Darwin Year 2009

DARWIN YEAR 2009

Modified Avrami Equation

JOURNAL OF POLYMER SCIENCE: PART A VOL. 3, PP. 3067-3078 (1965)

Modified Avrami Equation for the Bulk Crystallization

Kinetics of Spherulitic Polymers

I. H. HILLIER,* Chemistry Department, Imperial College,

London, England

Synopsis

An explanation of the anomalous fractional values of the Avrami exponent found for the crystallization of a number of polymers is

presented. The interpretation is based on a model which postulates the constant radial growth of spherulites, followed by an increase in crystallinity within them by a first order process. The model is supported by direct microscopic observations of other workers. Crystallization isotherms for polymethylene, poly(ethylene oxide), and poly(decamethy1ene terephthalate) are fitted to this model. Apart from the removal of the fractional values of the Avrami exponent, which have no physical meaning, this model gives a considerably better fit than the Avrami equation to most isotherms analyzed. The temperature dependence of the rate constants found for the two rate processes of this model is also discussed. An interpretation of the results of seeded experiments is presented in terms of this model.

INTRODUCTION

The crystallization kinetic of bulk polymers is usually interpreted ^[1], although with varying degrees of success, in terms of the Avrami equation:

where χ is the crystallinity, t the time, z a constant depending upon the nucleation and growth rates, and n an integer depending on the shape of the

growing crystalline body. As spherulites are observed in most crystalline polymers and in thin films are seen to grow with a constant radial rate, a value n = 3 (instantaneous nucleation) or n = 4 (sporadic nucleation) is expected if the density of the

spherulites is constant. Recent work on a number of polymers ^[2-7] has revealed that values of n of 3 or 4 are rarely fo

und. The results of detailed analysis of crystallization isotherms which appear in the literature are summarized in Table I on the following page. The Avrami exponent n may vary with temperature and be a noninteger less than 4 but rarely exceeds this value. Deviations of n from the integral values required by eq. (1) may be explained by postulating either (a) a nonconstant growth rate or (b) a nonconstant density of the growing spherulites.

A model in which the crystalline bodies are considered to be single crystal lamellae growing by a chain-folding mechanism has been shown to be a possible explanation of the observed kinetics of polymethylene ^[6]. This model leads to a nonconstant growth rate, the single crystal lamellae having a constant density.

A number of authors have independently proposed ^[8-10] that the “primary” (Avrami) and “secondary” (post-Avrami) crystallization procesees occurring in polyethylene may be described by the growth and subsequent relaxation of the crystalline regions, leading to a variable density within the sample. Gordon and Hilliel.8 have shown that such a scheme, in which the secondary relaxation is described by a general rate equation due to Hirai and Eyring ^[11] successfully describes the overall crystallization rate in bulk polymethylene. In this paper, it is shown that the fractional values of the Avrami exponent may be explained by the constant radial growth of spherulites (termed the primary crystallization in this work) followed by further crystallization within the spherulite which obeys a first-order law. This model is fitted to crystallization isotherms of polymethylene, poly(ethy1ene oxide) and poly(decamethylene terephthalate). It must be stressed that this postulated subsequent crystallization is distinct from the secondary crystallization which varies linearly with Ln(time), observed in polyethylene and other polymers. The mechanism of this secondary or post-Avrami crystallization has been fully discussed elsewhere ^[8], and is interpreted in terms of an increase in lamellar thickness. The firsborder process proposed in this paper differs from this post-Avrami crystallization both kinetically and in the morphological interpretation of the kinetics. The slow secondary crystallization is absent in the samples analyzed here.

References

1. Mandelkem, L., Growth and Perfection of Crystals, Chapman and Hall, London, 1958, pp. 467-497.

2. Sharples, A., and F. L. Swinton, Polymer, 4, 119 (1963).

3. Banks, W., M. Gordon, R. J.,Roe, and A. Sharples, Polymer, 4, 61 (1963).

4. Hatano, M., and S. Kambara, Polymer, 2, 1 (1961).

5. Gordon, M., and I. H. Hillier, Trans. Faraday Soc., 60, 763 (1964).

6. Banks, W., and A. Sharplea, Makromol. Chem., 59, 33 (1963).

7. Parrini, P., and G. Conieri, Maknrmol. Chem., 62, 83 (1963).

8. Gordon, M., and I. H. Hillier, Phil. Mag., 11, 31 (1965).

9. Peterlin, A., J. Appl. Phys., 35, 75 (1964)

10. Price, F. P., private communication.

11. Rirai, N., and H. Eyrihg, J. Appl. Phys., 29, 810 (1958)

Mi Proyecto de Grado

Mi Proyecto de Grado de Ingeniería

Titulo de Tesis: "Caracterización de nanocompuestos de PMMA/PCL y PMMA/PEO con bentonita modificada orgánicamente"

Fecha de Defensa: 30 de Abril de 2008

Lugar: Universidad Simón Bolívar

Título Académico: Ingeniero de Materiales

Observaciones: Proyecto de Grado aprobado con Mención de Honor

Calculation of the Glass Transition Temperatures of Polymers. Part I.

Calculation of the Glass Transition Temperatures of Polymers. Part I. Homopolymers and Copolymers with Alkyl Side Chains

W. A. LEE, Materials Department, Royal Aircraft Establishment, Farnborough, Hampshire, U.K.

From: Journal of Polymer Science Part A-2 Polymer Physics, Volume 8, Issue 4 (p 555-570)

Synopsis

Four equations, relating the glass transition temperatures Tg, of homopolymers and copolymers to invariant additive temperature parameters (ATP) associated with their constituent groups, but weighted in different ways, have been applied to the calculation of the Tg, of seven series of polymers having alkyl side chains. It is shown that the Tg, of the 32 polymers considered may be calculated, within 7K of the observed values, without the use of interaction coefficients from 15 independent variables, representing summations of the ATP's. The present calculations are confined to those structures which may be formed by a recombination of the structures corresponding to these independent variables. It is an essential feature of the approach that a distinction is made between groups with different nearest neighbors. Alternative methods of calculation are considered. The temperature parameter for a sequence of three or more methylene groups is estimated as 141K, in conformity with the transition in polyethylene at 148K. Nearest-neighbor interactions, stereoregularity, and crystallinity effects are discussed.

INTRODUCTION

The glass-to-rubber transition temperature Tg, is of special interest in the development of new amorphous polymers because many properties of technological importance show a significant change in magnitude, or in temperature dependence, at this temperature. A method for calculating the Tg, of polymers from a knowledge of the chemical structure alone is therefore of great value in designing new polymers with desired properties and is of considerable theoretical interest. Many previous attempts have been reported, but the relations proposed [1-10] have been limited in application, though usefully descriptive of specific polymer systems.

References

1. M. Gordon and J. S. Taylor, J. Appl. Chem., 2, 493 (1952); Rubber Chem. Technol. 26, 323 (1953)

2. L. Mandelkern, G. M. Martin, and F. A. Quinn, J . Res. Nat. Bur. Stand., 58, 137 (1957)

3. T. G. Fox, Bull. Am. Phys. Soc., 1, 123 (1956)

4. L. A. Wood, J. Polym. Sci., 28, 319 (1968)

5. E. A. DiMarzio and J. H. Gibbs, J. Polym. Sci., 40, 121 (11959)

6. A. J. Marei, I. V. Rokityanskii, and V. V. Samoletova, Soviet. Rubber Technol. (Engl. Trams.), 19, 1 (1960)

7. R. A. Hayes, J. Appl. Polym. Sci., 5, 318 (1961)

8. G. Kanig, Kolbid-Z., 190, 1 (1963); RAE Library Transl. 1135

9. W. F. Bartoe, SPE Trans., 4, 98 (1964)

10. W. E. Wolstenholrne, Polym. Eng. Sci., 8, 142 (1968)

Caracterización de Nanocompuestos de PEO/PMMA con Bentonita Modificada Orgánicamente

Caracterización de Nanocompuestos de PEO/PMMA con Bentonita Modificada Orgánicamente

Trabajo que presente en el VI Congreso de la Sociedad Venezolana de Física
(del 2 al 9 Marzo 2008)

Polymerization Systems Engineering

Polymerization Systems Engineering – A Literature Review

L . T . Fan and J . S . Shastry

Institute for Systems Design and Optimization

and Department of Chemical Engineering.

Kansas State University. Manhattan, KS 66506

Taken from:

Journal of Polymer Science Macromolecular Reviews, Volume 7, Issue 1 (p 155-187)

INTRODUCTION

Man-made synthetic polymers are widely employed as substitutes for metal, wood, stone, glass, paper and a variety of macromolecular substances. These applications of polymer require specific properties such as toughness, flexibility, insulation, etc., which are related to the molecular weight, structure, molecular-weight distribution, and copolymer composition of the product polymer. These ultimate properties of the polymer are largely acquired in the reactor. The reactor must remove the heat of polymerization; provide necessary residence time; provide uniform mixing for good temperature control and reactor homogeneity; control the degree of backmixing in continuous polymerizations; and provide surface exposure (Schlegel [1972]). In addition, the reactor system must be amenable to control and be stable under normal operation. Polymerization systems engineering is a branch of systems engineering that deals with polymerization reactor systems ; this field of systems engineering encompasses analysis, modeling, dynamic and stability studies, design (or synthesis) and control of polymerization reactor systems. While many papers have been published on specific aspects of polymerization systems engineering, no comprehensive review on this subject is available. The purpose of this work is to review in general the research in the area of polymerization systems engineering and, in particular, the research on analysis, selection, design, control and optimization of polymerization reactors.

It is hoped that this review will serve as a supplement to the two related reviews published recently. ‘The one by Lenz [1970] reviewed the works on “applied polymerization reaction kinetics” and is generally concerned with the study of the “chemistry” of polymerization reactions and their rates. It also included work related to different initiation systems and different methods of polymerization. In contrast, Seymour [1970] reviewed some recent developments in plastics science and technology and in treating and characterizing the final polymer product. The latest developments in synthetic elastomer technology, cellular plastics, synthetic fibers, polymer coatings, and several other topics were also included. The present review covers the area of polymer science and technology not included in these two reviews. To produce polymer products, considerable effort is required “after” the rate constants have been determined and “before” the polymer is molded; it includes analysis, design, construction, operation, control and optimization of reactor systems for production of polymers. The review is divided into six sections. In the first section, basic concepts related to polymerization reactions are presented; the other sections are devoted to various aspects of polymerization systems engineering such as thermodynamics, modeling and simulation, optimal design, dynamic optimization, stability analysis and optimal systems synthesis

Polymer Extrusion

The Role of Rheology in Polymer Extrusion (.pdf)

Viscoelastic Effects in Multilayer Polymer Extrusion (.pdf)