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TH EDITION

ATKINS'

HYSICAL

CHEMISTRY

PETER ATKINS • JULIO DE PAULA

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ATKINS'

PHYSICAL

CHEMISTRY

OXFORD

UNIVERSITY PRESS Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto

With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States and Canada by W. H. Freeman and Company © Peter Atkins 1978, 1982, 1986, 1990, 1994, 1998 and © Peter Atkins & Iulio de Paula 2002, The moral rights of the authors have been asserted Database right Oxford University Press (maker) First published 2006

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Typeset by Graphicraft Limited, Hong Kong Printed in Italy on acid-free paper by Lito Terrazzi S.LI.

ISBN 9780198700722 ISBN 0198700725

1 3 5 7 9 10 8 6 4 2

Preface

We have taken the opportunity to refresh both the content and presentation of this text while-as for all its editions-keeping it flexible to use, accessible to students, broad in scope, and authoritative. The bulk of textbooks is a perennial concern: we have sought to tighten the presentation in this edition. However, it should always be borne in mind that much of the bulk arises from the numerous pedagogical features that we include (such as Worked examples and the Data section), not necessarily from density of information. The most striking change in presentation is the use of colour. We have made every effort to use colour systematically and pedagogically, not gratuitously, seeing it as a medium for making the text more attractive but using it to convey concepts and data more clearly. The text is still divided into three parts, but material has been moved between chapters and the chapters have been reorganized. We have responded to the shift in emphasis away from classical thermodynamics by combining several chapters in Part 1 (Equilibrium), bearing in mind that some of the material will already have been covered in earlier courses. We no longer make a distinction between 'concepts' and 'machinery', and as a result have provided a more compact presentation of ther- modynamics with fewer artificial divisions between the approaches. Similarly, equi- librium electrochemistry now finds a home within the chapter on chemical equilibrium, where space has been made by reducing the discussion of acids and bases. In Part 2 (Structure) the principal changes are within the chapters, where we have sought to bring into the discussion contemporary techniques of spectroscopy and approaches to computational chemistry. In recognition of the major role that phys- ical chemistry plays in materials science, we have a short sequence of chapters on materials, which deal respectively with hard and soft matter. Moreover, we have introduced concepts of nanoscience throughout much of Part 2. Part 3 has lost its chapter on dynamic electrochemistry, but not the material. We regard this material as highly important in a contemporary context, but as a final chapter it rarely received the attention it deserves. To make it more readily accessible within the context of courses and to acknowledge that the material it covers is at home intellectually with other material in the book, the description of electron transfer reactions is now a part of the sequence on chemical kinetics and the description of processes at electrodes is now a part of the general discussion of solid surfaces. We have discarded the Boxes of earlier editions. They have been replaced by more fully integrated and extensive Impact sections, which show how physical chemistry is applied to biology, materials, and the environment. By liberating these topics from their boxes, we believe they are more likely to be used and read; there are end-of- chapter problems on most of the material in these sections. In the preface to the seventh edition we wrote that there was vigorous discussion in the physical chemistry community about the choice of a 'quantum first' or a 'thermo- dynamics first' approach. That discussion continues. In response we have paid particu- lar attention to making the organization flexible. The strategic aim of this revision is to make it possible to work through the text in a variety of orders, and at the end of this Preface we once again include two suggested road maps. The concern expressed in the seventh edition about the level of mathematical ability has not evaporated, of course, and we have developed further our strategies for showing the absolute centrality of mathematics to physical chemistry and to make it accessible. Thus, we give more help with the development of equations, motivate

PREFACE ix

Traditional approach

Equilibrium thermodynamics Chapters 1-

Chemical kinetics Chapters 21, 22, and 24

Quantum theory and spectroscopy Chapters 8-11,13-

Special topics Chapters 12, 18-20,23, and 25

Statistical thermodynamics Chapters 16 and 17

Molecular approach

Quantum theory and spectroscopy Chapters 8-11, 13-

Statistical thermodynamics Chapters 16 and 17

Chemical kinetics Chapters 21, 22, and 24

Equilibrium thermodynamics Chapters 1-

Special topics Chapters 12, 18-20, 23, and 25

About the book

There are numerous features in this edition that are designed to make learning phys- ical chemistry more effective and more enjoyable. One of the problems that make the subject daunting is the sheer amount of information: we have introduced several devices for organizing the material: see Organizing the information. We appreci- ate that mathematics is often troublesome, and therefore have taken care to give help with this enormously important aspect of physical chemistry: see Mathematics and Physics support. Problem solving-especially, 'where do I start?' -is often a challenge, and we have done our best to help overcome this first hurdle: see Problem solving. Finally, the web is an extraordinary resource, but it is necessary to know where to start, or where to go for a particular piece of information; we have tried to indicate the right direction: see About the Online Resource Centre. The following paragraphs explain the features in more detail.

Organizing the information

Checklist of key ideas

D 1. A gas is a form of matter that fills any container it occupies. 012.

o 2. ;;:;:::~o::~":;~::r:~::~;;:~:~,;.~ pressure.

D 3. The pressure is the force divided by the area to which the force 013. is applied. The standard pressure is p-ft-= 1 bar (10^5 Pa).

4. coefficients^ B,

o 5. Temperature is

pressure, molar volume, and te critical point.

16. A supercritical fluid is a dense temperature and pressure.

o 7 Thermal equilibrium is a conditior a diathermic boundary.

o 8. The Zeroth Law of thermodynamics states that, if A is in

thermal equilibrium with E, and B is in thermal equilibrium with C, then C is also in thermal equilibrium with A. o 9. The Celsius and thermodynamic temperature scales are related by IlK=; erc + 273.15.

o 10. A perfect gas obeys the perfect gas equation, p V =; nRT, exactly

t&"\ IMPACT ON NANOSCIENCE ~ /20.2 Nanowires We have already remarked (Impacts 19.1, 19.2, and 119.3) that research on nano- metre-sized materials is motivated by the possibility that they will form the basis for cheaper and smaller electronic devices. The synthesis of nonowires, nanometre-sized atomic assemblies that conduct electricity, is a major step in the fabrication of nanodevices. An important type of nanowire is based on carbon nanotubes, which, like graphite, can conduct electrons through delocalized re molecular orbitals that form from unhybridized 2p orbitals on carbon. Recent studies have shown a cor- relation between structure and conductivity in single-walled nanotubes (SWNTs) that does not occur in graphite. The SWNT in Fig. 20.45 is a semiconductor. If the hexagons are rotated by 60° about their sixfold axis, the resulting SVvNT is a metallic conductor. Carbon nanotubes are promising building blocks not only because they have useful electrical properties but also because they have unusual mechanical properties. For example, an SWNT has a Young's modulus that is approximately five times larger and a tensile strength that is approximately 375 times larger than that of steel. Silicon nanowires can be made by focusing a pulsed laser beam on to a solid target composed of silicon and iron. The laser ejects Fe and Si atoms from the surface of the

Checklist of key ideas Here we collect together the major concepts introduced in the chapter. We suggest checking off the box that precedes each entry when you feel confident about the topic.

Impact sections Where appropriate, we have separated the principles from their applications: the principles are constant and straightfor- ward; the applications come and go as the subject progresses. The Impact sections show how the principles developed in the chapter are currently being applied in a variety of modern contexts.

xii ABOUT THE BOOK

Further information

Further information 5.1 The Debye-HOckel theory of ionic solutions Imagine a solution in which all the ions have their actual positions, but in which their Coulombic interactions have been turned off. The difference in molar Gibbs energy between the ideal and real solutions is equal to w~, the electrical work of charging the system in this arrangement. For a salt MpXq, we write ~ G~'" wt= (PJ1+ + qJ1J - (pJ1.~de:ll+ qj1~deal) := p(j1+ ~ .uldc.1l) +q(fl- - J1~d"al) From eqn 5.64 we write p+ - ,uldenl = J1 -_ ,u~d~a1= RTln y± $0 it follows that

This equation tells us that we must first find the final distribution of the ions and then the work of charging them in that distribution. The Coulomb potential at a distance r from an isolated ion of charge z/ in a medium of permittivity e is

The ionic atmosphere causes the potential to decay with distance more sharply than this expression implies. Such shielding is a familiar problem in electrostatics, and its effect is taken into account by replacing the Coulomb potential by the shielded Coulomb potential, an expression of the form

966 Appendix2 MATHEMATICAL TECHNIQUES A2.6 Partial derivatives

where r 0 is called the Debye length. W potential is virtually the same as the un small, the shielded potential is much s potential, even for short distances (Fig.

i;J 0.6- '?>

---

(5.73)

~ 0.

(5.74)

(5.75)

Fig.5.36 The variation of the shielded C distance for different values of the Deb Debye length, the more sharply the pot case, a is an arbitrary unit oflength.

lQ: ~::~::;~;d:r~t:h~:l~:~r~~~~;

Then plot this expression against roan interpretation for the shape of the plot

A partial derivative of a function of more than one variabl of the function with respect to one of the variables, all th constant (see Fig. 2.*). Although a partial derivative sho when one variable changes, it may be used to determine when more than one variable changes by an infinitesimal' tion of x and y, then when x and y change by dx and dy, re df= (!L) ox y dx+ (!L) ay ,dy where the symbol a is used (instead of d) to denote a part dfis also called the differential off For example, if!= ax^3 (!L) ax y^ =^ 3ax^2 y

1000 DATA SECTION

Table 2.8 Expansion coefficients, a, and isothermal compressibilities, /(T a/(lO-4K-l) (^) "TI(IO-6aun-l) Liquids Benzene 12.4 (^) 92. Carbon tetrachloride 12.4 90. Ethanol 11.2^ 76. Mercury 1.82^ 38. water (^) 2.1 49. Solids Copper 0.501 0. Diamond (^) 0.030 0. Iron 0.354 0589 Lead (^) 0.861 2. The values refer to 20nC. Data:A.lP(a),Kl{K'T)·

Table 2.9 Inversion temperatures, n points, and [oule--Thomson coefficien TI/K Tf/K Air 603 Argon 723 83. Carbon dioxide 1500 194. Helium 40 Hydrogen 202 14. Krypton (^1090) 116. Methane 968 90. Neon 231 24. Nitrogen 621 63. Oxygen 764 54. 5:Data: AlP,JL, and M.W. Zemansky, sublimes. Heat /l/ld NewYork(1957).

Further information In some cases, we have judged that a derivation is too long, too detailed, or too different in level for it to be included in the text. In these cases, the derivations will be found less obtrusively at the end of the chapter.

o. Dista

Appendices Physical chemistry draws on a lot of background material, espe- cially in mathematics and physics. We have included a set of Appendices to provide a quick survey of some of the informa- tion relating to units, physics, and mathematics that we draw on in the text.

Synoptic tables and the Data section Long tables of data are helpful for assembling and solving exercises and problems, but can break up the flow of the text. We provide a lot of data in the Data section at the end of the text and short extracts in the Synoptic tables in the text itself to give an idea of the typical values of the physical quantities we are introducing.

Mathematics and Physics support

Comment 1. A hyperbola is a curve obtained by plottingy against x with xy= constant.

Comment 2. The partial-differential operation (az/ox))' con~ists of taking the first derivative of z(x,y) with respect to x, treating y as a constant. For example, ifz(x,y) =x^2 y, then (~)^ ~ (d (^1) x'Y1l ~Y <Ix' ~ 2yx dXy ox ...r dx Partial derivatives are reviewed in Appendix l,

978 Appendix 3 ESSENTIAL CONCEPTS OF PHYSICS

Classical mechanics

AJ.l The linear momentum of a particle is a vector property and points in the direction of motion.

Problem solving

Classical mechanics describes the behaviour of objects in expresses the fact that the total energy is constant in the a other expresses the response of particles to the forces act A3.3 The trajectory in terms of the energy The velocity, u, of a particle is the rate of change of its p u=- dr dt The velocity is a vector, with both direction and magni velocity is the speed, v. The linear momentum, p, of a p its velocity, u, by p=mv Like the velocity vector, the linear momentum vector po of the particle (Fig. A3.1). In terms of the linear moment ticle is

Illustration 5.2 Using Henry's law To estimate the molar solubility of oxygen in water at 25°C and a partial pressure of21 kPa, its partial pressure in the atmosphere at sea level, we write bo = Po, - 21 kPa _ 2.9 x 1O-~mol kg"! I Ko! 7.9 X 104 kPa kg mol:" The molality of the saturated solution is therefore 0.29 mmol kg"". To convert this quantity to a molar concentration, we assume that the mass density of this dilute solution is essentially that of pure water at 25°C, or PHlO = 0.99709 kg dm-^3. It fol- lows that the molar concentration of oxygen is [02] = bOl x PHp = 0.29 mmol kg"! x 0.99709 kg dm"! = 0.29 mmol dm'" A note on good practice The number of significant figures in the result of a calcu- lation should not exceed the number in the data (only two in this case). Self-test 5.5 Calculate the molar solubility of nitrogen in water exposed to air at 25°C; partial pressures were calculated in Example 1.3. [0.51 mmol dm'"]

ABOUT THE BOOK Xlll

Comments A topic often needs to draw on a mathematical procedure or a concept of physics; a Comment is a quick reminder of the pro- cedure or concept.

Appendices There is further information on mathematics and physics in Appendices 2 and 3, respectively. These appendices do not go into great detail, but should be enough to act as reminders of topics learned in other courses.

Illustrations An Illustration (don't confuse this with a diagram!) is a short example of how to use an equation that has just been intro- duced in the text. In particular, we show how to use data and how to manipulate units correctly.

Exercises

14.1a The term symbol for the ground state oENI is 2~g. What is the total spin and total orbital angular momentum of the molecule? Show that the term symbol agrees with the electron configuration that would be predicted using the building-up principle. 14.1b One of the excited states of the Cl molecule has the valence electron configuration la~l aCl1r;'1Jr~. Give the multiplicity and parity of the term. 14.2a The molar absorption coefficient of a substance dissolved in hexane is known to be 855 dm; mol"! cm"' at 270 nrn. Calculate the percentage reduction in intensity when light ofthat wavelength passes through 2.5 mm of a solution of concentration 3.25 mmol dm'". 14.2b The molar absorption coefficient of a substance dissolved in hexane is known to be 327 dm' mol-l^ cm'" at 300 rim. Calculate the percentage reduction in intensity when light of that wavelength passes through 1.50 mm of a solution of concentration 2.22 mmol dm'". 14.3a A solution of an unknown component of a biological sample when placed in an absorption cell of path length 1.00 cm transmits 20.1 per cent of light of340 nm incident upon it. If the concentration of the component is O.Ill mmol dm", what is the molar absorption coefficient? 14.3bof an absorbing When light of wavelength substance at a concentration 400 nrn passes 0.667 through mmol 3.5 mmdm", theof a solution transmission is 65.5 per cent. Calculate the molar absorption coefficient of the solute at this wavelength and express the answer in cm' mol". , ""~ -.,-_.,~

Wavenum fig. 14. 14.7b The following data were obtained for t in methyl benzene using a 2.50 mm cell. Calc coefficient of the dye at the wavelength ernpl [dyej/Imoldrn") 0.00]0 0.0050 O. TI(pcrcent) 73 21 4.

Problems

Assume all gases are perfect unless stated otherwise. Note that I atm = 1.013 25 bar. Unless otherwise stated, thennochemical data arc for 298.15 K. Numerical problems 2.1 A sample consisting of 1 mol of perfect gas atoms (for which CV•m = ~R) is taken through the cycle shown in Fig. 2.34. (a) Determine the temperature at the points 1, 2, and 3. (b) Calculate q, w, I1U, and AH for each step and for the overall cycle. If a numerical answer cannot be obtained from the information given, then write in +, -, 0, or? as appropriate.

E lOO

0...^ e 0.

1 2

kJ,

22.44 44. Volume, Vldm' Fig. 2. 2.2 A sample consisting of 1.0 mol CaCGl(s) was heated to 800°C, when it decomposed. The heating was carried out in a container fitted with a piston that was initially resting on the solid. Calculate the work done during complete decomposition at 1.0 atm. What work would be done if instead of having a piston the container was open to the atmosphere?

Table 2.2. Calculate the standard enthalpy 0 from its value at 298 K. 2.8in a calorimeter A sample of the sugarand then ignitedn-ribose in the pres(CSHLOC temperature rose byO.910 K. In a separate e the combustion of 0.825 g of benzoic acid, f combustion is -325 I k] mol'", gave a temp the internal energy of combustion of c-ribo 2.9 The standard enthalpy of formation of bis{benzene)chromium was measured in a reaction Cr(C 6 H 6 h(s) -e Cr(s) + 2 C 6 H 6 (g) Find the corresponding reaction enthalpy a of formation of the compound at 583 K. Th heat capacity of benzene is 136.1 r K-I^ mol" 81.67 J K""I mol-^1 asa gas. 2.10; From the enthalpy of combustion da I1ft •• alkanes =^ kl (M/Cgmethane^ mol-I)}"through holdsoctane, and^ test the ex find the Predict 11ft" for decane and compare to th 2.11 It is possible to investigate the thermo hydrocarbons with molecular modelling m software to predict 6ft" values for the alka calculate I1ft""values, estimate the standar CnH1(n+]J(g) by performing semi-empirical or PM3 methods) and use experimental sta values for CO2{g) and H20(l). (b) Compar experimental values of 11<!/""(Table 2.5) an the molecular modelling method. (c) Test t I1lf"" == kj (M/(g mol"! ))" holds and find the

ABOUT THE BOOK ~

Exercises and Problems The real core of testing understanding is the collection of end-

of-chapter Exercises and Problems. The Exercises are straight-

forward numerical tests that give practice with manipulating

numerical data. The Problems are more searching. They are di-

vided into 'numerical', where the emphasis is on the manipu- lation of data, and 'theoretical', where the emphasis is on the manipulation of equations before (in some cases) using nu-

merical data. At the end of the Problems are collections of

problems that focus on practical applications of various kinds, including the material covered in the Impact sections,

About the Online Resource Centre

The Online Resource Centre provides teaching and learning resources. It is free of charge, complements the textbook, and offers additional materials which can be downloaded. The resources it provides are fully customizable and can be incorpor- ated into a virtual learning environment. Go to: www.oxfordtextbooks.co.ukJorc/pchem8e/

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The material includes:

Living graphs

A Living graph is indicated in the text by the icon 181:attached to a graph. This feature can be used to explore how a property changes as a variety of parameters are changed. To encourage the use of this resource (and the more extensive Explorations in Physical Chemistry) we have added a question to each figure where a Living graph is called out.

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10.16 The boundary surfaces of clorbitals. Two nodal planes in each orbital intersect at the nucleus and separate the lobes of each orbital. The dark and light areas denote regions of opposite sign of the wavefunction. h ~./ Exploration To gai~ insight into the ~ shapes of the j orbitals, use mathematical software to plot the boundary surfaces ofthe spherical harmonics Y3,m,( e,qJ}.

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About the authors

Iulio de Paula is Professor of Chemistry and Dean of the College of Arts & Sciences at Lewis & Clark College. A native of Brazil, Professor de Paula received a B.A. degree in chemistry from Rutgers, The State University of New Jersey, and a Ph.D. in biophys- ical chemistry from Yale University. His research activities encompass the areas of molecular spectroscopy, biophysical chemistry, and nanoscience. He has taught courses in general chemistry, physical chemistry, biophysical chemistry, instrumental analysis, and writing.

Peter Atkins is Professor of Chemistry at Oxford University, a fellow of Lincoln College, and the author of more than fifty books for students and a general audience. His texts are market leaders around the globe. A frequent lecturer in the United States and throughout the world, he has held visiting prefessorships in France, Israel, Japan, China, and New Zealand. He was the founding chairman of the Committee on Chemistry Education of the International Union of Pure and Applied Chemistry and a member ofIUPAC's Physical and Biophysical Chemistry Division.

Acknowledgements

A book as extensive as this could not have been written without significant input from many individuals. We would like to reiterate our thanks to the hundreds of people who contributed to the first seven editions. Our warm thanks go Charles Trapp, Carmen Giunta, and Marshall Cady who have produced the Solutions manuals that accompany this book. Many people gave their advice based on the seventh edition, and others reviewed the draft chapters for the eighth edition as they emerged. We therefore wish to thank the following colleagues most warmly:

Ioe Addison, Governors State University Ioseph Alia, University of Minnesota Morris David Andrews, University of East Anglia Mike Ashfold, University of Bristol Daniel E. Autrey, Fayetteville State University Ieffrey Bartz, Kalamazoo College Martin Bates, University of Southampton Roger Bickley, University of Bradford E.M. Blokhuis, Leiden University Iirn Bowers, University of Exeter Mark S. Braiman, Syracuse University Alex Brown, University of Alberta David E. Budil, Northeastern University Dave Cook, University of Sheffield Ian Cooper, University of Newcastle-up on- Tyne T. Michael Duncan, Cornell University Christer Elvingson, Uppsala University Cherice M. Evans, Queens College-CUNY Stephen Fletcher, Loughborough University Alyx S. Frantzen, Stephen F. Austin State University David Gardner, Lander University Roberto A. Garza-L6pez, Pomona College Robert 1. Cordon, University of Illinois at Chicago Pete Griffiths, Cardiff University Robert Haines, University of Prince Edward Island Ron Haines, University of New South Wales Arthur M. Halpern, Indiana State University Tom Halstead, University of York Todd M. Hamilton, Adrian College Gerard S. Harbison, University Nebraska at Lincoln Ulf Henriksson, Royal Institute of Technology, Sweden Mike Hey, University of Nottingham Paul Hodgkinson, University of Durham Robert E. Howard, University of Tu Isa Mike Jezercak, University of Central Oklahoma Clarence Iosefson, Millikin University Pramesh N. Kapoor, University of Delhi Peter Karadakov, University of York

Miklos Kertesz, Georgetown University Neil R. Kestncr, Louisiana State University Sanjay Kumar, Indian Institute of Technology Ieffry D. Madura, Duquesne University Andrew Masters, University of Manchester Paul May, University of Bristol MitcheU D. Menzmer, Southwestern Adventist University David A. Micha, University of Florida Sergey Mikhalovsky, University of Brighton Ionathan Mitschele, Saint Ioseph's College Vicki D. Moravec, Tri-State University Gareth Morris, University of Manchester Tony Morton-Blake, Trinity College, Dublin Andy Mount, University of Edinburgh Maureen Kendrick Murphy, Huntingdon College John Parker, Heriot Watt University Iozef Pectcrs, University of Leuven Michael J. Perona, CSU Stanislaus Nils-Ola Persson, Linkoping University Richard Pethrick, University of Strathclyde John A. Pojman, The University of Southern Mississippi Durga M. Prasad, University of Hyderabad Steve Price, University College London S. Rajagopal, Madurai Kamaraj University R. Rarnaraj, Madurai Kamaraj University David Ritter, Southeast Missouri State University Bent Ronsholdt, Aalborg University Stephen Roser, University of Bath Kathryn Rowberg, Purdue University Calumet SA Safron, Florida State University Kari Salmi, Espoo-Vantaa Institute of Technology Stephan Sauer, University of Copenhagen Nicholas Schlotter, Hamline University Roseanne J. Sension, University of Michigan A.1. Shaka, University of California Joe Shapter, Flinders University of South Australia Paul D. Siders, University of Minnesota, Duluth Harjinder Singh, Panjab University Steen Skaarup, Technical University of Denmark David Smith, University of Exeter Patricia A. Snyder, Florida Atlantic University OUe Soderrnan, Lund University Peter Stilbs, Royal Institute of Technology, Sweden Svein Stolen, University of Oslo Fu-Ming 'I'ao, California State University, Fullerton Eimer Tuite, University of Newcastle Eric Waclawik, Queensland University of Technology Yan Waguespack, University of Maryland Eastern Shore Terence E. Warner, University of Southern Denmark