Raoul Kopelman Festschrift - The Journal of Physical Chemistry (ACS

The Journal of

Physical Chemistry VOLUME 98, NUMBER 30, JULY 28,1994

0 Copyright 1994 b y fhe American Chemical Society

Raoul Kopelman

Photograph by D.C.Goinp

Autobiographical Sketch If erve this speck w e , it so by a narrow margin. Nevertheless, I enjoy ittremendously, and this goes for both the friendshipand thescienceof my wntributingcolleagues. I was asked to provide an autobiographical sketch, and I am giving here the historical connection betwan a five year old "wunderkind" ofsorts and a sixty plus year old child at heart who still highly enjoys the game. Having present and future students in mind, I mainly emphasize the "initial conditions". I was born in Vienna, Austria, on October 21, 1933. When I was five. my father, Josef Koppelman, a well-known film producer, came back from ten months in Buchenwald; he could not believe how fast I had turned into a whiz kid in math. I could multiply in my head large numbers faster than I can today with the aid of a calculator. On April 1, 1939, my mother, KlaraChaja, my father, and I fled Vienna to go to Jerusalem. 0022-3654/94/2098-7219304.50/0

In sixth grade of elementary scho Tel-A ,I got on oan from my teacher a small booklet in German on chemical experimentation. With four other classmates we formed a chemistryclub. It was heavy on'thwreticians" (Joshua Jortner, Assa Lifshitz,andmyself) andshorteron experimentalists. During the winter break and onwards, we had a wonderful time, whether making and detonating explosives (illegally, of wurse. during a politically highly sensitive period) or subjecting bugs to carbon dioxide, pureoxygen, oravacuumcreated by burning magnesium in oxygen. In contrast to the thwry in the German booklet, nothing would kill a Middle Eastern bug, although now I think that we probably did not wait long enough. Joshua and I went together to high school, sharing a lot of experiences. including the world's best math teacher, Joseph Klein, and worst chemistry teacher. 0 1994 American Chemical Society

7220 The Journal of Physical Chemistry, Vol. 98, No. 30, 1994 Joshua became a chemistry student at the Hebrew University in Jerusalem, as did Assa, while I studied chemical engineering at “The Technion” at Haifa. As my father died when I was sixteen, to attend college I concomitantly had a full-time job at a night high school, teaching mainly Hebrew literature. In my senior year I took an additional full-time, day-time job at the Israel Mining Company. I analyzed the contents of ores, the old fashioned gravimetric way. With the encouragement of my boss, I adopted a novel literature method, using a color indicator and speeding up the process by a factor of three or more. Thus, the analysis results of the newly discovered iron ores were ready in time for an important socioeconomicdebatein the Israeli Knesset. At the time I did not quite understand why I was asked to report my results in terms of percent iron oxide, rather than just iron. In the Knesset the Minister of Finance quoted our numbers as percent pure iron, hence, claiming that our ores were comparable to premium Norwegian ores. Thus, it passed that a megainvestment was made in the Acre Steel Works. My chemical engineering education was sufficient to convince me right away that this would be a disastrous undertaking, as it indeed turned out to be. I had chosen my career with the idea of helping society. Now my first professional success achieved the opposite. Suddenly, I had lost my enthusiasm for engineering and socioeconomics. Science became the strange attractor. At that time we had an influx of brilliant American-Jewish scientists at the Technion, including David Bohm, David Fox, Nathan Rosen, and Otto Schnepp. Due to them, especially Otto, as well as Uriah Garbatzki, my first physical chemistry professor, and the two teaching assistants Mordechai Folman and Shai Shavit I was hooked on physical chemistry. My senior project under Arjeh Samuel, the son of the well-known German-JewishIndian spectroscopist, was done on the ancient Beckman DU spectrophotometer,all manual, of course. It was an interesting little project on the drastic solvent effects in water-alcohol mixtures, concerning the spectrum of the thiosulfate ion (I also rediscovered the fact that this ion could be eaten up by ancient bacteria). Samuel was excited enough to submit the work to Nature, just before leaving the country. It came back with a recommendation to submit it to JACS. Nevertheless, being an undergraduate I let it go, starting thus my string of unpublished papers, including several much better later works, such as my Columbia Ph.D. thesis and works from Harvard, Caltech, and Michigan. My real introduction to science occurred in the summer of 1955. Before leaving for the summer, Otto Schnepp suggested that I read Eyring, Walter, and Kimball’s book on quantum chemistry. This kept me busy, in addition to my two full-time jobs and getting ready for my wedding to Chava Blodek on September 15, 1955. A week later my MSc. work started in earnest, coupled with a TA-ship (Phys. Chem. Lab.). The first project was a flop. I spent almost a year trying to see the absorption spectra of the higher electronic states of hexamethylbenzenecrystals (trying to check out an assignment by Dunn and Ingold). Otto had to intervene and say “enough!”. The substitute crystal was hexachlorobenzene. I got a beautiful crystal and spectrum at first try (Chava helped me grow crystals over the weekend). I really lucked out-reproducing it tookmany months since one needed a 3x3 mm cross section of a submicrometer thick single crystal with no holes. This was a lot of fun! The data indicated a deviation from hexagonal structure, at least in theexcitedstate. Corroboratingdata were takenin theinfrared. Here I built my own polarizer, made of exact elliptical silver chloride films, cut out in total darkness with a plastic spoon since no degrading metal tool was allowed. Every time, nowadays, when I toss out a disposableplastic knife I still resent its absence in those days.

During my MSc. work, I took some wonderful courses, and when I arrived later at Columbia, the committee hardly believed that I took quantum mechanics with David Bohm in person and GroupTheory with David Fox. Regarding the latter, the lectures were in English, the text in German (Wigner), and I produced class notes in Hebrew. Here I had to make up many new Hebrew terms. Twenty years later when, on sabbatical, I taught Group Theory at the Physics Department at Tel-Aviv, I discovered to my surprise that I already knew the officially accepted Hebrew terms. By the end of 1956, Otto made a monumental decision, as far as I was concerned: he decided to go on sabbatical to the U.S. for two years. He encouraged me to apply to US. Ph.D. programs. Conceptually and financially, this seemed to me like a trip to the moon. I applied to a dozen of the best U.S. schools and to a few of lower rank, to improve my chances (lucky there were no application fees back then). I was astounded to get admitted to all of them, with TA-ship offers. Based on little knowledge, I whittled them down. Berkeley and George Pimentel were out because the official admittance letter went by sea-mail (even though I had an official letter re the TA-ship). Harvard (and Bill Klemperer) were eliminated because it paid $100 less per year. The final decision was between Minnesota (Bill Lipscomb and Bryce Crawford)and Columbia (Ralph Halford), my eventual choice. At that time, I was one of the first three Israeli students to receive a Fulbright travel grant. Columbia had a wonderful chemistry department, from old timers like Louis P. Hammet and Vicky La-Mer to “youngsters” like George Frenkel and Ron Breslow. The physics department was absolutely the best, with five Nobel prize winnders and as many future Nobelists. There was interdepartmental collaboration (e.g., Charles Towns and Benjamin Daily). My colleague graduatestudentswere a bright lot, such as HerbStrauss, Gershon Vinkov, and many others. Most impressive were the undergraduates. In my first semester,I taught in the physical chemistry lab and had only four seniors: Martin Friedlander, Jerry Goodisman,Roald Hoffman, and Bob Pecora. The other veteran TA chose to supervise some twenty chemical engineering students and ended up with less work. I rediscovered early on the truth of the 1800 year old Hebrew proverb of Jehuda Hanassi: “I have learned a lot from my teachers, more from my colleagues, and most of all from my students”. The truth of this pearl of wisdom has become clearer and clearer to me as the years pass by. As soon as I joined Ralph Halford he became the Department Chair. The year after that he was Dean of the Graduate School and in my third and last year he was also Vice Provost. In my first summer I learned as much as possible from Joe Blanc and Charlie Brecher-both were writing up their Ph.D. theses. Soon I was alone in the lab, learninga lot of independence. I maintained a monthly meeting with Halford, at his distant office, scheduled always a month in advance. My third and last year was wonderful. By then I had already finished the Ph.D. quota-a polarized IR spectrum of a single crystal grown at low temperature (methyl acetylene) and was working on a second crystal (dimethyl acetylene) which was an intellectual delight (below). Charlie Brecher came back to the lab as a postdoc, and Isaac Freund joined as a new graduate student. Halford was stubbornly meticulous about his papers, and they were scholasticpearls. However, I did not plan to come back as a postdoc to turn my thesis into a paper. Discussing it with Halford, I condensed my 200 page draft into a 19 page thesis (plus figures), so as to double as a paper. Even so, it was never published. Halford always used to say: “It just needs another half-hour of polishing”. Still, I learned a lot from Halford’s brilliant approach to science. Scientifically, it was a classic Ph.D. project. I observed low temperature higher order phase transitions which kept intact the crystal’s optical singledness and the spectrum’s polarizations.

The Journal of Physical Chemistry, Vol. 98, No. 30, 1994 7221 There is practically free methyl group rotation above the transition while it is quite hindered below it. A Mathew function analysis showed that the intramolecular barrier was extremely low, which was completely inconsistent with Linus Pauling’s “banana bond” theory. Visiting Harvard, I found out to my delight that Dudley Hershbach and E. Bright Wilson had come to the same conclusion from their gas-phase measurements. My thesis also derived the first group theoretical optical selection rules for a molecule with free internal rotation-a concept later enlarged on by LonguettHiggins, John Hougen, and Phil Bunker. At that time, it was dubbed by some as “Kopelman’s rule of parsimony” because it minimized the size of the supergroup. For my postdoctoral education I did choose to work with Bill Klemperer as his first postdoc, even though I had competing offers paying up to twice the salary. My first visit happened to be on the day Len Wharton and Bill’s molecular beam machine worked for the first time. I was hooked by the enthusiasm and the challenging atmosphere. When I arrived in fall 1960, I gave Bill details about Maiman’s first lectureon the successful operation of a laser. Bill immediately suggested that I look into the utilization of the laser for Raman spectroscopy. It was one of the many ideas of Bill whose time has come later. Quoting Herb S t r a w , Bill was “bubbling over” with new ideas. It was a wonderful learning experience, and some of these ideas came in handy years later. I need not describe the exciting place Harvard was a t the time. I also learned a lot, in addition to Bill, from E. Bright Wilson, Dave Buckingham, and many other exciting professors, as well as from graduate students like Len Wharton, Jerry Goodisman, and Roald Hoffman, and undergraduate students such as Roy Gordon and Dick Zare. Experimenting with many of Bill’s new ideas even resulted in some work: dipole moments of excited states, unpublished environmental effects on internal rotation, and decent far-infrared molecular spectra (free of water vapor lines). Still, I feel that I took much more than I gave. In 1962 our first son, Orion, was born and we moved back to Haifa where I had a junior faculty position waiting. Little did I suspect that the transition back would be harder than coming to the States. Worse than the meager means was thedepartmental politics. The best were the wonderful undergraduate and graduate students. Being in charge of moving and renovating the physical chemistry student lab, I introduced the use of computers. Unfortunately, a t the time, many considered them as “antieducational“ tools. An undergraduate project (Aviva Maoz) resulted in the solution to the then 30 year old mystery of the C. P. Snow ethylene or olephinic “mystery bands”. Combined high materials purity and the growing of single crystals at low temperatures were the key-an important lesson for my future work. Our second son, Leeron, was born in 1963 and in the fall of 1964 we all arrived in Pasadena, California, again penniless. I have often said that my two years a t Caltech were the best in my life. I fell into a wonderful situation. Wilse Robinson and his group were engaged in some of the most exciting research efforts in physical chemistry/chemical physics. There were the new experimental methods and conceptual breakthroughs regarding radiationless transitions, molecular energy transfer, exciton phenomena, matrix isolation, liquid structure, and many related problems ranging from atomic excitations in interstellar matter to the primary process of photosynthesis. There was a beautiful atmosphere of discussions and collaborations among the luminaries, including Max Delbruck, George Hammond, Harden McConnel (who would still come back from Stanford), and many, many others. Personally, I also benefited from discussions with Aaron Kuperman, Bill Goddard, Vince McCoy, Rudolph Massbauer, Richard Feynman, Amnon Yariv, etc., etc. and over at UCLA with Mostafa El-Sayed, among others. The Robinson group was really wonderful and I’ll only mention the

three students I collaborated and co-published with: Elliot Bernstein, Steve Colson, and Dave Hanson. I am listing here some of the Caltech work I shared with Wilse Robinson’s group, as it became the basis for much future work, including my own: (1) Exciton exchange (and other) matrix elements are uniquely defined in both magnitude and sign, provided that the group theory is consistently applied and there are sign or phase sensitive measurements, such as polarizations. (2) The entire exciton band shape can be determined from carefully measured indirect vibrational-to-electronic transitions. (3) Using isotopic mixed crystals it is indeed possible to determine individual pairwise interactions, using both quasiresonance shifts and resonance pair splittings, due to, respectively, localized guest excitons and “miniexcitons” (a later name for our “resonance pair” excitations). This enables matrix element by matrix element tests of any theory, for both magnitude and sign (it is still a challenge for theorists). These concepts were also the obvious forerunners of the later coined exciton and electron superexchange. (4) Vibrational exciton interactions, like electronic ones, are not necessarily dominated by transition dipoles, thus resulting in exciton band shifts and splittings even for gerade (Raman active) normal modes. ( 5 ) The interplay of intramolecular and intermolecular resonances, e.g., Fermi and exciton as a tool for molecular crystal studies. (6) The “orientation symmetry” of guest molecules in host crystals. We arrived in beautiful Ann Arbor the summer of 1966, and two years later we moved into our home and our daughter Shirli was born. Professionally, I was again largely on my own for better or worse. While waiting for my own space and spectrometer, I started my experimental work in Tom Dunn’s lab, sharing the apparatus with his Ph.D. student, Rick Francis, which really smoothed the way (and shaped the future cryostats). Soon, thereafter, I had my own group of wonderful Ph.D. students, followed soon by a great group of postdocs (see list). There were also wonderful professional interactions with my early colleagues in chemistry, Tom Dunn, Larry Bartell, Sy Blinder, Chris Nordman, Bob Taylor, Ed Westrum, and the long retired Kasimir Fajans, as well as in physics (D. M. Dennison) and mathematics (Frank Harary). However, the proverbial words about the primary role of one’s students became more and more evident, including undergraduates (see list). In spite of wonderful sabbaticalsand other stays-Tel Aviv, Stuttgart, Munich, UCSD, ETH, Bar Ilan, and the Hebrew University-the anchor of my research and teaching has remained here at the University of Michigan. However, it has delocalized itself from physical chemistry to analytical chemistry, physics, applied physics, biophysics, toxicology, and more. I started my career in science and technology with the idea of applying my talents to the service of society and humanity through both research and teaching. I got hooked by the wonderful intellectual challenges. I also ended up with a lot of wonderful friendships. I feel that I am doing right now the most exciting work of my life, as I always have. My aim has been to shed some light on certain small uncharted domains of science. Presently, my group and I are doing it with a very small point of light indeed. The resulting opto-chemical probes may even bring improvements to medical technology. Acknowledgment. This special issue is indeed a wonderful birthday present. My deep gratitude goes to Yossi Klafter, Katja Lindenberg, and Paras Prasad both for their efforts here and for the organization of a symposium last October. Special thanks go also to this Journal‘s editors as well as to my Michigan colleagues for their support of the symposium and volume. My deepest appreciation goes to all the scientific contributors of this volume. They represent my teachers, colleagues, and students and, most of all, the friendships that engulfed me during both good and less than good times. At the risk of repetition, I

7222 The Journal of Physical Chemistry, Vol. 98, No. 30, 1994 would like again to thank my teachers, my colleagues, and my students for their insights and friendship. Finally, I would like to thank my late parents, who raised and educated me under very trying circumstances. I would also like to thank my sisters in New York, my extended family, and my sister in Vienna with her late husband who were always there for me. Especially, I would like to thank my children for bearing

with my strange addictionand crazy hours. My deepest gratitude goes to my wife for her moral support, dedication, and assistance all these years. Raoul Kopelman Ann Arbor May 1994

J . Phys. Chem. 1994,98,1223-I224

Biographical Notes Positions The University of Michigan, Kasimir Fajans Professor of Chemistry, Physics and Applied Physics, 1994-present The University of Michigan, Professor of Chemistry and Physics and Member of Applied Physics and Biophysics Programs, 199l-present The University of Michigan, Professor of Chemistry, 197 l-present Hebrew University of Jerusalem, Department of Applied Physics and Materials Sciences, Visiting Professor, 1989 Bar-Ilan University, Israel, Department of Physics, Visiting Professor, 1988 The Swiss Federal Institute of Technology, Zurich, Department of Physical Chemistry, Visiting Professor, 1988 University of California, San Diego, Institute for Nonlinear Science, Visiting Professor, 1987-88

University of Stuttgart, Institute of Physics, Visiting Professor, 198 1 Tel-Aviv University, Institute of Chemistry, Visiting Professor, 1980-8 1 Tel-Aviv University, Institute of Chemistry, Visiting Professor, 1972-73 The University of Michigan, Associate Professor of Chemistry, 1968-7 1 The University of Michigan, Assistant Professor of Chemistry, 1966-68 California Institute of Technology, Senior Research Fellow, 1964-66 Israel Institute of Technology, Lecturer in Chemistry, 1962-64 Harvard, Research Associate in Chemistry, 1960-62 Education Ph.D. Chemistry, Columbia University, 1960 M.S. Chemistry, Israel Institute of Technology, 1957 Dipl. Engin. Chemical Engineering, Israel Institute of Technology, 1956 B.S. Chemical Engineering, Israel Institute of Technology, 1955 Research Interests 1. Excitation dynamics in molecular aggregates and wires: excitons and phonons in crystalline and glassy materials, composite polymers, porous membranes, photosynthetic antenna, sodium channels, and DNA-fluorophore adducts. 2. Heterogeneous reaction kinetics: rate laws and reactant self-ordering at interfaces and in confined dimensions. 3. Monte Carlo computer and supercomputer simulations of critical transport phenomena and fractal-like chemical kinetics. 4. Laser microspectroscopy and scanning photon and exciton tunneling microscopy. 5. Submicron intracellular fiber-optic chemical and biochemical sensors.

Teaching Interests Physical Chemistry and Solid-state Physics, Undergraduate and Graduate, Lecture and Laboratory Honors and Awards Collegiate Professorship (Chair), 1994 Margaret and Herman Sokol Award, 1993 Fellow, American Physical Society, since 1984 Faculty Recognition Award, The University of Michigan, 1990 Distinguished Faculty Award, The University of Michigan, 1989 Fulbright Research Award, 1987-89 NIH National Research Service Award, 1987-88 NSF Creativity Award, 1986 Fellow of the Max Planck Institute, Stuttgart, 198 1 NIH Senior International Fellowship (Fogarty), 1979 NATO Senior Fellowship, 1976 N I H Special Research Fellowship (overseas), 1972-73

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Fulbright Exchange Student, 1957-60 Professional Service Chairman of Fulbright Committee in Chemistry, 1990-92 Editorial Board, J. Phys. Chem., 1985-88 Editorial Board, J. Cryst. Mol. Struct., 1972-84 Research Cohort Current: 8 graduate students, 3 post-docs, 2 visiting scholars, 1 undergraduate. Prior: 25 Ph.D. dissertations, ca. 30 post-doctoral collaborators.

J. Phys. Chem. 1994’98,1225-1226

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Scientific Contributions Raoul Kopelman is a scientist of great imagination and versatility, a mentor and friend of many students and colleagues, and a rare and kind human being. A special issue in his honor is a small way in which we can convey our appreciation for him and the value that we place on his friendship. In his autobiography Raoul tells of his early years and the way in which those years and the people that he encountered shaped his scientific youth. Already as a student and as a postdoc, he was “in the thick of things” and a participant in many of the exciting scientific and social events of the times. He ends this fascinating early story at about the time when he arrived at the University of Michigan. That was almost 30 years ago. Since then, he has built an enormous record of achievements and honors. It is difficult to distill these accomplishments into a few short paragraphs. Some of them can be inferred from the extensive lists of awards, publications, and collaborations that accompany this story. A short description of his more recent accomplishments perhaps demonstratesthe breadth and magnitude of his creativity.

1. A Nanometer Subwavelength Photon Source (World’s Smallest Light Source) Mimicking green plant photosynthetic antenna, Raoul Kopelman and Aaron Lewis produced an exciton light source with a diameter as small as 40 nm. This light source is the prerequisite for near-field optical microscopy, a new microscopy that circumvents the optical diffraction limit. With the aid of such light sources, including fiber-optic tips, optical microscopy has now been performed with a resolution down to 12 nm.

2. Sub-Micrometer Optical Fiber pH Sensors Kopelman’s group has utilized near-field optics principles for the nanofabrication of optochemical sensors with volumes that are a billion times smaller than the state of the art. Femtoliter samples can now be analyzed optically and yield precise pH measurements with an absolute detection limit of zeptomoles. In addition, the response time has been reduced from seconds to milliseconds. These pH sensors have been used for in situ measurements of individual biological cells and rat embryos (8-12 days old). This resulted in the first direct monitoring of chemical changes as a function of growth in intact embryos. Furthermore, the biochemical effects of drugs in the environment can easily be monitored in a single embryo, i.e., pH changes that are induced by the reaction of the embryo to the drug. 3. First Experimental Observation of Reactant Segregation for Elementary Bimolecular Reactions Earlier theoretical and computer simulationpredictionsof selfordering in dilute solutions (see below) have been confirmed experimentally in Kopelman’s laboratory. The entire approach represents a paradigm change from the accepted EinsteinSmoluchowski formalism for diffusion-limitedreaction kinetics. More recent computer simulations have led to the discovery of self-ordering in steady state reactions. 4. Energy Transport in “Molecular Wires” Kopelman’s research group has demonstrated experimentally efficient exciton transport in single chains of macromolecules. While electron wires have only been produced down to a diameter of 80 A, these exciton wires have a diameter of about 5-8 A. This demonstrated earlier deductions by Kopelman on molecular exciton transport and also yielded a new method for the characterization of polymer blends and molecularly doped polymers.

5. Nanospectroscopy Based on Kopelman’s new nanometer-sized light sources and near-field optical microscopy, microspectroscopy has been re-

placed by nanospectroscopy. In a heterogeneoussampledifferent spectra have been obtained from domains that are as little as 40 nm apart. This has been demonstrated on polymeric samples and Langmuir-Blodgett films, and was the forerunner of today’s single molecule spectroscopy. 6. Fractal Reaction Kinetics

Some of Raoul Kopelman’s most conspicuous successes have been in the new area of “fractal” science. It is fair to say that the area is enjoying a popularity almost amounting to notoriety in view of the multitude of workers who have plunged into the field with more enthusiasm than care. What has distinguished Kopelman’s approach is its definitive nature and chemical relevance. He has erected a meticulous and quantitative framework enabling him to make testable predictions and to explain important results in a variety of areas that have long resisted interpretation. Experiments and supercomputer simulations carried out by members ofKopelman’s researchgroupstimulated many theorists, often in collaboration with Kopelman, to develop a new theory of reaction kinetics pertaining to certain types of reactions. This theory differs drastically from the venerable EinsteinSmoluchowski laws of diffusion-controlledreaction kinetics. The new reaction laws apply to the biochemistry of the cell (and have just explained the observed puzzling orders of cytoplasmic enzymesubstrate reactions), soil chemistry (explaining anomalies of pesticide degradation), heterogeneous catalysis (e.g., hydrogen on supported platinum in petroleum reforming), solution photochemistry inside porous membranes, solid state reactions (exciton fusion in molecular crystals, polymer blends and other disordered materials), and energy transport in photosynthetic antennae. They may also apply to electric charge separations in clouds and to neuron gating kinetics. Conceptually, the revolutionary outcomeis associatedwith the fact that nonequilibrium, diffusion-controlled reactions in low dimensions or dimensionalities will routinely result in self-ordering or self-organization of the reactant particles. ~

7. Transport of Energy in Solids A 25-year old Nobel-prize-winning concept, “Anderson localization”, was believed to account for the migration of energy in solids under many circumstances; 25 years ago, Kopelman undertook to develop an alternative “percolation”approach which is now favored in a wide variety of cases. The Hoshen-Kopelman multiple cluster algorithm is still used worldwide in Monte-Carlo simulations. It has been applied by Kopelman to obtain refined critical exponents and to test basic concepts such as the “fracton (spectral) dimension”. These more recent achievements should not obscure those of Kopelman’s earlier work. His first studies at the University of Michigan establishedexperimentalmethods for obtaining exciton parameters in molecularcrystals via the techniquesof “resonance pairs” (isotopically mixed crystals) and “hot band spectra” (pure crystals). He also refined group-theoretic concepts (interchange symmetry) that became the basis for much of the present international research on exciton dynamics. Shortly thereafter, Kopelman discovered the existence of localized in-band rotational phonons in molecular crystals (proving it experimentally via isotope shifts). Results were basic for later developments on energy relaxation in mixed crystals, glasses, and molecularlydoped polymer films. At the same time, Kopelman conceived of a phonon side-band method for obtaining the complete phonondensity-of-states. In some cases, this method turns out to be competitivewith the traditional neutron scattering technique but requires equipment thousands of times less expensive.

1226 The Journal of Physical Chemistry, Vol. 98, No. 30, 1994 This record of accomplishments is truly extraordinary! The lists and descriptions of accomplishments speak to Raoul Kopelman’s scientific stature but do not speak to the side of Raoul that makes him such a very special person. He has helped many of us in ways beyond those of any ordinary teacher. He is recognized by his students and colleagues as a human being of unusual sensitivity and patience. He never bears a grudge. He is always cheerful. He is everyone’s ideal colleague.

Raoul Kopelman is a scientific statesman who has influenced many of us in the best sense of the world. He has inspired us and has given us his friendship. We thank him for these wonderful gifts. Katja Lindenberg Paras Prasad Joseph Klafter

J. Phys. Chem. 1994,98, 7227

Scientific Collaborators Undergraduate Copublishers. A. Lubetzky-Maoz, R. Le-Sar, E. Fauman Masters Students (in chronological order). R. Poupko (Technion, Israel Institute of Technology); P. H. Chereson, P. H. Friedman, S. D. Woodruff, F. W. Ochs, E. M. Monberg, P. Argyrakis, D. Hooper, D. Ahlgren, P. Klymko, S. Gentry, R. Parson, 1. Poupko-Newhouse, J. Newhouse, L. A. Harmon, C. Li, Y.-E. Koo, E. Cltment, L. Li-Bovet, Z.-Y. Shi, J. Holder, R. Schoonover, I. Choi, S. Smith, A. Lin, M. Shortreed, G. Merritt, A. Yen, Y. Chen. PLD. Students (completed, in chronological order). F. W. Ochs, P. H. Chereson, P. H. Friedman, S. D. Woodruff, E. M. Monberg, P. Argyrakis, D. Ahlgren, P. Klymko, S.Gentry, R. Parson, I. Poupko-Newhouse, J. Newhouse, L. A. Harmon, C. Li, Y.-E. Koo, E. Clement, L. Li-Bovet, Z.-Y. Shi, J. Holder, R. Schoonover. Postdoctoral Fellows (in chronological order). J. Laufer, H.-K. Hong, P. N. Prasad, J. Hoshen, P. H. Friedman, E. Sommer, N. Schlotter, P. Argyrakis, L. W. Anacker, J. Newhouse, J. Prasad, S. Parus, L. A. Harmon, L. Li, Y.-E. Koo, S.-K. Kook, R. Zenobi, Z.-Y. Shi, D. Birnbaum, W. Tan, Z. Rosenzweig. Research Collaborators (in alphabetical order). P. Argyrakis, D. Ben-Avraham, E. Bernstein, J. E. Bertie, G. H. Bishop, C. S. Blackwell, A. Blumen, E. Cltment, S. Colson, M. Drake, A. H. Francis, H. T. Grahn, V. Habib, D. Hanson, C. Harris, R. J. Harrison, S.Harush,S. Havlin, N. E. Hulburt, G. F. Imbush, M. Isaacson, J. Jortner, A. Keramiotis, J. Klafter, Y.-E. Koo, J. Langmore, H. Laralde, G. E. Leroi, A. Lewis, K. Lieberman, R. Lieberman, K. Lindenberg, V. Makarov, R. Merlin, E. Monson, J. S. Moore, T. Norris, B. Orr, S.Parus, K. Ploog, F. D. Quinn, L. Sander, K. Sazaki, W . 3 . Sheu, E. J. Stanley, D. Stauffer, H. Taitelbaum, B.Thorsrud, G. Weiss, B. West, Z. Wu, G. Zumofen. Teachers. 0. Schnepp, R. Halford, W. Klemperer, G. W. Robinson.

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Bibliography (Annotated since 1985) 1.

2.

3. 4.

5.

6. 7. 8.

Low TemperatureUltraviolet Spectroscopy-An Appraisal of Applicability to the Organo-Chemical Industry, R. Kopelman, Dipl. Eng. Thesis, Technion, Israel Institute of Technology (1957). Electronic Spectra of Hexamethylbenzeneand Hexachlorobenzene Crystals. R. Kopelman, MSc. Thesis, Israel Institute of Technology (1957). Infrared Spectrum of Hexachlorobenzene, R. Kopelman, and 0. Schnepp, J. Chem. Phys. 30, 597 (1959).

20. 21.

Near-Ultraviolet Spectrum of Crystalline Hexachlorobenzene, 0. Schnepp, and R. Kopelman, J . Chem. Phys. 30, 868 (1959).

22.

Infrared Spectra of Dimethyl AcetyleneCrystal: Internal Rotation and Phase Transition, R. Kopelman, Ph.D. Dissertation, Columbia University (1960).

23.

Dipole Moments of Excited Electronic States, R. Kopelman, and W. Klemperer, J . Chem. Phys. 36, 1693 (1962). Far-IR Spectrum of Dimethyl Acetylene: Internal Rotation and Evidence for a Dbh Effective Symmetry, R. Kopelman, J . Chem. Phys. 41, 1547 (1964). Vibrational Exciton Splitting, Fermi Resonance and Crystal Structure of Methyl Iodide, R. Kopelman, J . Chem. Phys. 44, 3547 (1966).

Electronic Spectrum of Ethylene Single Crystal: Search for the Olefin Mystery Band, A. Lubezky, and R. Kopelman, J . Chem. Phys. 45, 2526 (1966). 10. Frenkel Exciton Selection Rules for k = 0 Transitions in Molecular Crystals, S.D. Colson, R. Kopelman,and G. W. Robinson, J . Chem. Phys. 47, 27,5426 (1967). 11. Interchange Symmetry I: Molecules, Crystals and Excitons, R. Kopelman, J . Chem. Phys. 47,2631 (1967). 12. Benzene Vibrational Exciton Spectrum, R. Kopelman, J . Chem. Phys. 47, 3227 (1967). 13. Book Review: The Triplet State: Proceedings of an International Symposium at the American University of Beirut (Feb. 1967), edited by A. B. Zahlan, et al., Cambridge University Press: Cambridge, 1967,Am. Sci. 56,267A (1968). 14. Direct Observationof the Entire Exciton Band of the First Excited Singlet States of Crystalline Benzene and Naphthalene, S. D. Colson, D. M. Hanson, R. Kopelman, and G. W. Robinson, J . Chem. Phys. 48,2215 (1968). 15. Electronic and VibrationalExciton Structure in Crystalline Benzene, E. R. Bernstein, S. D.Colson,R.Kopelman, and G. W. Robinson, J . Chem. Phys. 48,5596 (1968). 16. Information on the Exciton Band Structure of the lBzu State of Crystalline Naphthalene by the Variation of Energy Denominators Method Using Isotopic Substitution, D. M. Hanson, R. Kopelman,and G. W. Robinson, J . Chem. Phys. 51, 212 (1969). 17. Vibrational Exciton Density of States in Solid Benzene, J. C. Laufer, and R. Kopelman, J . Chem. Phys. 53, 3674 (1970). 18. Frenkel Exciton Superexchange, Pair Interactions, and Dispersion Relation: lBzu Naphthalene Crystal, H.-K. Hong, and R. Kopelman, Phys. Rev. Lett. 25, 1030 (1970).

9.

19.

24.

25.

26.

27.

28.

29. 30. 31.

32.

33.

34.

Excitons in Pure and Mixed Molecular Aggregates, R. Kopelman, Rec. Chem. Progr. 31, 211 (1970). Exciton Superexchange, Resonance Pairs and Complete Exciton Band Structure of IBzU Naphthalene, H.-K. Hong, and R. Kopelman, J. Chem.Phys. 55,724( 1971). Vibronic Exciton Density of States in Some Molecular Crystals, R. Kopelman, and J. C. Laufer, In Electronic Density of States, edited by L. H. Bennett, National Bureau of Standards Special Publication No. 323,U S . Government Printing Office: Washington, DC (1 97l), p 261. Contribution to the Theory of Frenkel Excitons in Disordered Molecular Crystals, H.-K. Hong, and R. Kopelman, J . Chem. Phys. 55, 3491 (1971). On the Unit Cell Group and Factor Group in the Theory of the Electronic and Vibrational Spectra of Crystals, J. E. Bertie and R.Kopelman, J. Chem. Phys. 55,3613 (1971). Randon Lattice Calculations on Frenkel Excitons in Disordered Molecular Crystals--'B2, Naphthalene, H.K. Hong, and R. Kopelman, J. Chem. Phys. 55,5380 (1971). Book Review: The Irreducible Representations of Space Groups, A. Casher, M. Gluck, and Y. Gur, edited by J. Zak, W. A. Benjamin, Inc.: New York, 1969,J.Am. Chem. SOC.93, 2827 (1971). Localized In-band Rotational Phonons in Mixed Molecular Crystals: Electronic Spectra of Naphthalene Doped Biphenyl and Durene, P. H. Chereson, P. S.Friedman, and R. Kopelman,J. Chem.Phys. 56,3716-37 17 (1972). Raman Phonon Spectra of Isotopic Mixed Naphthalene Crystals: Librational Exciton Model and the Amalgamation Limit, P. N. Prasad, and R. Kopelman, J. Chem. Phys. 57, 863 (1972). Method of Heavily Doped Isotopic Mixed Crystals for Determinations of Exciton Splittings and Normal Modes: Raman Spectra of Naphthalene, P. N. Prasad, and R. Kopelman, J . Chem. Phys. 57,856-862 (1972). Carbon-13 Impurity Effect on the aZu Infrared Exciton Spectrum of the Benzene Crystal, J. C. Laufer, and R. Kopelman, J . Chem. Phys. 57, 3202 (1972). Optical Mapping of the Phonon Density of States in Molecular Solids, R. Kopelman, F. W. Ochs, and P. N. Prasad, Phys. Status Solidi 54, K37 (1972). Multicomponent Cluster States in Dilute Mixed Molecular Crystals, with Application to Bz,, Naphthalene Excitons, H.-K. Hong, and R. Kopelman,J. Chem.Phys. 57,3888 (1972). Entire Phonon Spectrum of Molecular Crystals by the Localized Exciton Sideband Method: Naphthalene, R. Kopelman, F. W. Ochs, and P.N. Prasad, J . Chem. Phys. 57, 5409 (1972). Vibrational, Torsional and Librational Excitons in Molecular Crystals and their Interactions: Raman Active Phonons in Neat and Isotopic Mixed Durene, P. N. Prasad, and R. Kopelman, J . Chem. Phys. 58, 126 (1973). Phonons in Disordered Molecular Solids: Raman Spectra of Heavily-Doped Mixed Crystals of Benzene and Perdeuterobenzene, H.-K. Hong, and R. Kopelman, J . Chem. Phys. 58, 384 (1973).

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Coherent Potential Theory for Interacting Bands: Phonons and Excitons in Substitutionally Disordered Molecular Crystals, H.-K. Hong, and R. Hopelman,J . Chem.Phys. 58, 2557 (1973).

36.

Temperature Dependenceof a Vibrational Exciton: Some Methyl Motions of Durene, P. N. Prasad, and R. Kopelman, J . Chem. Phys. 58, 5031 (1973).

51.

Exciton States in Organic Alloys: Naphthalene-Perdeuteronaphthalene, P. Argyrakis, E. M. Monberg, and R. Kopelman, Chem. Phys. Lett. 36, 349 (1975).

52.

Exciton Percolationand Energy Transfer in Isotopic Mixed Molecular Crystals: Naphthalene. 7th Molecular Crystal Symposium, Nikko, Japan (1975) p 37.

53.

Raman Spectra and Intermolecular Forces in IsotopicallyMixed MolecularCrystals of Acetylene, C. S. Blackwell, R. Kopelman, and G. E. Leroi, Molecular Spectra of Dense Phases, Proceedings of 12th European Congress on Molecular Spectroscopy, Strassbourg,France (19 7 9 , edited by M. Grosmann, S. G. Elkomos, and J. Ringeissen, Elsevier: New York (1976), p 409.

37.

Molecular Motions and Lambda PhaseTransition: Raman and Far-IR Studies of Neat and Isotopic Mixed Hexamethylbenzene Crystal, P. N. Prasad, S. D. Woodruff, and R. Kopelman, Chem.Phys. 1,173 (1973).

38.

Phonon Raman Spectra, Molecular Motions, and Phase Transition of DimethylacetyleneCrystal, P. N. Prasad, and R. Kopelman, Chem. Phys. Lett. 20, 513 (1973).

54.

External, Internal and Semi-Internal Vibrations in Molecular Solids: SpectroscopicCriteria for Identification, P. N. Prasad, and R. Kopelman, Chem. Phys. Lett. 21, 505 (1973).

Excitons in Ternary Mixed Molecular Crystals: A Prototype for the Primary Step of Photosynthesis? R. Kopelman, J. Lumin. 12/13, 775 (1976).

55.

Perturbed Sites and Host-Guest-Host Exciton Cascase in the Biphenyl Isotopic Mixed Crystal Phosphorescence, P. S.Friedman, P. N. Prasad, and R. Kopelman, Chem. Phys. 13, 121 (1976).

56.

Percolation and Cluster Distribution. I. Multiple Labeling Technique and Critical Concentration Algorithm, J. Hoshen, and R. Kopelman, Phys. Rev. B 14, 3438 (1976).

57.

Green’s Functions for a Face Centered Orthorhombic Lattice, J. Joshen, and R. Kopelman, J . Math. Phys. 17, 2067 (1976).

58.

Off-Line Computer Applications to High Resolution UVVisible Spectroscopy, F. W. Ochs, and R. Kopelman, Appl. Spectrosc. 30, 306 (1976).

59.

Exciton Percolation in Molecular Alloys and Aggregates, R. Kopelman, Topics in Applied Physics Vol. 15: Radiationless Processes in Molecules and Condensed Phases, edited by F. K. Fong, Springer-Verlag: Berlin (1976), p 297.

60.

Exciton Percolation in Mixed Molecular Crystals and Aggregates: From Naphthalene to Photosynthesis, R. Kopelman, J . Phys. Chem. 80, 2191 (1976).

61.

Exciton Percolation I. Migration Dynamics, J. Hoshen, and R. Kopelman, J . Chem. Phys. 65, 2817 (1976).

62.

Molecular Exciton Cluster States and Spectra with Application to Benzene, J. Hoshen, and R. Kopelman, Phys. Status Solidi B 81, 479 (1977).

63.

VibrationalExcitons, Resonant Energy Transfer and Local Structure in Liquid Benzene, R. LeSar, and R. Kopelman, J . Chem. Phys. 66, 5035 (1977).

64.

Quantitative Tests of Mixed Crystal Exciton Theory. 11. Energy Denominator Study of Naphthalene IBz,, Resonance Pairs, F. w. Ochs, and R. Kopelman, J . Chem. Phys. 66, 1599 (1977).

65.

Exciton Percolation and Exciton Coherence, P. Argyrakis, and R. Kopelman, J . Chem. Phys. 66, 3301 (1977).

66.

Long Range Exciton Percolation and Superexchange: Energy Denominator Study on 3Blu Naphthalene, R. Kopelman, E. M. Monberg, and F. W. Ochs, Chem. Phys. 19, 413 (1977).

67.

Phase 111 Crystal Structure and 115K Phase Transition of Hexamethylbenzene, S. D. Woodruff, and R. Kopelman, J . Cryst. Mol. Struct. 7 , 29 (1977).

39.

40.

41.

42.

Exciton and Band Structure and Energy Transfer in Neat and Isotopic Mixed Crystals of Hexamethylbenzene,S. D. Woodruff, P. H. Chereson, and R. Kopelman, 6th Molecular Crystal Symposium, Schloss Elmau, West Germany (1973). Spectroscopic Evidence for a Continuous Change in Molecular and Crystal Structure: Deformation of Biphenyl in the Low Temperature Solid, P. S. Friedman, R. Kopelman, and P. N. Prasad, Chem. Phys. Lett. 24, 15 (1974). Phonon Sidebands of Localized Excitons in Molecular Crystals with Methyl Torsions: Hexamethylbenzene, S.D. Woodruff, P. N. Prasad, and R. Kopelman, J . Chem. Phys. 60,2365 (1974).

43.

Exciton Surface States in Molecular Crystals, J. Hoshen, and R. Kopelman, J . Chem. Phys. 61,330 (1974).

44.

Comment: Phonon Spectrum of Molecular Crystals from Exciton Sidebands, R. Kopelman, F. W. Ochs, and P. N. Prasad, Chem. Phys. Lett. 29, 134 (1974).

45.

Quantitative Tests of Mixed Crystal Exciton Theory: I. Naphthalene Monomer lBzu and 3BluSpectra, F. W. Ochs, P. N. Prasad, and R. Kopelman, Chem. Phys. 6, 253 (1974).

46.

An Energy Denominator Study of the Phonon Side Band in Isotopic Mixed Naphthalene Crystals, F. W. Ochs, P. N. Prasad, and R. Kopelman, Chem. Phys. Lett. 29, 290 (1974).

47.

Excitons in Pure and Mixed Molecular Crystals, R. Kopelman, Excitedstates, Vol. 11, edited by E. C. Lim, Academic Press: New York (1975), p 33.

48.

Triplet Exciton Percolation and Superexchange: Naphthalene CloH~-CloDs,R. Kopelman, E. M. Monberg, F. W. Ochs, and P. N. Prasad, J . Chem. Phys. 62,292 (1975).

49.

On the ApplicationofGroupTheory to Molecular Excitons, J. Hoshen, R. Kopelman, and J. Jortner, Chem. Phys. 10, 185 (1975).

50.

Exciton Percolation: Isotopic Mixed IBzu Naphthalene, R. Kopelman, E. M. Monberg, F. W. Ochs, and P. N. Prasad, Phys. Rev. Lett. 34, 1506 (1975).

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Exciton Percolation. 11: Naphthalene 1B2”Supertransfer, R. Kopelman, E. M. Monberg, and F. W. Ochs, Chem. Phys. 21, 373 (1977).

69.

Exciton Band of a One-Molecule-per-Unit-Cell-Crystal: HexamethylbenzeneFirst Singlet, S. D. Woodruff, and R. Kopelman, Chem. Phys. 22, 1 (1977).

70.

Exciton Percolation, Migration and Coherence, R. Kopelman, 8th Molecular Crystal Symposium, Santa Barbara, USA (1977), p 194.

71.

Percolation and Cluster Distribution. 11. Layers, Variable Range Interactions and Other SiteProblems, J. Hoshen, R. Kopelman, and E. M. Monberg, J. Stat. Phys. 19,

85.

High Density ExcitationCalculationsin Molecular Solids: A Monte Carlo Study, P. Argyrakis, J. Hoshen, and R. Kopelman, In Fast Reactions in Energetic Systems, edited by C. Capellos, and R. F. Walker, D. Reidel: Dordrecht, Holland (1980), p 685.

86.

Exciton Percolation, Tunneling and Thermalization: Naphthalene First Singlet and Triplet, E. M.Monberg, and R. Kopelman, V. L. Broude Memorial Issue, edited by D. M. Hanson,Mol. Cryst.Liq. Cryst. 57,271 (1980).

87.

Percolation Analog for a Two Component Liquid Vapor System, J. Hoshen, Chem. Phys. Lett. 75, 347 (1980).

88.

Diffusive and PercolativeLattice Migration: Excitons,R. Kopelman, and P. Argyrakis, J. Chem. Phys. 72,3053

219 (1978). 72.

Critical Concentrations for Triplet Exciton Tunneling in Binary Naphthalene Crystals: The Case for Percolation, E. M. Monberg, and R. Kopelman, Chem. Phys. Lett.

(1980). 89.

Isotopic Mixed Crystal Exciton Spectra in the Far Infrared: Naphthalene, D. C. Ahlgren, and R. Kopelman, Chem. Phys. 48,47 (1980).

90.

Percolation in Molecular Solids, R. Kopelman, Org. Coat. Plast. Chem. 42, 371 (1980).

91.

Correlated Random Walk Simulations in Simple and Binary Lattices, P. Argyrakis, and R. Kopelman,Phys. Rev. B 22, 1830 (1980).

92.

Correlated Hopping Model for Singlet Exciton Transport in Lightly Doped Naphthalene Crystals, P. Argyrakis, and R. Kopelman, Chem. Phys. 51, 9 (1980).

93.

Reply to comment on “ExperimentalTest of the AndersonMott Transition Model for Excitation Transport”, D. C. Ahlgren, and R. Kopelman,J. Chem.Phys. 73,1005

58,492 (1978). 73.

Exciton Percolation 111.Stochasticand CoherentMigration on Random Binary and Ternary Lattices, P. Argyrakis, and R. Kopelman, J. Theor. Biol. 73, 205 (1978).

74.

Vibrational Exciton Cluster States, Percolation and Pairwise Interactions: Benzene Az, Band, R. LeSar, and R. Kopelman, Chem. Phys. 29, 289 (1978).

75.

Phonon and Exciton Amalgamation-a Criterion for True Solid Solutions: Vibrations of Chemically and Isotopically Mixed ParadihalobenzeneCrystals, J. C. Bellows, P. N. Prasad, E. M. Monberg, and R. Kopelman, Chem. Phys. Lett. 54, 439 (1978).

76.

Electronic Energy Transfer in Mixed Organic Solids: Anderson Localization or Delocalization? E. M. Monberg, and R. Kopelman, Chem. Phys. Lett. 58, 497

(1980). 94.

Critical Exciton Transport and the Excitation Radius, R. Kopelman, D. C. Ahlgren, P. Argyrakis, S. T. Gentry, D. Hooper, J. Hoshen, P. Klymko, and J. S. Newhouse, 9th Molecular Crystal Symposium, Mittelberg-Kleinwalsertal (1980).

95.

Universityand Critical Exponents of Energy Transport in Binary Crystals: 3B2uNaphthalene, D. C. Ahlgren, and R. Kopelman, Chem. Phys. Lett. 77, 135 (1981).

96.

Optical Spectroscopy of Electronic Centers in Solids, G. F. Imbusch, and R. Kopelman, Topics in Applied Physics, Vol. 49: Laser Spectroscopy of Solids, edited by W. M. Yen, and P. M. Selzer, Springer-Verlag: Berlin (1981), p 1.

97.

Excitation Dynamics in Molecular Solids, A. H. Francis, and R. Kopelman, Topics in Applied Physics, Vol. 49: Laser Spectroscopy of Solids, edited by W. M. Yen, and P. M. Selzer, Springer-Verlag: Berlin (1981), p

(1978). 77.

Percolation and Cluster Distribution. 111. Algorithms for the Site-Bond Problem, J. Hoshen, P. W. Klymko, and R. Kopelman, J. Stat. Phys. 21, 583 (1979).

78.

Time Resolved Exciton Migration in Mixed Naphthalene Crystals: Triplet and Singlet Critical Concentrations, D. C. Ahlgren, E. M. Monberg, and R. Kopelman, Chem. Phys. Lett. 64, 122 (1979).

79.

Variable Range Cluster Model of Exciton Migration: Dimensionalityand Critical Exponents for Naphthalene, R. Kopelman, E. M. Monberg, J. S. Newhouse, and F. W. Ochs, J . Lumin. 18/19, 41 (1979).

80. Book Review: Collective Phenomena and the Applications of Physics to Other Fields of Science, edited by N. A. Chigier, and E. A. Stern, Brain Research Publication Inc.: Fayetterville, NY, 1975, J. Am. Chem. SOC.101,

241.

1062 (1979). 81.

Book Review: Molecular Symmetry and Group Theory, by A. Vincent, John Wiley and Sons: London, 1977, J. Am. Chem. SOC.101, 1358 (1979).

82.

Exciton PercolationKineticsand Exciton Coherency: lBzu Naphthalene, P. Argyrakis, and R. Kopelman, Chem. Phys. Lett. 61, 187 (1979).

83.

Monte Carlo Experiments on Cluster Site Distribution in Percolation, J. Hoshen, D. Stauffer, G. H. Bishop, R. J. Harrison, and F. D. Quinn, J. Phys. A 12,1285 (1 979).

84.

ExperimentalTest of the Anderson-MottTransition Model for ExcitonTransport, D. C. Ahlgren, and R. Kopelman, J. Chem. Phys. 70, 31333134 (1979).

98.

Percolation of Molecular Excitons, R. Kopelman, ACS Symposium Series 162: Characterization of Molecular Structures of Polymers by Photon, Electron and Ion Probes, edited by D. W. Dwight, H. R. Thomas, and T. J. Fabish, American Chemical Society: Washington, DC, (1981), p 57.

99.

Critical Exciton Annihilation: Diffusion, Percolation or Anderson Transition? P. W. Klymko, and R. Kopelman, J. Lumin. 24/25, 457 (1981).

100. Dynamics of Energy Transport in Ternary Molecular

Solids. I. Naphthalene Steady State Fluorescence, P. Argyrakis, and R. Kopelman, Chem. Phys. 57, 29 (1981).

The Journal of Physical Chemistry, Vol. 98, No. 30, 1994 7231 10 1 . Percolativevs. Homogeneous Energy Transport Kinetics: Time Resolved Donor and Acceptor Fluorescence of Isotopic Mixed Naphthalene Crystals, R. P. Parson, and R. Kopelman, Chem. Phys. Lett. 87, 258 (1982). 102. Exciton Transport in Naphthalene Alloys: A Transition from Percolation to Diffusion, S. T. Gentry, and R. Kopelman, Chem. Phys. Lett. 93, 264 (1982). 103. Heterogeneous Exciton Kinetics: Triplet Naphthalene Homofusion in an Isotopic Mixed Crystal, P. W. Klymko, and R. Kopelman, J. Phys. Chem. 86, 3686 (1982). 104. Experimental Investigationsand Re-evaluation of Energy Transport in Mixed Crystals, S. T. Gentry, P. W. Klymko, and R. Kopelman, Xth Molecular Crystal Symposium, St. Iovite, Quebec (1982). p 98. 105. Energy Transport in Mixed Molecular Crystals, R. Kopelman, Modern Problems in Solid State Physics, Vol. 4: Spectroscopy and Excitation Dynamics of Condensed Molecular Systems, edited by V. M. Agranovich, and R. M. Hochstrasser, North-Holland: Amsterdam (1983), p 139. 106. Single and Multiple Random Walks on Random Lattices: Excitation Trapping and Annihilation Simulations, R. Kopelman, J. Hoshen, J. S. Newhouse, and P. Argyrakis, J . Stat. Phys. 30, 335 (1983). 107. Singlet Exciton Transport in Substitutionally Disordered Naphthalene Crystals: Percolation and Generalized Diffusion, S.T. Gentry, and R. Kopelman, J. Chem. Phys. 78, 373 (1983). 108. Quasiresonant Excitation Transfer in Molecular Aggregates, R. P. Parson, and R. Kopelman, J . Chem. Phys. 79, 1444 (1983). 109. Analog-Metal to Nonmetal Exciton Transition: Effect of Isotopic Alloying on Naphthalene Triplets, S.T. Gentry, and R. Kopelman, Phys. Rev. B 27, 2579 (1983). 110. Dynamics of Energy Transport in Ternary Molecular Solids. 11. time Evolution of Naphthalene Fluorescence, P. Argyrakis, and R. Kopelman, Chem. Phys. 78,25 1 (1983). 1 1 1 . Incoherent Excitation Transport in Energetically Disordered Media, R. Parson, and R. Kopelman, Chem.Phys. Lett. 99, 213 (1983). 1 12. Excitation Transport in Naphthalene Aggregates: Mixed Crystals,Amorphous Thin Films and Polymeric Glasses, R. Kopelman In Electronic Excitations and Interaction Processes in Organic Molecular Aggregates, edited by P. Reineker, H. Haken, H. C. Wolf, Springer Series in Solid-state Sciences49, Springer: Berlin (1983), p 202. 1 13. Energy Trapping and Funnels in Mixed Naphthalene Crystals, P. Argyrakis, D. Hooper, and R. Kopelman, J. Phys. Chem. 87, 1467 (1983).

1 14. Band Model for Excitation Transport in Disordered Solids, R. Parson, and R. Kopelman, Chem. Phys. Lett. 100, 59 (1983).

1 17. Dynamics of Anisotropic Exciton Hopping in Molecular Crystals, P. Argyrakis, A. Blumen, R. Kopelman, and G. Zumofen, J. Phys. Chem. 88, 1973 (1984).

1 18. Random Walk on Percolation Clusters, P. Argyrakis, and R. Kopelman, Phys. Rev. B 29, 511 (1984). 1 19. Two-Particlecontinuous-TimeRandom Walksand Binary

Reactions in Disordered Media, R. Parson and R. Kopelman, Chem. Phys. Lett. 104, 320 (1984). 120. Fractal to Classical Crossover of Chemical Reactions, J. S. Newhouse, P. Argyrakis, and R. Kopelman, Chem. Phys. Lett. 107, 48 (1984). 12 1 . Reaction Kinetics on Fractals: Random Walker Simulations and Exciton Experiments, R. Kopelman, P. W. Klymko, J. S. Newhouse, and L. W. Anacker, Phys. Rev. B 29, 3747 (1984). 122. Single Random Walker on Disordered Lattices, P. Argyrakis, L. W. Anacker, and R. Kopelman, Proceedings of a Symposium on Fractals, NBS, Nov. 1983, J . Stat. Phys. 36, 579 (1984). 123. Fractal Chemical Kinetics: Reacting Random Walkers, L. W. Anacker, R. Kopelman, and J. S.Newhouse, Proceedings of a Symposium on fractals, NBS, Nov. 1983, J. Stat. Phys. 36, 591 (1984). 1 24. Exciton Energy Funnels in 8-Methylnaphthalene-Doped Naphthalene Crystals, S.T. Gentry, and R. Kopelman, J . Phys. Chem. 88, 3170 (1984). 1 25. Triplet Exciton Transport in Isotopic Mixed Naphthalene Crystals. I. Kinetic Analysis of Trapping and Fusion, S. T. Gentry, and R. Kopelman, J . Chem. Phys. 81, 3014 (1984).

126. Triplet Exciton Transport in Isotopic Mixed Naphthalene Crystals. 11. Master Equation Analysis, S. T. Gentry, and R. Kopelman, J. Chem. Phys. 81, 3022 (1984). 127. Fractal to Euclidean Crossover and Scaling for Random Walkers on Percolation Clusters, P. Argyrakis, and R. Kopelman, J . Chem. Phys. 81, 1015 (1984). 128. Exciton Transport in Disorderd Crystals: Velocity Correlation Functions,R. Parson, and R. Kopelman, Chem. Phys. 89, 265 (1984). 129. Non-Equilibrium Excitation Transport in Energetically Disordered Media, R. Parson,and R. Kopelman, J. Phys. Chem. 88, 2931 (1984). 130. Luminescent Fractal Reactions: Exciton Fusion on Percolation Clusters, L. W. Anacker, P. W. Klymko, and R. Kopelman, J. Lumin. 31/32, 648 (1984). 1 3 1 . Fractal-Like Exciton Transport and Fusion in Disordered Naphthalene, L. A. Harmon, and R. Kopelman, J . Lumin. 31/32, 660 (1984). 1 3 2. Fractal Chemical Kinetics: Simulationsand Experiments, L. W. Anacker, and R. Kopelman, J . Chem. Phys. 81, 6402-6403 (1984). 1 3 3. Fractal Reactions in Disordered Materials: Computer

1 16. Exciton Heterofusion: A Quantitative Measure of Trans-

Simulations and Excitation Fusion Experiments, R. Kopelman, in Fractal Aspects of Materials: Metal and Catalyst Surfaces, Powders and Aggregates, edited by B. B. Mandelbrot,and D. E. Passoja, Materials Research SOC.:Pittsburgh (1984), p 21.

port in Mixed Crystals, R. Kopelman, S.T. Gentry, P. W. Klymko, and J. S. Newhouse, J. Opt. SOC.Am. 73, 1389 (1983).

134. Fractal Exciton Fusion: Simulations on Long-Range PercolationClusters, J. S. Newhouse, and R. Kopelman, J . Lumin. 31/32, 657 (1984).

1 1 5 . Fractal Reaction Kinetics: Exciton Fusion on Clusters, P. W. Klymko, and R. Kopelman,J . Phys. Chem. 87,4565 (1983).

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13 5. Fractal Energy Transport: Randon Walk Simulations on Long-Range Percolation Clusters, P. Argyrakis, and R. Kopelman, J. Lumin. 31/32, 654 (1984). 136. Fractal-Like Energy Transport and Fusion in a Naphthalene-Doped Polymeric Glass, E. I. Newhouse, and R. Kopelman, J. Lumin. 31/32, 651 (1984). 137. A Self-consistent Theory of Nonequilibrium Excitation Transport in Energetically Disordered Systems, R. P. Parson, and R. Kopelman, J . Chem. Phys. 82, 3692 (1985). 138. Scaling and Short-Time Corrections for Random Walks on 2-Dimensional Exactly Percolating Clusters, A Keramiotis,P. Argyrakis, and R. Kopelman,Phys. Rev. B 31, 4617 (1985). 139. Long-Range Random Walk on Percolation Clusters, P. Argyrakis, and R. Kopelman, Phys. Rev. B 31, 6008 (1985). 140. Fractal Chemical Kinetics: Binary Steady State Reaction on a Percolating Cluster, J. S. Newhouse, and R. Kopelman, Phys. Rev. B 31, 1677 (1985). 14 1. Fractal to Euclidean Crossover and Scaling for Random Walks. 11. Three-Dimensional Lattice, P. Argyrakis, and R. Kopelman, J. Chem. Phys. 83, 3099 (1985). 142. Fractal-Like Exciton Kinetics in Membranes, Glasses and Films, R. Kopelman, Proceedings of the 5th Int. Conf. on Dynamical Processes in the Excited State of Solids, J. Phys. (Paris) C7, 9 (1985). [Invitedpaper] 143, Fractal-Like Exciton Kinetics in Grain Boundaries, Embedded Aggregates, Plugged Pores and Powder Interfaces, R. Kopelman, L. A. Harmon, E. I. Newhouse, S. J. Parus, and J. Prasad, In Fractal Aspects of Materials, edited by R. B. Laibowitz, B. B. Mandelbrot, and D. E. Passoja, Materials Research Society: Pittsburgh (1989, p 81. [Invited paper] 144. Fractal and Fractal-Like Reaction Kinetics: Random Walk Simulations, L. W. Anacker, and R. Kopelman, Proceedings of 1985 Materials Research Society Conference (1985). [Contributed paper] 145. Fractal Exciton Kinetics, R. Kopelman,ProceedingsXIth Molecular Crystal Symposium, Lugano, Switzerland (1985), p 157. [Contributed paper] 146. Diffusion-Controlled Reaction Kinetics on Fractal and Euclidean Lattices: Transient and Steady-State Annihilation, L. W. Anacker, R. P. Parson, and R. Kopelman, J . Phys. Chem. 89, 4758-4761 (1985). 147. Fractal-Like Exciton Dynamics: Geometrical and Energetical Disorder, R. Kopelman, In Fractals in Physics, edited by L. Pietronero and E. Tosatti, Proceedings of 6th International Symposium on "Fractals in Physics", Elsevier: Amsterdam (1986), p 369. [Contributed paper1 148. Fractal Aspects of HeterogeneousChemical Reactions, P. Argyrakis, and R. Kopelman, In Advances in Chemical Reaction Dynamics, edited by P. M. Rentzepis and C. Capellos, D. Reidel: Holland (1986), p 339. [Contributed paper] 149. Fractal-Like Exciton Kinetics in Porous Glasses, Organic Membranes and Filter Papers, R. Kopelman, S.Parus, and J. Prasad, Phys. Rev. Left. 56, 1742 (1986). 150. Fractal Nature of Geometric and Energetic Disorder: Exciton Kinetics in Crystalline Films, Glasses and Membranes,R. Kopelman, In Transport and Relaxation in Random Materials, edited by J. Klafter, R. J. Rubin, and M. F. Shlesinger,World Scientific Publishing Co.: Singapore (1986), p 177. [Invited review chapter]

151. Optical Spectroscopy of Electronic Centers in Solids, G. F. Imbusch, and R. Kopelman, Topics in Applied Physics, Vol 49: Laser Spectroscopy of Solids, 2nd Edition, edited by W. M. Yen and P. M. Selzer, SpringerVerlag: Berlin (1986), p 1. [Invited review chapter] 152. Excitation Dynamics in Molecular Solids, A. H. Francis, and R. Kopelman, Topics in Applied Physics, Vol. 49: Laser Spectroscopy of Solids, 2nd Edition, edited by W. M. Yen and P. M. Selzer, Springer-Verlag: Berlin (1986), p 241. [Invited review chapter] 153. Reaction Kineticson Clusters and Islands, J. S.Newhouse, and R. Kopelman, J . Chem. Phys. 85,6804 (1986). 154. Fractal Behavior of Correlated Random Walks on Percolating Clusters, P. Argyrakis, and R. Kopelman, J. Chem. Phys. 84, 1047-1048 (1986). 155. Reaction Kineticson Powders, Porous Media and Fractals: Experiments and Simulations, R. Kopelman, and S. J. Parus, In Fractal Aspects of Materials, 11, edited by D. W. Schaefer, R. B. Laibowitz, B. B. Mandelbrot, and S. H. Liu, Materials Research Society: Pittsburgh (1986), p 50. [Invited paper] 156. Rate Processes on Fractals: Theory, Simulation and Experiments, R. Kopelman, J. Stat. Phys. 42, 185 (1986). [Refereed invited review paper] 157. Photoexcitation Dynamics and Photodimerization in Nanometer Wires, Polymer Blends, Powders, Porous Membranes and Glasses, R. Kopelman, C. S. Li, S.J. Parus, and J. Prasad, Proceedings of Third International Conference on Unconventional Photoactive Solids, Schloss Elmau, W. Germany (October, 1987), p 112. [ h i ted paper] 158. Low Dimensional Exciton Reactions,R. Kopelman, Philos. Mag. B 56, 7 17 (1987). [Invited review paper] 159. Fractal-LikePhotoexcitationKinetics: StructuralPatterns and their Modification in Disordered Films, Blends, Porous Materials and Powders, R. Kopelman, In Fractal Aspects of Materials III, edited by A. J. Hurd, D. A. Weitz, and B. B. Mandelbrot, Materials Research Society: Pittsburgh (1987), p 112. [Invitedreviewpaper] 160. Book Review: Spectroscopy of Molecular Excitons, by V. L. Broude, E. I. Rashba, and E. F. Sheka, Springer: Berlin, 1985, J. Am. Chem. SOC.109, 7241 (1987). 161. Excitation Time Modulation: A New Technique for Heterogeneous Media, R. Kopelman, In Nonlinear Optics and Spectroscopy of Organic Materials, edited by T. Kobayashi, RIKEN Symp. Proc.: Tokyo (1987), p 6. [Invited paper] 162. Refined Monte Carlo Simulations of Static Percolation, J. Hoshen, R. Kopelman, and J. S. Newhouse, J . Phys. Chem. 91, 219 (1987). 163. Fractal-Like Molecular Reaction Kinetics: Solute Photochemistry in Porous Membranes, J. Prasad, and R. Kopelman, J. Phys. Chem. 91, 265 (1987). 164. Steady-State Chemical Kinetics on Fractals: Segregation of Reactants, L. W. Anacker, and R. Kopelman, Phys. Rev. Lett. 58, 289 (1987). 165. Exciton Dynamics in Thin Wires, R. Kopelman, L. Li, S. J. Parus, and J. Prasad, J . Lumin. 38, 289 (1987). 166. Exciton Kinetics in Ultrathin Molecular Wires and Pores, J. Prasad, and R. Kopelman, Phys. Rev. Lett. 59,2103 (1987). 167. Self-stirred vs. Well-Stirred Reaction Kinetics, P. Argyrakis, and R. Kopelman, J.Phys. Chem. 19,2699 (1987).

The Journal of Physical Chemistry, Vol. 98, No. 30, 1994 7233 168. Steady-State Chemical Kinetics on Fractals: Geminate

and Nongeminate Generation of Reactants, L. W. Anacker, and R. Kopelman, J. Phys. Chem. 91, 5555 (1987). 169, Simulations of One-Dimensional and Fractal Luminescence Kinetics, L. Li, and R. Kopelman, J. Lumin. 401 41, 688 (1988). 170. RecombinationKinetics in Low Dimensions, P. Argyrakis, and R. Kopelman, J . Lumin. 40141,690 (1988). 17 1. One-Dimensional Luminescence Kinetics: A Submicron Probe, J. Prasad, and R. Kopelman, J . Lumin. 40141, 643 (1988). 172. Fractal-Like Triplet-Triplet Annihilation Kinetics in

Naphthalene-Doped Poly(methylmethacrylate), E. I. Newhouse, and R. Kopelman, Chem. Phys. Lett. 143, 106 (1988). 173. Random Walks on Fractals: Higher Moments, L. W.

Anacker, P. Argyrakis, and R. Kopelman, J . Phys. A 21, 569 (1988). 174. Steady-State Chemical Kinetics on Surface Clusters and

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184. Self-organization of Reactants on Fractal Surfaces: A

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A Product, L. Li, E. Clement, P. Argyrakis, L. A. Harmon, S. J. Parus, and R. Kopelman, In Fractal Aspects of Materials: Disordered Systems, edited by D. A. Weitz, L. M. Sander, and B. B. Mandelbrot, Materials Research Society: Pittsburgh (1 988), p 21 1. [Contributed paper]

18 5. Diffusion-Controlled Reactions and Segregation Phenom-

ena in Low Dimensional Media: Influenceof the Source, E. Clement, L. Li, L. W. Anacker, L. A. Harmon, R. Kopelman, and L. M. Sander, In Fractal Aspects of Materials: Disordered Systems, edited by D. A. Weitz, L. M. Sander, and B. B. Mandelbrot, Materials Research Society: Pittsburgh (1988), p 307. [Znuited paper] 186. Reactant Segregation on Fractals, L. A. Harmon, L. Li,

L. W. Anacker, and R. Kopelman, In Fractal Aspects of Materials: Disordered Systems, edited by D. A. Weitz, L. M. Sander, and B. B. Mandelbrot, Materials Research Society: Pittsburgh (1988), p 303. [Contributed paper] 187. Delayed Fluorescence, Reaction Kinetics and Organic

175. Random Walks on Percolating Clusters with Energetic

Materials, R. Kopelman, Proceedings of SPZE: Fluorescence Detection, edited by E. R. Menzel, The International Society for Optical Engineering: Bellingham, WA, 910, 181 (1988). [Znvitedpaper]

Disorder, P. Argyrakis, and R. Kopelman, J. Phys. A

1 8 8. Exploring Fractal-Like Reaction Kinetics, R. Kopelman,

Islands: Segregation of Reactants, J. S. Newhouse, and R. Kopelman, J. Phys. Chem. 92, 1538 (1988).

21, 2753 (1988). 176. Transport and Reactions in Disordered Media, R. Ko-

pelman, In Unconventional Photoactive Solids, edited by H. Scher, Plenum Press: New York (1988), p 11. [Invited review paper] 177. Exciton Transport in Naphthalene-Doped Poly(methy1-

methacrylate): Spacial and Energetic Disorder, E. I. Newhouse, and R. Kopelman, In UnconventionalPhotoactiveSolids, edited by H. Scher, Plenum Press: New York (1988), p 63. [Contributed paper] 178. Fractal-Like Exciton Kinetics in Porous Glasses, Mem-

branes and Powders, J. Prasad, S. J. Parus, and R. Kopelman, In UnconventionalPhotoactiveSolids,edited by H. Scher, Plenum Press: New York (1988), p 21. [Contributed paper] 179. Reaction Kinetics on Fractal and Euclidean Structures

with Energetic Disorder: Random Walk Simulations, L. W. Anacker, and R. Kopelman, In Unconventional Photoactive Solids, edited by H. Scher, Plenum Press: New York (1988), p 29. [Contributed paper] 180. Excitation Transport Kinetics in Vapor-Deposited Naph-

thalene, L. A. Harmon, and R. Kopelman, In Unconventional Photoactive Solids, edited by H. Scher, Plenum Press: New York (1988), p 83. [Contributed paper1 18 1. Steady-State Segregation in Diffusion-Limited Reactions, K. Lindenberg, B. J. West, and R. Kopelman, Phys. Rev. Lett. 60, 1777 (1988). 182. Fractal Reaction Kinetics, R. Kopelman, Science 241, 1620-1626 (1988). [Refereed invited review paper] 18 3. Exciton Reactions in Ultrathin Molecular Wires, Filaments

and Pores: A Case Study of Kinetics and Self-ordering in Low Dimensions, R. Kopelman, S. J. Parus, and J. Prasad, In Excited State Relaxation and Transport Phenomena in Solids, edited by J. L. Skinner and M. D. Fayer, Special Issue Chem. Phys. 128,209 (1988). [Refereed invited paper]

and L. W. Anacker, In Science at the Johnvon Neumann National Computer Center, 1987, edited by G. Cook, Consortium for Scientific Computing: Princeton, NJ (1988), p 73. [Non-refereed paper] 189. A Nanometer Dimension Optical Device, A. Lewis, and R. Kopelman, Israel Patent No. 87139 (1988). 190. Pattern Formation in Diffusion-Limited Reactions, B. J.

West, R. Kopelman, and K. Lindenberg, Proceedings of 1988 Conference on External Noise and its Interaction with Spatial Degrees of Freedom in Nonlinear Dissipative Systems, Los Alamos, Special Issue, J . Stat. Phys. 54, 1429-1439 (1989). [Refereed invitedpaper] 19 1. Excitons in Molecular Aggregates and a Hypothesis on

the Sodium Channel Gating, E. B. Fauman, and R. Kopelman, Comments Mol. Cell. Biophys. 6 , 47-61 (1989). [Refereed invited review paper] 192. Diffusion Controlled Reaction Kinetics, R. Kopelman, In

The Fractal Approach to Heterogeneous Chemistry: Surfaces, Colloids, Polymers, edited by D. Avnir, John Wiley & Sons: New York (1989), p 295. [Refereed invited review chapter] 193. Low-Dimensional Reaction Kineticsin Porous Disordered

Media and Reactant Self-organization, R. Kopelman, J. Prasad, and S. J. Parus, In Molecular Dynamics in Restricted Geometries, edited by J. Klafter and J. M. Drake, John Wiley & Sons: New York (1989), p 145. [Refereed invited review chapter] 194. Reaction Kinetics and Self-ordering in Restricted Ge-

ometries: Excitation Fusion in Molecular Aggregates, R. Kopelman, S. J. Parus, and Z.-Y. Shi, In Dynamical Processes in Condensed Molecular Systems, edited by J. Klafter, J. Jortner, and A. Blumen, World Scientific Publishing Co.: Singapore (1989), p 231. [Refereed invited review paper] 195. Density of Nearest-Neighbor Distances in Diffusion-

Controlled Reactions at a Single Trap, G. Weiss, R, Kopelman, and S . Havlin, Phys. Rev. A 39,466 (1 989).

7234 The Journal of Physical Chemistry, Vol. 98, No. 30, 1994 196. Self-ordering in DiffusionControlled Reactions: Exciton Fusion Experiments and Simulations on Naphthalene Powder, Percolation Clusters and Impregnated Porous Silica, S. J. Parus, and R. Kopelman, Phys. Rev. B 39, 889 (1989). 197. Stirring in Chemical Reactions, P. Argyrakis, and R. Kopelman, J. Phys. Chem. 93, 225 (1989). 198. Steady-State vs. Pulsed Excitation Recombination Kinet-

ics: Simulations and Experiments on Pores, Powders and Random Media, S. J. Parus, and R. Kopelman, Mol. Cryst. Liq. Cryst. 175, 119 (1989). 199. Fractal to Classical Crossover of Chemical Reactions, J. S. Newhouse, P. Argyrakis, and R. Kopelman, In Fractals, Selected Reprints, edited by A. J. Hurd, American Assoc. of Phys. Teachers: College Park, MD (1989), p 109. [Refereed invited paper] 200. Phonon-Side-Bands of Ordered and Disordered Media: Naphthalene Crystals and Molecularly Doped Polymers, Y.-E. Koo, and R. Kopelman, J. Phys. Chem. 93,1677 (1989).

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201. Source Term and Excluded Volume Effects on the Diffusion Controlled A B 0 Reaction in OneDimension: Rate Laws and Particle Distributions, E. Clement, L. M. Sander, and R. Kopelman, Phys. Rev. A 39, 6455-6465 (1989).

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202. Steady-State Diffusion Controlled A + B 0 Reactions in Two and Three Dimensions: Rate Laws and Particle Distributions, E. Clement, L. M. Sander, and R. Kopelman, Phys. Rev. A 39, 6466-6471 (1989). 203. Steady-State Diffusion Controlled A A 0 Reaction in Euclidean and Fractal Dimensions: Rate Laws and Particle Self-Ordering, E. Clement, L. M. Sander, and R. Kopelman, Phys. Rev. A 39, 6472-6477 (1989). 204. Molecular Reaction Kinetics Inside Channel Pores: Delayed Fluorescenceof Naphthalene in Methanol, J. Prasad, and R. Kopelman, Chem. Phys. Lett. 157,535538 (1989). 205. Trapping on Fractals: A Model for Light Harvesting, Coagulation Catalysis and Enzyme Reactions, L. W. Anacker, and R. Kopelman, Science at the John von Neumann National Supercomputer Center, 1988, Consortiumfor ScientificComputing: Princeton,NJ (1 989), p 1 1 . [Non-refereed paper] 206. A New Technique to Differentiate Between Geminate and Nongeminate Recombination of Triplet Excitons, J. Prasad, and R. Kopelman, In Fractal Aspects of Materials, edited by J. H. Kaufman, J. E. Martin, and P. W. Schmidt, Materials Research Society Extended Abstracts: Pittsburgh (1989), p 127. [Contributed paper1 207. Steady-State Reactions on Fractals: Rate Laws and SelfOrganization, E. Clement, R. Kopelman, and L. M. Sander, In Fractal Aspects of Materials, edited by J. H. Kaufman, J.E. Martin,andP. W. Schmidt, Materials Research Society Extended Abstracts: Pittsburgh (1 989), p 13 1. [Invited review paper] 208. Excitation Time Modulation Studies of Molecular Aggregates in Doped Polymers, Z.-Y. Shi, I. E. Newhouse, and R. Kopelman, In Fractal Aspects of Materials, edited by J. H. Kaufman, J. E. Martin, and P. W. Schmidt, Materials Research Society Extended Abstracts: Pittsburgh (1989), p 135. [Contributedpuper]

209. Pulsed vs. Steady-State Exciton RecombinationKinetics: Experiments and Simulations on Pores, Powders and Random Media, S. J. Parus, Z.-Y. Shi, and R. Kopelman, In Fractal Aspects of Materials, edited by J. H. Kaufman, J. E. Martin, and P. W. Schmidt, Materials Research Society Extended Abstracts: Pittsburgh (1989), p 139. [Contributed paper] 2 10. Reactant Trapping and Steady State Self Ordering on Fractals, L.W. Anacker, E. Clement, and R. Kopelman, In Fractal Aspects of Materials, edited by J. H. Kaufman, J. E. Martin, and P. W. Schmidt, Materials Research Society Extended Abstracts: Pittsburgh (1989), p 143. [Contributed paper] 2 1 1 . Self-ordering and Kinetics of Excitations in Low Dimensions and Disordered Media, R. Kopelman, and L. Li, In Fractal Aspects of Materials, edited by J. H. Kaufman, J. E. Martin, and P. W. Schmidt, Materials Research Society Extended Abstracts: Pittsburgh (1 989), p 27 1. [Contributed paper] 2 12. Molecular Exciton Microscopy, R. Kopelman, A. Lewis, and K. Lieberman, Biophys. J. 55, 450a (1989). [Contributed paper] 2 13. Reaction Kinetics in Low and Fractal Dimensions: An Application to Polymer Morphology, Zhong-You Shi, Ching-Shan Li, and R. Kopelman, Proceedings Polymer Division of “Molecular Dynamics in Small Finite Systems” Conference, American Chemical Society: Washington, DC (1989). [Invited review paper] 2 14. Segregation Measures for Diffusion-Controlled A B Reactions, L. A. Harmon, L. Li, L. W. Anacker, and R. Kopelman, Chem. Phys. k t t . 163,463-468 (1989). 2 1 5 . Exciton Microscopy and Scanning Optical Nanoscopy, R. Kopelman, In X-Ray Microimaging for the Life Sciences, edited by D. Attwood and B. Barton, Lawrence Berkeley Laboratory: Berkeley, CA (1989), pp 166173. [Contributed paper] 2 1 6. A Nanometer Dimension Optical Device with Microimaging and NanoilluminationCapabilities,R. Kopelman, and A. Lewis, US Patent No. 07/380,099 (1989). 217. Fractal-Like Exciton Fusion Kinetics in Dilute Polymer Blends, R. Kopelman, C. . Li, and Z.-Y. Shi, In Fractal Aspects of Materials, edited by J. H. Kaufman, J. E. Martin, and P. W. Schmidt, Materials Research Society Extended Abstracts: Pittsburgh (1989), pp 275. [Contributed paper] 218. Excimer and Exciton Fusion of Blends and Moleclarly Doped Polymers-A New Morphological Tool, Z.-Y. Shi, C. S. Li, and R. Kopelman, In Polymer Based Molecular Composites, edited by J. E. Mark, and D. W. Schaefer, Materials Research Society Symposium Proceedings, 171, 245-254 (1990). [Refereed invited review .DaDerl . 219. Diffusion Limited A + B Reaction: Spontaneous Segregation, K. Lindenberg, B. J. West, and R. Kopelman, In Noise and Chaos in Nonlinear Dynamical Systems, edited by F.Moss, L. Lugiato,and W. Schleich, Cambridge University Press: Cambridge (1990), pp 142-171. [Invited refereed review chapter] 220. A Light Source Smaller than the Optical Wavelength, K. Lieberman, S. Harush, A. Lewis, and R. Kopelman, Science 247, 59-61 (1990). 2 2 1 . Fractal-LikeTriplet Excitation Kineticsand Chromophore Morphology in Blends of Poly( 1-vinylnaphthalene)and Poly(methy1methacrylate), C. S. Li, and R. Kopelman, Macromolecules 23, 2223-2231 (1990).

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The Journal of Physical Chemistry, Vol. 98, No. 30, 1994 7235 222. Photophysical Degradation of Poly( 1-vinylnaphthalene) and Poly(methy1 methacrylate) Blends, C. S. Li, and R. Kopelman, J. Phys. Chem. 94, 2135-2140 (1990). 223. Triplet Excitation Transport Kinetics in Vapor-Deposited Naphthalene, L. A. Harmon, and R. Kopelman,J. Phys. Chem. 94, 3454-3461 (1990). 224. Statistical Properties of Nearest-Neighbor Distances at an Imperfect Trap, H. Taitelbaum, R. Kopelman, G. H. Weiss, and S. Havlin, Phys. Rev. A 41,3116-3120 (1990). 225. Diffusion Limited A + B 0 Reaction: Correlated Initial Condition,K. Lindenberg,B. J. West, and R. Kopelman, Phys. Rev. A 42, 890-894 (1990). 226. Nearest-NeighborDistanceDistributionand Self-ordering in Diffusion Controlled Reactions: I. A A Simulations, P. Argyrakis, and R. Kopelman,Phys. Reu. A41,21142120 (1990). 227. Nearest-NeighborDistanceDistributionand Self-ordering in Diffusion Controlled Reactions: 11. A B Simulations, P. Argyrakis, and R. Kopelman, Phys. Rev. A41, 2121-2126 (1990). 228. Reactions in Fractal and Small Dimensions at the Steady State: Anomalous ChemicalKinetics and Reactant SelfOrdering, L. W. Anacker, and R. Kopelman, In Science at the John uon Neumann National Supercomputer Center, 1989, Consortium for Scientific Computing: Princeton, NJ (1990), pp 29. [Non-refereedpaper] 2 2 9 Bimolecular Reaction A B 0 at Steady State on Fractals: Anomalous Rate Law and Reactant SelfOrganization, E. Clement, R. Kopelman, and L. M. Sander, Chem. Phys. 146, 343-350 (1990). 230. Energy Transfer and Relaxation in Low Dimensional Systems, edited by J. Klafter, and R. Kopelman,Special Issue, Chem.Phys. 146,283-472(1990). [Invitededitor] 23 1 . Dynamics in Small Confining Systems, Extended Abstracts, edited by J. M. Drake, J. Klafter, and R. Kopelman,Materials Research Society: Pittsburgh, PA (1990), pp 1-248. [Coeditor of Proceedings] 232. Segregation Properties of an A B 0 Reaction with Initially Separated Components, S. Havlin, R. Kopelman, H. Taitelbaum, and G. H. Weiss, In Dynamics in Small Confining Systems, edited by J. M. Drake, J. Klafter, and R. Kopelman, Materials Research Society: Pittsburgh, PA (1990), pp 117-118. [Invited paper] 233. Light Microscopy Beyond the Limits of Diffraction and to the Limits of Single Molecule Resolution, A. Lewis, K. Lieberman, S. Haroush, V. Habib, R. Kopelman, and M. Isaacson, In Optical Microscopy for Biology, edited by B. Herman, and K. Jacobson,Wiley-Liss, Inc.: New York (1990), pp 615-639. [Invited refereed book chapter] 2 3 4. Characterization of Self-segregation Tendencies in TwoComponent Reacting Systems on Fractals, s. Havlin, R. Kopelman, R. Schoonover, and G. H. Weiss, In Dynamics in Small Confining Systems, edited by J. M. Drake, J. Klafter, and R. Kopelman, Materials Research Society: Pittsburgh, PA (1990), pp 149-152. [Inuited paper1 235. New Technique to Differentiate Between Geminate and Nongeminate Recombination of Triplet Excitons, J. Prasad, and R. Kopelman, J . Lumin. 45, 258-259 (1990). [Refereed contributed conference paper] 236. One Dimensional Exciton Fusion Kinetics in Dilute Polymer Blends, R. Kopelman, C. S. Li, and Z.-Y. Shi, J . Lumin. 45, 40-42 (1990). [Refereed contributed conference paper]

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237. Kinetics and Self-ordering of Excitations in Low Dimensions, R. Kopelman, L. W. Anacker, E. Clement, L. Li, and L. Sander, J. Lumin. 45,323-326 (1990). [Refereed invited conference paper] 238. Steady-State vs. Pulsed Excitation Recombination Kinetics: Simulations and Experiments on Pores, Powders and Random Media, S. J. Parus, and R. Kopelman, J. Lumin. 4 5 , 4 3 4 4 (1990). [Refereed contributed conference paper] 239. Nanometer Light Source and Molecular Exciton Microscopy, R. Kopelman, A. Lewis, and K. Lieberman, J. Lumin. 45, 298-299 (1 990). [Refereed contributed conference paper] 240. ExcitationTime Modulation Studiesof Molecularly Doped Polymers, Z.-Y. Shi, and R. Kopelman, J. Lumin. 45, 275-276 (1990). [Refereed contributed conference paper1 24 1 . Trapping Reaction in Low Dimensions: Steady-StateselfOrganization, E. Clement, R. Kopelman, and L. M. Sander, Europhys. Lett. 11, 707-712 (1990). 242. Subwavelength Molecular Optics: The World’s Smallest Light Source? R. Kopelman, K. Lieberman, and A. Lewis, Mol. Cryst. Liq. Cryst. 183, 333-340 (1990). [Refereed contributed conference paper] 24 3 . Reaction Front Dynamics in Diffusion-Controlled ParticleAntiparticle Annihilation: Experiments and Simulations, Y.-E. Koo, L. Li, and R. Kopelman, Mol. Cryst. Liq. Cryst. 183,187-192 (1990). [Refereedcontributed conference paper] 244. Monte Carlo Simulations, R. Schoonover, and R. Kopelman, Mol. Cryst. Liq. Cryst. 183, 181-186 (1990). [Refereed contributed conference paper] 245. Towards Nanophotonics: Temporal Patterns of Photons Create Spatial Patterns of Excitons in Molecular Dots and Wires, Z.-Y. Shi, and R. Kopelman, Mol. Cryst. Liq. Cryst. 183, 143-153 (1990). [Invited refereed conference paper] 246. Trapping Reaction Kinetics and Nearest-Neighbor Distributions on Low Dimensional and Fractal Lattices, R. Schoonover, and R. Kopelman, In Dynamics in Small Confining Systems, edited by J. M. Drake, J. Klafter, and R. Kopelman, Materials Research Society: Pittsburgh, PA (1990), pp 213-216. [Contributed paper] 247. Steady-State Simulations of Chemical Kinetics in LowDimensional Media: Mobile and Immobile Reactants, L. W. Anacker, andR. Kopelman, In Dynamics insmall Confining Systems, edited by J. M. Drake, J. Klafter, and R. Kopelman, Materials Research Society: Pittsburgh, PA (1990), pp 97-100. [Contributed paper] 248. Simulations of Diffusion Limited A + B 0 Reactions: Finite Size Effects and Scaling, P. Argyrakis, and R. Kopelman, In Dynamics in Small Confining Systems, edited by J. M. Drake, J. Klafter, and R. Kopelman, Materials Research Society: Pittsburgh, PA (1990), pp 195-198. [Contributed paper] 249, Nanometer Crystal Light Sources, W. Tan, R. Kopelman, K. Lieberman, and A. Lewis, In Dynamics in Small Confining Systems, edited by J. M. Drake, J. Klafter, and R. Kopelman, Materials Research Society: Pittsburgh, PA (1990), pp 225-228. [Contributed paper] 250. Hydrogen-Deuterium Exchange Kinetics on Supported Platinum Islands, J. S. Holder, and R. Kopelman, In Dynamics in Small Confining Systems, edited by J. M. Drake, J. Klafter, and R. Kopelman, Materials Research Society: Pittsburgh, PA (1990), pp 217-220. [Contributed paper]

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7236 The Journal of Physical Chemistry, Vol. 98, No. 30, 1994 25 1 . Exciton KineticsStudiesof Dispersed Aggregates: TripletTriplet Fusion in Naphthalene Doped PMMA, Z.-Y. Shi, and R. Kopelman, In Dynamics in Small Confining Systems, edited by J. M. Drake, J. Klafter, and R. Kopelman, Materials Research Society: Pittsburgh, PA (1990), pp 221-224. [Contributed paper] 252. Scaling Properties of Diffusion Limited Reactions, W. S. Sheu, K. Lindenberg, and R. Kopelman, Phys. Rev. A 42, 2279-2283 (1990). 2 5 3 , Diffusion-Limited A B 0 ReactionsWith and Without Sources: Scaling Relations on Fractals, K. Lindenberg, W . 4 . Sheu, and R. Kopelman, In Dynamics in Small Confining Systems, edited by J. M. Drake, J. Klafter, and R. Kopelman, Materials Research Society: Pittsburgh, PA (1990), pp 113-116. [Invited paper] 254. Chemical Segregation in a Capillary, Y.-E. Koo, and R. Kopelman, In Dynamics in Small ConfiningSystems, edited by J. M. Drake, J. Klafter, and R. Kopelman, Materials Research Society: Pittsburgh, PA (1990), pp 199-202. [Contributed paper] 255. Molecular Exciton Wires and Nanometer Optics, R. Kopelman, Proceedings of Emil-Warburg Symposium in Dynamical Processes in Condensed Molecular Systems, edited by A. Blumen, J. Klafter, and D. Haarer, World Scientific: Singapore (1990), pp 173-187. [Invited refereed conference paper] 256. Evanescent Luminescence and Molecular Exciton Microscopy, R. Kopelman, W. Tan, A. Lewis, and K. Lieberman, Workshop on Advanced Laser Technology For Chemical Measurements, U. S.Dept. of Energy, Oak Ridge National Laboratory: Oak Ridge, TN (1990), pp 70-73. [Invited extended abstract] 257. Statistical Properties of the Distance Between a Trapping Center from a Uniform Density of Diffusing Particles in Two Dimensions, S.Havlin, H. Larralde, R. Kopelman, and G. H. Weiss, Physica A 169,337-351 (1990). 25 8, Space and Time-Resolved Diffusion-Limited Binary Reaction Kinetics in Capillaries: Experimental Observation of Segregation, Anomalous Exponents, and Depletion Zone, Y.-E. Lee Koo, and R. Kopelman, J. Stat. Phys. 65, 893-918 (1991). 259. Exciton Microscopy and Reaction Kinetics in Restricted Spaces, R. Kopelman, In Physical and Chemical Mechanisms in Molecular Radiation Biology, edited by W. A. Glass, and M. Varma, Plenum Press: New York, Basic Lifesciences 58,475-502 (1991). [Invited refereed conference paper] 260. Exciton Patterns in Molecular Dots and Wires and Applicationto Polymer Morphology, R. Kopelman, Z.Y. Shi,andC. S . Li, J. Lumin.48/49,143-146 (1991). [Contributed refereed conference paper] 26 1 . Evanescent Luminescence and Nanometer-Size Light Source, R. Kopelman, K. Lieberman, A. Lewis, and W. Tan. J.Lumin. 48149,871-875 (199). [Invitedrefereed conference paper] 262. Nearest Neighbor Distances in Diffusion-Controlled Reactions Modelled by a Single Mobile Trap, R. Schoonover, D. Ben-Avraham,S.Havlin, R. Kopelman, and G. H. Weiss, Physica A 171, 232-238 (1991). 263. Scaling Properties of Diffusion Limited Reactions on Fractal and Euclidean Geometries, K. Lindenberg, W.S.Sheu, and R. Kopelman, J. Stat. Phys. 65, 12691283 (1991). 264. Diffusive Motion in a Fractal Medium in the Presence of a Trap, S.Havlin, R. Kopelman, R. Schoonover, and G. Weiss, Phys. Rev. A 43, 5228-5232 (1991).

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265. Toward Nanometer-Scale Optical Devices, Microscopy, and Spectroscopy,R. Kopelman, W. Tan., S.Smith, A. Lewis, and K. Lieberman, Microbeam Analysis, edited by D. G. Howit, Microbeam Analysis Society: San Francisco, CA (1991), pp 91-94. [Invited conference paper1 266. The Diffusion Limited Reaction A + B 0 on a Fractal Substrate, E. Clement, R. Kopelman, and L. M. Sander, J. Stat. Phys. 65, 919-924 (1991). 267. Low DimensionalReactionKinetics and Self-organization, R. Kopelman, L. W. Anacker, E. Clement, L. Li, and S.Sander, Proceedingsof Conferenceon 'Mathematics in Chemistry", Texas, Nov. 1989, Chemom. Intell. Lab. Syst. 10,127-132 (1991). [Invited refereed conference paper1 268. Reaction Kinetics in Restricted Spaces, R. Kopelman,and Y.-E. Koo, special issue edited by J. Klafter, and J. M. Drake, Isr. J. Chem. 31, 147-157 (1991). [Invited refereed paper] 269. Scanning Exciton Microscopy and Single Molecule Resolution and Detection, R. Kopelman, w. Tan, A. Lewis, and K. Lieberman, Proceedings of the International Society for Optical Engineering: Optical Methods for UltrasensitiveDetection and Analysis: Techniques and Applications, edited by B. L. Feary, Proc. SPIE-Int. 1435,96101 (1991). [Invited keynote address conference paper] 270. Bimolecular Diffusion-LimitedReaction Kinetics at SteadyState, E. Clement, L. Sander, and R. Kopelman,NATO ASI Ser., Ser. B 258, 431-436 (1991). 271. Visualizing Chemical Kinetics in Fractal Domains, N. E. Hurlburt, L. W. Anacker, and R. Kopelman, IEEE Proc. Visualization 91, 364-367 (1991). 272. Scaling Properties of Diffusion Limited Reactions on Fractals, K. Lindenberg,W.-S. Sheu, and R. Kopelman, Phys. Rev. A 43, 7010-7072 (1991). 273. SpectralAnalysis of Surfacesat SubwavelengthResolution, R. Kopelman, S. Smith,' W. Tan, R. Zenobi, K. Lieberman, and A. Lewis, Proc. SPIE-Int. SOC.Opt. Eng. 1637, 33-40 (1992). [Invited conference paper] 274. Scanning Molecular Exciton Microscopy: A New Approach to Gene Sequencing,R. Kopelman, J. Langmore, B. Orr, Z.-Y. Shi, S.Smith, W. Tan, and V. Makarov, Human Genome Program Workshop Reports, DOE/ ER-O554P, 1991-92,130-131 (1992). [Invited conference extended abstract] 275. Diffusion Controlled Elementary Reactions in Low Dimensions, R. Kopelman, and Y.-E. Koo, In Advances in Chemical Kinetics and Dynamics,edited by J. Barker, JAI Press, Inc.: Greenwich, CT 1, 113-138 (1992). [Invited refereed review chapter] 276. Exotic Behavior of the Reaction Front in the A + B C Reaction-Diffusion System, H. Taitelbaum, Y.-E. L. Koo, S.Havlin, R. Kopelman, and G. Weiss, Phys. Rev. A 46, 2151-2154 (1992). 277. Development of SubmicronChemical Fiber Optic Sensors, W. Tan, Z.-Y. Shi, and R. Kopelman, Anal. Chem. 64, 2985-2990 (1992). 278. Nonclassical Kinetics and Reaction Probability for Bimolecular Reactions in Low Dimensional Media, z.-Y. Shi, and R. Kopelman, J. Phys. Chem. 96,6858-6861 (1992). 279. Microfluorescenceand Microstructure of Tetracene Aggregates in PMMA, S.-K.Kook, and R. Kopelman, J. Phys. Chem. 96, 10672-10676 (1992).

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The Journal of Physical Chemistry, Vol. 98, No. 30, 1994 7237 280. Influence of External Steady Source Structure on Particle Distributions and Kinetics of Diffusion-Limited Reactions. I: A A -, 0 Simulations, L Li, and R. Kopelman, J . Phys. Chem. 96, 8079-8084 (1992).

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281. Submicrometer Intracellular Chemical Optical Fiber Sensors, W. Tan, Z.-Y. Shi, S. Smith, D. Birnbaum, and R. Kopelman, Science 258, 778-781 (1992).

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282. Reaction Order vs. Probability for Bimolecular Steady State Reactions: A A A and A A 0 in One Dimension, Z.-Y. Shi, and R. Kopelman, Chem. Phys. 167, 149-155 (1992).

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283. Nanometer Optical Fiber pH Sensor, R. Kopelman, W. Tan, and Z.-Y. Shi, Proc. SPIE-Int. SOC.Opt. Eng. 1796, 157-162 (1992). [Invited conference paper] 284. A Nanometer Dimension Optical Device with Microimaging and Nanoillumination Capabilities, R. Kopelman, and A. Lewis, US. Patent No. 5,148,307 (1992). 285. A Nanometer Dimension Optical Device with microimaging and Nanoillumination Capabilities-Methods, R. Kopelman, and A. Lewis, US.Patent No. 7,899,694 (1992). 286. Subwavelength Optical Probes, R. Kopelman, W. Tan, and Z.-Y. Shi, DOE Workshop on Advanced Laser Technology for Chemical Measurements, Santa Fe, 1992. [Invited conference paper] 287. Diffusion Controlled Binary Reactions in Low Dimensions: Refined Simulations, P. Argyrakis, and R. Kopelman, Phys. Rev. A 45, 5814-5819 (1992).

295. Spatially Resolved Spectra of Micro-Crystals and NanoAggregates in Doped Polymers, D. Birnbaum, S.-K. Kook, and R. Kopelman, In Dynamics in Small Confining Systems, edited by J. M. Drake, J. Klafter, R. Kopelman, and D. D. Awshalom, Mater. Res. SOC. Symp. Proc. 290,227-232 (1993). [Refereedconference paper1 296. Non-Classical Kinetics in Hydrogen-Deuterium Exchange Reaction on Metal Catalyst, I. Choi, and R. Kopelman, In Dynamics in Small Confining Systems, edited by J. M. Drake, J. Klafter, R. Kopelman, and D. D. Awshalom, Mater. Res. SOC.Symp. Proc. 290, 267-271 (1993). [Refereed conference paper] 297. Dynamics in Small Confining Systems, edited by J. M. Drake, J. Klafter, R. Kopelman, and D. D. Awshalom, Mater. Res. SOC.Symp. Proc. 290, 1-377 (1993). 298. Experimental Study of A B C Reaction-Diffusion Systems in a Capillary, Y.-E. L. Koo, R. Kopelman, A. Yen, and A. Lin, In Dynamics in Small Confining Systems, edited by J. M. Drake, J. Klafter, and D. D. Awshalom, Mater. Res. SOC.Symp. Proc. 290, 273278 (1993). [Refereed conference paper]

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299. Elementary Rate Laws of Diffuion-Limited Species in the A T -T Reaction in Low Dimensions, R. Schoonover, and R. Kopelman, In Dynamics in Small Confining Systems, edited by J. M. Drake, J. Klafter, R. Kopelman, and D. D. Awshalom, Mater. Res. SOC.Symp. Proc. 290, 255-260 (1993). [Refereed conference paper]

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300. Local Reaction Probability Effects in Non-Classical Kinetics: Batch and Steady State, Z.-Y. Shi, and R. Kopelman, In Dynamics in Small Confining Systems, edited by J. M. Drake, J. Klafter, R. Kopelman, and D. D. Awshalom, Mater. Res. SOC.Symp. Proc. 290,279286 (1993). [Refereed conference paper]

289. Near-Field Fiberoptic Chemical Sensors and Biological Applications, W. Tan, Z.-Y. Shi, B. Thorsrud,C. Harris, and R. Kopelman, J . SOC.Photo.-Opt. Instrum. 4Eng. 2068, 59-68 (1993). [Refereed conference paper]

301. Energy Transfer, Nanomber Crystals and Optical NanoProbes, W. Tan, and R. Kopelman, In Dynamics in Small Confining Systems, edited by J. M. Drake, J. Klafter, R. Kopelman, and D. D. Awshalom, Mater. Res. SOC.Symp. Proc. 290,287-292 (1993). [Refereed conference paper]

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0 Batch Reactions: Effect of 288. Non-Classical A B Mobility on Rate, Order, Aggregation and Segregation, P. Argyrakis, and R. Kopelman, Phys. Rev. E 47 (5), 3757-3760 (1993).

290. Influence of External Steady Source Structure on Particle Distributions and Kinetics of Diffusion-Limited Reactions. 11: A B 0 Simulations, L. Li, and R. Kopelman, Chem. Phys. 174, 367-375 (1993).

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291. Near Field Optical and Exciton Imaging, Spectroscopy and Chemical Sensors, R. Kopelman, W. Tan, Z.-Y. Shi, and D. Birnbaum, In Near Field Optics, edited by D. W. Pohl, and D. Courjon, Kluwer: Dordrecht (1993), pp 11-24. [Invited refereed conference paper] 292. Diffusion-Limited Binary Reactions: The Hierarchy of Non-Classical Regimes for Random Initial Conditions, P. Argyrakis, R. Kopelman, and K. Lindenberg, Special Issue on Transport Properties in Disordered Systems, edited by G. Zumofen, J. Klafter, and A. Blumen, Chem. Phys. 177 (3), 693-707 (1993). [Inuitedrefereedpaperl293. Near-Field Optical Microscopy, Spectroscopy and Chemical Sensors, R. Kopelman, and W. Tan, In Spectroscopic and Microscopic Imaging of the Chemical State, edited by M. D. Morris, Marcel Dekker, Inc.: New York, (1993), pp 227-254. [Invited review chapter] 294. One-Dimensional A + B = 0 Reaction with One Immobile Species, P. Argyrakis, and R. Kopelman, In Dynamics in Small Confining Systems, edited by J. M. Drake, J. Klafter, R. Kopelman, and D. D. Awshalom, Materials Research Society Symposium Proceedings 290, 261266 (1993). [Refereed conference paper]

302. Diffusion-Limited Binary Reactions: A Hierarchy of NonClassical Regimes, P. Argyrakis, R. Kopelman, and K. Lindenberg, In Dynamics in Small Confining Systems, edited by J. M. Drake, J. Klafter, R. Kopelman, and D. D. Awshalom, Mater. Res. SOC.Symp. Proc. 290,365372 (1993). [Refereed conference paper] 303. Near-Field Scanning Optical Spectroscopy: Spatially Resolved Spectra of Micro-Crystals and Nano-Aggregates in Doped Polymers, D. Birnbaum, S. K. Kook, and R. Kopelman, J . Phys. Chem.97,3091-3094 (1993). 304. Tip/Sample Interactions, Contrast and Near-Field Microscopy of Biological and Solid State Samples, S.Smith, E. Monson, G. Merritt, W. Tan, D. Birnbaum, Z.-Y. Shi, B. A. Thorsrud, C. Harris, H. T. Grahn, K. Ploog, R. Merlin, B. Orr, J. Langmore, and R. Kopelman, J . SOC.Photo.-Opt. Instrum. Eng. 1855, 81-92 (1993). [Invited conference paper] 305. Near-Field Optics: Imaging Single Molecules, R. Kopelman, and W. Tan, Science 262, 1382-1384 (1993). [Invited] 306. Phenylacetylene Dendrimers with Extended n-conjugation, Z. Xu,Z.-Y. Shi, W. Tan, R. Kopelman, and J. S.Moore, Polym. Prep. (Am. Chem. SOC.,Div. Polym. Chem.) 34, 130-131 (1993). [ACS conference]

7238 The Journal of Physical Chemistry, Vol. 98, No. 30, 1994 307. Application of Cluster Distributions to Energy Transfer in Naphthalene Choleic Acid Crystals, S. K. Kook, D. Hanson, and R. Kopelman, J. Phys. Chem. 97,1233912342 (1993). 308. The Hierarchies of Non-Classical Regimes for DiffusionLimited Binary Reactions: A Review, K. Lindenberg, P. Argyrakis, and R. Kopelman, In Chaos and Order: The New Synthesis, edited by M. Millonas, Springer: Berlin (1994) (in press). 309. Non-Classical Crossovers in Binary Reactions in OneDimensional Systems, P. Argyrakis, P. Kopelman, and K. Lindenberg, J. Lumin. 58,413416 (1994). [Refereed conference paper]

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310. The Diffusion-Limited Reaction A + A 0 in the Steady State: Influence of Correlations in the Source, E. Clement, R. Kopelman, and L. Sander, Special Issue on Dissipative Dynamics I., edited by N. Agmon, and R. D. Levine, Chem. Phys. 180,337-341 (1994). [Invited refereed paper] 31 1 . Energy Transfer and Transport, R. Kopelman, and J. Klafter, Annu. Rev. Phys. Chem. (in preparation). [Invited review]

312. Special Issue of J. Phys. Chem.,dedicated to R. Kopelman (July 1994). 3 1 3 . Diffusion-Limited Binary Reactions: The Hierarchy of Non-Classical Regimes for Correlated Initial Conditions, K. Lindenberg, P. Argyrakis, and R. Kopelman, Joshua Jortner Festschrift, J. Phys. Chem. 98, 33893397 (1994).

314. Subwavelength Spectroscopy, Exciton Supertips and Mesoscopic Light-Matter Interactions, R. Kopelman, w. Tan, and D. Birnbaum, J. Lumin. 58,380-387 (1994). [Invited refereed conference paper] 315. Near Field Optics: Chemical Sensors, Photon Supertips and Subwavelength Spectroscopy, W. Tan, D. Birnbaum,C. Harris,R. Merlin,B. Orr, Z.-Y. Shi,S. Smith, B. Thorsrud, and R. Kopelman, Elsevier Science Publishers: Amsterdam (in press, 1994). [Invited]

3 16. Photonanofabrication and Optical Nanoprobes. W.Tan, Z.-Y. Shi, and R. Kopelman, Mol. Cryst. Liq. Cryst. UPS 6 (in press, 1993). 3 17. 100 Femtosecond/100 Nanomter Near-Field Probe, S. Smith, B. Orr, R. Kopelman, and T. Norris, Proc. NearField Opt. II, Ultramicroscopy (in press). 3 18. Implementation of an NSOM System for Fluorescence Microscopy, E. Monson, G. Merritt, S. Smith, J. Langmore, and R. Kopelman, Proc. Near-Field Opt. 11, Ultramicroscopy (in press). 3 19. Molecular Supertips for Near-Field Optics, W.Tan, Z.Y. Shi, and R. Kopelman, Proc. Near-Field Opt. II, Ultramicroscopy (in press). 3 20. Real-Time Responses to Chemical and Environmental Insults: Ultramicrofiberoptic pH Measurements Inside Intact Organogenesis-Stage Rat Conceptuses, W. Tan, B. Thorsrud, C. Harris, and R. Kopelman, Curr. Biol. (submitted, 1993). 3 2 1 . Femtosecond Near-field Scanning Optical Microscopy, S. Smith, B. G. Orr, R. Kopelman, andT. Norris, CLEO (1994). 322. Near-field Optical Microscopy, Spectroscopy and Chemical Sensors, R. Kopelman, and W. Tan, Appl. Spectrosc. Rev. 29, 39-66 (1994). 323. Diffusion Limited Reaction Kinetics Revisited, K. Lindenberg, P. Argyrakis, and R. Kopelman, Mostafa ElSayed Festschrift, J. Phys. Chem. (1995). 3 24. Non-Classical Elementary Reaction Kinetics, R. Kopelman, and K. Lindenberg, Chem. Rev. (in preparation). [Invited review] 325. Miniaturized Fiber Optic Biochemical Sensors with Fluorescent Dye Doped Polymers, W.Tan, Z.-Y. Shi, and R. Kopelman, Sens. Actuators B (in press). 326. Subwavelength Fiber Optic Chemical and Biological Micro-Sensors, R. Kopelman, W.Tan, and Z.-Y. Shi, US.Patent (submitted, 1992). 327. Submicrometer Optical Fiber Sensor and Method of Fabrication Thereof, R. Kopelman, W.Tan, and Z.-Y. Shi, US.Patent (submitted, Feb. 1994).