through the veins and arteries. Once the neck region was entered, an iodine containing dye was inserted into the catheter and the flow of blood in the neck area could be monitored on the TV screens. This revealed a hole in one of the arteries or veins in front of the spinal cord. (This par- ticular problem is called a fistula and was probably a con- genital problem that fmally surfaced.) Next came the dis- cussions of what to do and how to do it.

On Wednesdav the decision was made to perform an- other angiogram but this time its purpose was to shut off the flow of blood to this artem. The angioeram was sched- uled for Thursday morning. A; 900 AMh'was whisked off to start the procedure. For the next two hours a slow block- age of the artery was performed in the following manner. First the catheter was inserted from the groin to the neck area and positioned just in front of the fistula. Then roughly one inch longsilk threads, that had been soaked in a oolvvinvl alcohol solution. were inserted into the cathe- te; and lodged in the a r t e i just in front of the fistula. As these threads formed a blockage in the artery, the polyvi- nyl alcohol caused the blood to clot and seal off the artery past the point of the blockage. As the artery was sealed off and blood clotting continued, the artery that had caused the paralysis was effectively rendered useless. This de- creased the pressure on the spinal cord so that osmotic forces could begin removing the blood from the spinal cord area.

Friday morning the physical therapist arrived and for the first time in a week my son walked a little on his own. On Mondav a third aneioeram showed that the blockage was compl& and discharge from the hospital followed i n Tuesdav. Further ~hvsical theraov took up the remainder of this week and b n Sunday, two weeks after the initial event, my son returned home. By Tuesday he was hack in school full time. He walked slowly and hesitantly to class, but he walked on his own.

Every time that I have told this story, the response has been that it is a miracle of modem medicine, which it cer- tainly is. But there is another miracle here that we teach- ers need to inform our students of and that is the miracle of some old, middle-aged, and modern chemistry and phys- ics. Not that many sears ago my son would have been writ- . . ten-offas unsalr&able because we could not see what his problem was nor get to the arca to fix it. Now with X-rays. b~ scans, MRI sc&~ and angiograms seeing the is a much simpler process. When I hear CT scan. MRI and . &

angiogram the names Roentgen, discoverer of X-rays in 1895, Bloch and Purcell, discoverers of NMR in 1946, and Shockley, Brattain and Bardeen, discoverers of the transis- tor in 1948, rush to my thoughts. The steroids that were administered to relieve the oressure in mv son's spinal cord were probably made from a process that was initiated bv Woodward as he determined how to svnthes~ze steroids i i 1951. The catheter and the polyvinyl hcohol, that were so instrumental in blockina the arterv. are the direct de- .. . . scendants of the pioneering work on polymers done by I3aekrland in 1907 and Carothers in 1928. All of these dis- coverers were "doctors" of the Ph.D. variety not the M.D. type.

What this experience has brought to my attentionis that neurosurgeons are the hands of modern medicine and the miracles that it can make. The spinal cord of modem med- icine is chemistry and physics. If the blood supply to the spinal cord is choked off, as we fear will happen in this era of lack of interest in the phvsical sciences. then the ulti- mate result will he of modem medicine. That is whv i t is imwrtant that we teach chemistrv and ohvsics and do a gobd job a t it. Our students must real&e-that chemists and physicists are every bit as important to the

recovery of my son's health as the neurosurgeons that ap- plied the fruits of the labor of chemists and physicists.

Who knows what the miracles of modern chemistry and physics will give us tomorrow.

Charles H. Atwood Mercer University Macon, GA 31207

Rolling Happy and Unhappy Balls and Their Coefficients of Friction

To the Editor:

The article "Happy and Unhappy Balls: Neoprene and Polynorbornene" [J. Chem. Educ. 1990,67, 198-1991 con- tains misconceptions about friction and rolling motion. A ball made from neoprene rubber (a Yla~ov" ball) rebounds elastically when bounced, while' a baii kade from poly- norbornene (or Norsorex. an "unhao~v" ball) does not bounce. When the two t&es of balls'&e allowed to roll down an inclined plane, the "happy" ball always beats the "unhappy" ball to the bottom. The authors claim that

The "unhappy" (polynorbornene) ball rolls more slowly be- cause of its higher coefficient of friction, which makes this type of rubber ideal for racine car tires. for which meat road adhe- sion is needed at high speed.

The coefficient of friction involves surface friction, which opposes the sliding motion of two surfaces in contact. While the coefficient of friction of polynorbornene may be meater than that of neoprene. an exoeriment involvina Foiling (without slipping) Lotion will not give any inform: tion about coefficients of surface friction. The experiment required to compare coefficients of surface friction would have to involve sliding, not rolling, of the balls.

Surface friction does not dissipate kinetic energy in the process of rolling as long as no slippage occurs. Ideally, all rigid homogeneous solid spheres should roll down an in- clined plane with the same acceleration and have the same velocity at the bottom of the plane, independent of the mass, radius, or density of the sphere. (The acceleration of a rolling solid sphere is 517 that of an object sliding down the same plane with no friction, and the translational ve- locity of t&e rolling sphere by the time it reaches the bot- tom of the incline is only (5/7)'n as great as if i t had been sliding.) A larger coefficient of friction does not slow down the rolling motion-it only assuresthat the sphere will roll, rather than slide, down the incline.

How, then, can one explain the observation that the un- happy hall always loses the race down the plane? A possi- ble explanation may be that there is greater adhesion (dif- ferent from surface friction) between the Norsorex ball and the plane resulting in a larger trailing edge force which slows down that ball. Another more likely explanation is that in the unhappy ball, internal irreversible deformation (perhaps on the microsco~ic level) occurs durina rollina. - -, absorbing some of the energy and leaving less energy available as translational kinetic enerm. This internal ir- reversible deformation is sometimes referred to as rolling friction (perhaps a misnomer), but it is hard to see how this property could be beneficial in racing tires. This explana- tion also correlates with the bouncing behavior and the be- havior of the two balls when compressed in a vise. The happy ball is deformed under stress but is capable of ... quickly returning to its originul shape oncr the stress is removed, thus recovering the enerby of deformation. How- ever, when the unhappy ball is deformed, u,hether in a vise or during a bounce, i t does nor quickly return to ~tsori'lnal shaoe once the stress is rcmoved Thus. when the unhaoov baliis bounced, kinetic energy is transformed irreversIb'6 into internal energy of the ball as deformation and heat. A

Volume 70 Number 10 October 1993 867

similar irreversible deformation occurs wntinuously dm- ing rolling of the unhappy ball, transforming some of the translational kinetic energy into internal energy of the ball.

The article goes on to "explain" the relative coefficients of friction of the two materials in terms of chlorine and cy- clopentane groups in the molecular structure. However, the relationship between wefficient of friction and molecu- lar structure is tenuous at best. and often has more to do with the physical condition of t6e surfaces rather than the molecular structure. In fact. the article mentions that the Norsorex (unhappy material) contains relatively large quantities of a nonvolatile compatible liquid such as high- viscosity naphthenic oil, and the presence of this liquid could acwunt for the "internal friction" which slows down the rolling motion.

Lois Nicholson Nat onal Research cobncl

Office of Sc en! flc and Engmeer ng Researcn Wash ngton. DC 20418

To the Editor:

In the article cited by Nicholson the chemical and physi- cal characteristics of both polychloroprene (neoprene) and polynorbornene (Norsorex) were discussed and the results of the experiments were explained in terms of the contrast- ing chemical structures of these elastomers. In several cases, the explanations were oversimplified, and this was arguably appropriate, but unfortuna&ly, in other cases the explanations given were incorrect, as pointed out in the abbve letter b;~icbolson.

The thrust of Nicholson's letter concerns the distinction between surface friction and internal friction. She cor- rectlv points out that rolling balls down a n incline does not meaHu>e relative coefficients of surface friction but some other property. The terminology used in the article is somewhat inexact, which probably prompted Nicholson's letter. Tire adhesion or "grip", rolling resistance, braking, tire wear, etc., are very complex pctiormanre phenomena and are not generally a reflect~on of any one single mate- rial properly. However, the rirticlc states that the unhappy ball has a "lugher coefficient of fricuon," and unfi~rtunately the word "coefficient" implie surface friction, when the factor involved here 1s mternal friction or viscous loss, i.e., the so-called rolling resistance, which is a familiar concept within the ruhhrr tire industry. The term'.rollmg friction," is 3 misnomer precisely hecauw it also implies surface fric- tion. Ih~wcvcr, the article is correct in speaking of the hen- elits of a less resilient (more highly damping, rubber in maintaining road contact. ~oadsu;faces &not perfect. During cornering or braking, a highly resilient rubber such as natural rubber or cis-polybutadiene will tend to bounce, and the driver can suddenly experience the extremely low coeff~cient of surface friction between rubber and air. The trade-off in switching to a less resilient rubber is increased tire wear and decreased gas mileaee. The article is correct - - in this proposition, also, since i t warns of excessive heat build-UD and in so doine implies that the friction is inter- - . nal ra t ier than surface.

Nicholson is also correct in referring to the likely higher trailing edge force for the Norsorex ball during rolling. The Norsorex ball has a lower modulus and deforms substan- tially more under its own weight than does the neoprene hall. This results not only in greater deformation, leading to higher internal frictional losses, but also results in a larger "footprint" and greater adhesive forces as the trail-

868 Journal of Chemical Educat~on

ing edge of the contact surface must continually separate - - . . during rolling.

Two incorrect statements in the Conclusions section of the article can be traced to incorrect technical information given to Kauffman et al. by the supplier of the balls (Arbor Scientific), viz., that the glass transition temperature (Tg) of the Norsorex ball is very low (-60 'C). Differential scan- ning calorimetm, however, revealed that the Norsorex ball (which is a compounded elastomer containing a nonvola- t i e plasticizer) &splayed two transitions: a Htrong, very broad transition a t -30 T and a much weaker, relatively sham transition at 12 'C. indicatine that i t is not com- - pletely homogeneous, but consists of two phases, one (low T. ohase) relativelv richer in ~lasticizer than the other (hiih Tg phase). ~h;s , rather th'an possessing a glass tran- sition tem~erature that has been lowered "bv almost 100 'C" and r ekn ing "considerable freedom of roiation [of the chains] a t temperatures as low as -60 'C" (p 199), the Norsorex ball, as shown conclusively by our DSC results, has a two-phase morphology, one phase of which is totally glassy a t 12 C and lower, and the other a t -30 T and lower.

The authors wish to thank Robert F Ohm, Technical Di- rector. Rubber Chemicals & Minerals. R. T. Vanderb~lt Co.. Inc., ~ o n v a l k , CT 06855, and ~ n d r d Marbach, ~ a n a g e r ; Norsorex, Atochem, Paris, France, for technical informa- tion.

Robson F. Storey and Raymond B. Seymour University of Southern Mississippi

Hattiesburg, MS 39440

George B. Kauffman California State University, Fresno

Fresno, CA 93740

Can a Carnot Cycle Ever Be Totally Reversible?

To the Editor:

In the paper on the efficiency of reversible heat engines by Seidman and Michalik [J. Chem. Educ. 1991,68, 20% 2101 it is stated that "Atkins makes just such a mistake when he asserts that a reversible Stirline cvcle has the - " same efficiency as that of a Carnot cycle operating between the same temperatures." Then there follows an analysis of a three stage reversible cycle and'the Stirling cycle.

The writer has found statements similar to the corollary to Carnot's theorem in a t least five engineering thermody- namics books. Also one will find in other books expressions for the thermodynamic efficiency which are not of the Car- not form. The apparent dilemma results from the fact that in general a regenerator, used to achieve the isochoric pro- cesses labelled staws 2 and 4 in the Seidman and Michalik paper, is not reveriible so that the Stirling cycle consists of an irreversible device operating between two isothermal reservoirs and, therefore, must necessarily have an effi- ciency lower than Carnot. However, a totally reversible re- generator used in a Stirling cycle must result in an overall Carnot cycle effkiency so that Atkins' statement is correct as a n ideal limiting case. What assumption begs the ques- tion is whether a regenerator or even a Carnot cycle can ever be totally reversible. The writer believes that the Curzon and Ahlborn [Amel: J. Phys. 1975,43,22-241 con- cept should replace the standard Carnot analysis.

Peter E. Liley Department of Mechanical Engineering

Purdue University West Lafayene, IN 47907-1288