eation in the early chapters is separated from the rest of the discussions on polymerization mechanism. Thus, repetition occurs, and the development of ideas on mechanism is hard to follow. The book will be most valuable if the reader first scans it to gain familiarity with thelocation of specific bits of information. While not designed as a texthook, it could serve as a reference for advanced courses on polymers, catalysis, and new aspects of physical or organic chemistry. Because stereoregular polymeriza,tion borders on other fields of chemistry, the book has interest for teachers, students and researchers in heterogeneous catalysis, reaction mechanisms, and inorganic and organic synthesis. It has vslue for those interested primarily in synthesia, struoture,
and use of polymers; while for those carrying out research involving stereoregular polymers, the book is R necessity.
In Chapter 1the problems to he treated in succeeding chapters are delineated. This chapter is most helpful in understmding what follows. HERBERTN. FRIEDLANDER In C h a ~ t e 2r the ~rincioleof minimum Standard Oil Company (Indiana)
Whiting, Indiana Contributions to the Theory of Chemical Kinetics
Tho? A. Bak. Ejnar Munksgaard, publisher, 6 Norregade, Copenhagen, Denmark, 1959. 104 pp. 9 figs. 16.5 X 23.5 em. Paper bound. drt kr 20. The titlo of the book indicates the approach to he made in the presentation of the material in the manuscript. Tho dipcussion is purely theoretical and entirely mathemittiesl.
expressions for rates which cannot be solved in closed form. The variables however beoome separated when it is assumed t h s t some of the intermediate products in the reaction are in quasi-stationary states. The general oriterian which makes more understandable this quasi-stationary and steady state kinetics is shown to he the principle of minimumentropy produotion. In Chapter 3 oscillation reactions are discussed. In recent years considerable attention has been paid to the possible existence of oscillating chemical reactions. What the author does is t o try to find the exact conditions for the occurrence of oscillating chemical reactions and to develop a method of solving the resulting equations. The equations are in general non-linear, second order differential equations, or systems of such equations; these present certain difficulties. The author used the method of Kryloff and Bogoliauboff on a simple example of an oscillating system proposed b y Volterra as a model of interacting biologioill species. He states, however, t h a t it is extremely douhtful whether the Volterra equations represent a ~ eoft chemical reactions which occur in nature, and that themechanismof the periodicreaction of iodic acid with hydrogen peroxide which shows oscillatory hehavior is of interest. Chapter 4 deals with the theory of electrodiffusion. I n the electrodiffusion process the particle is considered as performing random motion between state 1 and state 2 in discrete 1, 2 space. This matian is transformed into random motion on a continuous axis in the direction of the field when the field acts on the particle. This random motion in the direction of the field can be desoribed as a diffusion. The author's caloulations show that the thermal diffusion interaction with field induced diffusion vanishes asymtotically as the time approaches infinity. A shtionary state solution for an alternating field is also presented. In Chapter 5 there is a discussion of the meehrtnical description of the irreversible process. The usual derivation of the Maxwell-Boltsmann equation was reinvestigrtted and the equation shown to be only an approximation to the correct equation. The author then attempts to improve upon the approach to the problem by starting with a more sophisticated mcchanicd description and going as far ss possible without making statistical assumptions. H e does this hy starting with the Liouville equation and integrating it directly in action-angle variables. H e finds that irreversibility cannot be obtained from the laws of mechanics alone, but t h s t other assumptions, more reasonsble than the olassioal assumption about molecular chaos, must he made. The author points out some of the difficulties inherent in the problem of irreversibility and some of the things which have been neglected in previous theories. (Calinued on page A85Z) ~
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BOOK REVIEWS Chapter 6 concludes the hook with a presentation of the mechanical theory of chemical reactions. The various theories as to how 8. particle escapes from a potcntial minimum including the "shuttling action" of Brownian motion and the transition state approach are discussed. Then a classical approach, which adopts the quantum mechanical conoept of phonons, is presented. The case of the particle moving in n potential field with two minima, is also discussed. Using his theory the author estimates the rate constant for a simplified model of a chemical reaction. EDWARD 8. AMIB University of Arkansas Fayetfeville
Techniques of Polymer Characterization
Edited by P. W. A l l a . Academic Press, Inc., New York, 1959. xiv 256 pp. Figs. and table^. 15 X 22.5 cm. $9.50.
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The field of polymer chemistry has expanded so rapidly over such a short time that it is a characteristic of many workers in it that they have little or no formal training in their specialty. Rather, they have either picked it up as an apprentice by working in a polymer research laboratory or have developed their techniques by themselves with the help of the literature. "Techniques of Polymer Characterization" is directed primarily toward this lest group. As the title indicates, it is devoted to the study of the properties of high polymers as they show up in dilute solutions.
These are the properties af the polymer molecules themselves and not, in general, cooperative properties such as one finds, e.g., in crystallites in solid polymers. The subjects covered are: fraotionation, osmometry, miscellsneous number average molecular weight determinations, light scattering, viscometry, end-group analysis, and bbek and graft copolymer characterization. The approach is a practical one. The theom for each section is sketched enough to indicate the background for the metho>, hut no attemot is made to eive - fine details. On thr othrr 1l:tnd the twhuiquts them~ r l v r as n di?cursrd rxtr.nsivvlv itwl pnvlic~ ul.tr cure is t n k v ~to point mtt p l . c w wlwm one might make errors inadvertently and where especial pains must he taken. One often feels that the attitude is that of s. master talking to his apprentice. In addition, there is copious reference to the original literature. Since each chapter is written by a different author there is some variation in the approach hut none of the chapten could he called inadequate. From the point of view of subject matter, one might wish that somewhat more sprtce had been spent on light mattering, that polyelectrolyte behavior had been included to a greater extent, and that the small section on the effect of rate of shear on viscosity measurements had been expanded. From the point of view of approach, occasionally the experts were a little overenthusiastic. For example, after indicating that one cannot obtain homogeneous fractions from a heterogenous polymer, the author speaks (p. 58) of cases where nearly homogeneous fractions may be used to establish a molecular weight distribution curve. These are all relatively minor objections, however, and should not conceal the fact that this will he a. very useful hook, bath for the novice who wants to got a start in the field and for the old hand who wants to brush up on recent developments. The present hook is complemented in some respects by the recently published "Number Average Molecular Weights" hy Bonnar, Dimhst, and Stross (Interscience, 1958). In that hook considerable detail is given in showing how actual calculations w e carried out to convert experimental data into molecular charaoteristics. The present work however is muoh more com~letein its discussion of the exverirncnrnl nwthodu t11t.unn~lvt~s :xrd, oir,wrcc.. also covers inethod5 m l n,lntwl u, nl~n,lwr :xvrmyr rnc~lrcul:rrwrightc. ~
T n o ~ h E. s FERINQTON The College of Wooster Woosler,Ohio Liquids and Liquid Mixtures
J. S. Rowlinsa, Senior Lecturer in Chemistry, The University of Mancheater. Butterworths Scientifio Publications. Academic Press. Inc.. New York. 1959.' ix 360 pp. Figs. and tahles: 15 22 cm. $12.
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In the past the theoretical and experimental study of the thermodynamic hehavior of liquid mixtures has often been separated from the study of pure liquids. (Continued a page A854)
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