non-Gaussian elasticity is presented for real polymeric chains having fixed bond angles and restricted internal rotations. The theory contains the displacement-vector distribution given by Nagai, and the Flory-Wall-Hermans procedure is used for the calculation of network properties. Whereas the treatment is valid for all types of polymer chains, it is not totally satisfactory from a practical standpoint because of a slow series convergence if the chains are stiff. It is best utilized for flexible polymers under conditions of light crosslinking. Detailed network behavior is investigated only for polyethylene type chains having uncorrelated internal rotations. In this instance the fractional contribution fe/f of the internal energy of the total force f is found to be a function of elongation at high degress of stretching. It may decrease, or increase, depending upon the sign of fe/f at low elongations. Furthermore, the variation of fe/f with elongation is independent of the fixed bond angle of the chain backbone. Stress-strain behavior and energy-strain behavior are in opposition, i.e., when the non-Gaussian contribution to the stress is greatest, it is the least for the ratio fe/f, and vice versa. The presence of correlated internal rotations would not be expected to greatly alter these general conclusions.
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  • 86
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 15-26 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The gelation reaction of acetoguanamine with formaldehyde was investigated in the light of the gelation theory for tetrafunctional amino resins described in the previous paper. The gel time and extents of reaction of formaldehyde, amino groups, and imino groups varied with the molar ratio in the feed, but values of K (the ratio of the rate constant for condensation to that for addition) and k (the ratio of the rate constant for addition of the imino group to that of the amino group) were nearly constant. When the catalyst concentration was increased, the gel time, extents of reaction of each functional group, and the values of K and k varied; in particular K increased markedly. From the results of varying the molar ratio and concentration of acidic catalyst, it was found that the number of methylol groups per molecule of acetoguanamine at the gel point was influenced by the reaction conditions but the number of methylene linkages per molecular of acetoguanamine was nearly constant at about 0.6, regardless of reaction conditions. The number-average molecular weights up to the gel point varied with the reaction conditions, but at the gel point they were all nearly constant at about 385.
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  • 87
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1235-1241 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The literature on polymer morphology contains many studies of structural and orientation changes occurring upon uniaxial stretching of films and fibers, but it has only an occasional reference to such studies on biaxially stretched film. This paper presents data on a structural change due to simultaneous biaxial stretching up to 6 × 6 stretch ratio of quenched linear polyethylene slightly below the melting temperature. At low stretch ratios the b axis of the orthorhombic unit cell orients predominantly in the biaxial plane of stretching or film plane. At higher than 4 × 4 stretch ratio, a second crystal orientation appears which is a (110) orientation in the film plane. Differential scanning calorimetry scans show two melting peaks occurring concurrently with diffraction effects of two crystal orientations. The evidence for two populations of crystals differing in orientation are discussed in the light of current concepts of folded-chain lamellae and their fragmentation with elongation.
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  • 88
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1219-1234 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The low-frequency skeletal and intermolecular modes (below 900 cm-1) have been studied for a sample of “as-polymerized” Ziegler-Natta polyethylene for which extended-chain conformations have been proposed. These results have been compared with data from a sample of stirred-solution-crystallized polyethylene and with previous measurements for highly crystalline samples of folded-chain polyethylene. Measurements were also made of the temperature dependence of these modes for the as-polymerized material and of the polarization dependence of these modes for an oriented sample of solution-stirred polyethylene. In the neutron spectra and the corresponding derived frequency distributions, the observed major “singular” frequencies for both the skeletal and intermolecular modes are in reasonable accord with those previously observed for folded-chain samples of high crystallinity and in Raman measurements. In addition, these frequencies agree with those predicted by theory for the singular frequencies corresponding to the phase-frequency relationships for the skeletal and intermolecular modes of an infinitely extended chain in a crystal. However, in the spectra of the extended-chain materials, these singular frequencies, in general, appear sharpened and enhanced in intensity relative to those for previously reported results on folded-chain polyethylenes; consequently, assignment of their characteristic frequencies is easier. In addition, evidence is presented to show that, for the extended-chain materials, these frequencies broaden less rapidly with increasing temperature, and the corresponding average vibrational amplitudes are smaller than those observed for highly crystalline samples of folded-chain material. It is suggested that in these materials the reduction of the number of chain folds and the increased intramolecular ordering give rise to increased thermal stability of the configurations with regard to segmental rotation and to decreased vibrational amplitudes relative to folded-chain materials. When the aspolymerized materials is preheated above the normal melting point for polyethylene, the neutron spectra revert to those more characteristic of the folded-chain materials, indicating that a relaxation of chain extensions has occurred. However, on the basis of these results, on quantitative estimates of the characteristic relaxation time can be presented. Additional frequencies, besides those predicted by theory for the skeletal and intermolecular modes and those associated with either multiphonon contributions or the presence of chain folds, are observed. The origin of these frequencies remains unclear but may warrant further theoretical consideration.
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  • 89
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1255-1269 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: When oriented polyethylene is sheared at an angle to the orientation axis, kink bands often develop and grow, with a resulting change of the crystalline orientation. Beside the crystalline reorientation, the following changes within the kink bands have been observed with wide-angle x-rays: (a) partial transformation to a monoclinic from the normal orthorhombic unit cell; (b) partial alignment of the orthorhombic b axes; (c) rotation of the orthorhombic c axes of a fraction of the crystals around the kinks by an extra 40 to 60° beyond that of the fibrils; and (d) misalignment of the orthorhombic (hk0) planes by a few degrees. These results are suggested to arise, at least in part, from crystal flattening and from crystal twinning or pseudotwinning on planes intersecting the molecular axes.
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  • 90
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1243-1254 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The size and distortion of crystallites in samples of linear polyethylene were determined before and after plastic deformation. A slowly cooled sample, a quenched sample, and highly drawn films (draw ratio 16) were investigated by different methods. Wide-angle x-ray patterns were analyzed to study the average size of the crystalline mosaic blocks and their distortion. In addition, the longitudinal crystal thickness (in the chain direction) was evaluated by two other approaches, determination of the long period, and the melting temperature of irradiated samples. The results show clearly that the size of the crystalline mosaic blocks changes substantially with drawing of polyethylene. Not only is the lateral crystal thickness affected, but the longitudinal crystal dimensions also change during the drawing process. By the three independent methods we find that the longitudinal crystal thickness after drawing is independent of the value for the undrawn samples, as was reported earlier by Peterlin. The change in crystallite size after drawing is accompanied by a large decrease in crystal volume to about 10% of the value for the undrawn sample. The degree of distortion in the crystals seems not to be affected by the deformation process. These experimental data can be considered evidence for high chain mobility and for the possibility of rearrangement of chain molecules during the process of plastic deformation.
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  • 91
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1271-1285 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The viscoelastic behavior of two different ethylene-propylene copolymers was studied as a function of the molar ratios of the components and the distribution of the lengths of the ethylene and propylene sequences. The glass transition temperatures Tg agree with the values calculated from relations between Tg and component ratio established by other authors. The copolymer with longer ethylene and propylene sequences was found to exhibit a relaxation spectrum with a slope less steep than -0.5. This broadening is explained by the broader distribution of friction factors of the statistical segments in this copolymer and by differences in crystallike nearest-neighbor packing.
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  • 92
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1287-1303 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The viscoelasticity and volume expansion of the raw polymerizate of ethylene-propylene copolymer with vinyl chloride grafts, and of the individual components has been studied. The raw polymerizate (composite) and the pure ethylene-propylene-vinyl chloride graft copolymer were found to consist of two phases. The pure graft copolymer has an ethylene-propylene matrix containing some fraction of poly(vinyl chloride) (PVC) grafts and a microphase with the remainder of the PVC grafts. The raw polymerizate consists of a PVC matrix plasticized with ethylene-propylene chains and a microphase of the ethylene-propylene copolymer. An attempt has been made to calculate the participation of components in microphases and the minimum dimension of the PVC microphase aggregates.
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  • 93
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1325-1332 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The glass transition temperature Tg of partially sulfonated polystyrene has been measured dilatometrically as a function of degree of sulfonation. A semitheoretical relationship between Tg and degree of sulfonation has been derived by treating the strong-acid polymer as a highly polar copolymer of styrene and styrenesulfonic acid. The Tg of copolymer has been found to increase linearly up to 0.15 weight fraction of styrene-sulfonic acid wA as given by: \documentclass{article}\pagestyle{empty}\begin{document}$ T_g = T_{gB} + 200w_A $\end{document} where TgB is the glass transition temperature of loosely crosslined (1%) polystyrene matrix. Our experimental results agree well with theoretical relations developed on the basis of the iso-free-volume state of glass transition applied to sulfonated polystyrene. The marked linear increase in copolymer Tg with the styrenesulfonic acid is accounted for by the effect of progressively higher intermolecular forces due to the highly polar sulfonic acid substituents.
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    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 615-632 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A polymerization mechanism in which monomers and dimers add to a growing polymer chain with different rate constants and different stereospecificity is considered. A fraction of the dimers are in isotactic placement internally, and low conversion to polymer is assumed. The stereosequence distribution generated by this monomer-dimer model is calculated and found to be non-Markovian in general. A method of determining kinetic parameters of the mechanism from experimentally obtained placement sequence probabilities and related experimental tests for the applicability of the mechanism are also described. A few ramifications of the general monomer-dimer model are then discussed. A case of special interest is the one in which all the dimers have a single internal tacticity, a model recently proposed by Blumstein, et al., for a polymerization involving the surface of certain aluminosilicate minerals. For the case where all dimers are isotactic, it is found that although the propagation of consecutive syndiotactic placements alone is simple Markovian, the overall stereosequence distribution is non-Markovian. Another special case of interest is the limiting case with dimers only in the feed. This case turns out to correspond to a special case of the cyclopolymerization mechanism proposed previously by Reinmöller and Fox. Although the tacticity distribution of the placements created by the head (or tail) monomer units alone of the dimers is Bernoullian, the composite stereosequence distribution is again non-Markovian.
    Type of Medium: Electronic Resource
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  • 95
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 645-658 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The Fourier transform method of Vonk and Kortleve for the analysis of small-angle x-ray diffraction (SAXRD) from semicrystalline polymers has been compared with a modified direct method, originally due to Tsvankin. SAXRD data for three melt-crystallized polyethylene samples have been analyzed in terms of the mean true periodicity, mean crystal length, and mean length of amorphous segments. The two methods of analysis yield substantially equivalent results for all three samples. Calibration curves for the Tsvankin analysis are tabulated, and the relative merits of the two methods of analysis are discussed. With either method, information about the diffracting structure may be deduced that is not available from a simple measurement of the position of the SAXRD maximum. In fact, direct application of the Bragg law to any but the sharpest maximum yields a spacing (the long period) that lacks direct physical significance.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 96
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 659-668 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Measurements are described of the strength of a model adhesive joint subjected to (1) tensile rupture, with the interface containing a small unbonded region of varying size, and (2) pure shear deformation, in the form of a partly unbonded sheet. These, and previous measurements of resistance to peeling separation, are all shown to be consistent with an energy criterion for adhesive failure. The characteristic failure energy per unit area of interface has been determined for the model adhesive material as a function of the effective rate of detachment, over a wide range covering almost the entire spectrum of viscoelastic response. The values obtained are found to increase from levels only slightly higher than thermodynamic considerations would predict, i.e., 102-103 ergs/cm2, at low rates of crack propagation, up to a value of about 106 ergs/cm2 at high rates when the material responds in a glasslike manner. These results suggest that the failure energy has two components: the (reversible) work of adsorption and the (irreversible) work of deformation of the adhesive in effecting separation.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 97
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 687-715 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Light-scattering and viscometric measurements on dilute solutions of five branched polystyrene polymers are reported. The data include studies in decalin as a function of temperature, including the theta temperature, and in toluene. The results for the radius of gyration and the second virial coefficient are not in accord with the two parameter random-flight model. Possible causes of this descrepancy are considered. It is shown that the intrinsic viscosity of branched chains is not uniquely determined by the radius of gyration.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 98
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 669-686 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Dynamic mechanical and dielectric properties of various kinds of polystyrene, including bulk-polymerized, monodisperse, isotactic, and thermally degraded samples, have been measured below the glass temperature to 4°K. Five relaxation processes are found, designated β, γ, γ′, δ, and ε in order of descending temperature. The β peak (350°K at 10 kHz) is attributed to the local oscillation mode of backbone chains and the γ′ peak (180°K at 10 kHz) to rotation of phenyl groups. The δ peak (100°K at 10 kHz) is observed only in dielectric properties of the bulk-polymerized sample and is assigned to weak polar bonds, such as oxygen bonds in the chain. The δ peak (55°K at 10 kHz) which is prominent in dynamic mechanical properties is interpreted in terms of lattice defects due to a syndiotactic diad inserted between isotactic sequences in a chain or vice versa. The ε peak (ca. 25°K at 10 kHz) is first reported in the present work, but the mechanism involved is not yet clear.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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  • 99
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1379-1397 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The sedimentation-equilibrium method is extended to treat nonideal solutions of heterogeneous macromolecules. The solute is assumed to be heterogeneous not only in molecular weight but also in other quantities such as partial specific volume, second virial coefficient and specific refractive increment. General expressions for various observable molecular weights, especially for weight-average, z-average, and number-average molecular weights, are derived. Their dependences on sedimentation parameter and solute concentration are discussed in detail. For the extrapolation of observable molecular weights, giving a type of weight-average, and z-average, to infinite dilution to estimate the molecular weight and the second virial coefficient, average concentration is superior as a concentration variable to original concentration. The plots of observable molecular weight versus average concentration are usually less influenced by the choice of the sedimentation parameter, especially of rotor speed. The general expressions are applied to a few special cases; monodisperse polymer, polydisperse homologous polymer, and polymer blend. The results are compared with experiments on a monodisperse, polystyrene, a polydisperse poly(methyl methacrylate), and a mixture of the two polymers, all in 2-butanone at 25°C. The agreement between the theory and experiments is satisfactory.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 100
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 747-754 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The electronic states localized at defects in a polyene chain with alternating bond lengths have been investigated in the Hückel approximation by direct computation on large rings. The defects considered include substitutional impurities and bond distortions. None of the cases treated seem likely to be thermally activated donor or acceptor centers, but several examples of deep or shallow traps for electrons in the conduction band are found.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
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