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 particular problem is called a fistula and was probably a congenital problem that fmally surfaced.) Next came the discussions of what to do and how to do it. On Wednesdav the decision was made to perform another angiogram but this time its purpose was to shut off the flow of blood to this artem. The angioeram was scheduled for Thursday morning. A; 9 0 0 AMh'was whisked off to start the procedure. For the next two hours a slow blockage 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 cathete; 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 polyvinyl 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 decreased 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 ~hvsicaltheraov 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 certainly is. But there is another miracle here that we teachers need to inform our students of and that is the miracle of some old, middle-aged, and modern chemistry and physics. Not that many sears ago . my . son would have been written-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 transistor 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~zesteroids i i 1951. The catheter and the polyvinyl hcohol, that were so instrumental in blockina . the arterv... are the direct descendants of the pioneering work on polymers done by I3aekrland in 1907 and Carothers in 1928. All of these discoverers 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 medicine 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 ultiof modem medicine. That is mate result will he 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 applied 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 contains misconceptions about friction and rolling motion. A ball made from neoprene rubber (a Yla~ov"ball) rebounds elastically when bounced, while' a baii k a d e from polynorbornene (or Norsorex. a n "unhao~v"ball) does not bounce. When the two t&es of balls'&e allowed to roll down a n inclined plane, the "happy" ball always beats the "unhappy" ball to the bottom. The authors claim that The "unhappy" (polynorbornene) ball rolls more slowly because of its higher coefficient of friction, which makes this type of rubber ideal for racine car tires. for which meat road adhesion 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 inclined 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 a n object sliding down the same plane with no friction, and the translational velocity of t&e rolling sphere by the time it reaches the bottom 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 unhappy hall always loses the race down the plane? A possible explanation may be that there is greater adhesion (different 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~iclevel) occurs durina rollina. -, absorbing some of the energy and leaving less energy available as translational kinetic enerm. This internal irreversible 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 explanation also correlates with the bouncing behavior and the behavior 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. However, when the unhappy ball is deformed, u,hether in a vise or during a bounce, it 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
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Volume 70 Number 10 October 1993
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similar irreversible deformation occurs wntinuously dming 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 cyclopentane groups in the molecular structure. However, the relationship between wefficient of friction and molecular structure is tenuous a t best. and often has more to do with the physical condition of t6e surfaces rather than the molecular structure. I n fact. the article mentions that the Norsorex (unhappy material) contains relatively large quantities of a nonvolatile compatible liquid such as highviscosity 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! flcand Engmeer ng Researcn Wash ngton. DC 20418
To the Editor: I n the article cited by Nicholson the chemical and physical characteristics of both polychloroprene (neoprene) and polynorbornene (Norsorex) were discussed and the results of the experiments were explained in terms of the contrasting chemical structures of these elastomers. I n several cases, the explanations were oversimplified, and this was arguably appropriate, but unfortuna&ly, in other cases the explanations given were incorrect, a s pointed out in the abbve letter b;~icbolson. The thrust of Nicholson's letter concerns the distinction between surface friction and internal friction. She correctlv 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~onof any one single material 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 friction. Ih~wcvcr,the article is correct in speaking of the henelits of a less resilient (more highly damping, rubber in maintaining road contact. ~ o a d s u ; f a c e s¬ 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~cientof 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-UDand in so doine implies that the friction is internal r a t i e r 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 substantially 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 a s the trail-
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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 scanning calorimetm, however, revealed that the Norsorex ball (which is a compounded elastomer containing a nonvolat i e plasticizer) &splayed two transitions: a Htrong, very broad transition a t -30 T and a much weaker, relatively sham transition a t 12 'C. indicatine that it is not completely homogeneous, but consists of two phases, one (low T. ohase) relativelv richer in ~lasticizerthan the other (hiih Tgphase). ~ h ; s , rather th'an possessing a glass transition t e m ~ e r a t u r ethat has been lowered "bv almost 100 'C" and r e k n i n g "considerable freedom of roiation [of the chains] a t temperatures a s low a s -60 'C" (p 199), the Norsorex ball, a s 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 Director. Rubber Chemicals & Minerals. R. T. Vanderb~ltCo.. Inc., ~ o n v a l k CT , 06855, and ~ n d r dMarbach, ~ a n a g e r ; Norsorex, Atochem, Paris, France, for technical information.
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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: I n 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 a s that of a Carnot cycle operating between the same temperatures." Then there follows a n 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 thermodynamics books. Also one will find in other books expressions for the thermodynamic efficiency which are not of the Carnot form. The apparent dilemma results from the fact that in general a regenerator, used to achieve the isochoric processes labelled staws 2 and 4 in the Seidman and Michalik paper, is not reveriible so that the Stirling cycle consists of a n irreversible device operating between two isothermal reservoirs and, therefore, must necessarily have a n efficiency lower than Carnot. However, a totally reversible regenerator used in a Stirling cycle must result in a n overall Carnot cycle effkiency so that Atkins' statement is correct a s a n ideal limiting case. What assumption begs the question 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 concept should replace the standard Carnot analysis. Peter E. Liley Department of Mechanical Engineering Purdue University West Lafayene, IN 47907-1288
