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fragment, the distance to the detector, the size of the detector, and the angular distribution of the fragment. In our instrument, even a few tenths of an electronvolt of energy is sufficient to cause fragment loss if the energy is directed exactly perpendicular to the ion beam axis. Fragment ejection parallel to the beam axis may cause broadening in the arrival time spectrum. While we have made preliminary observations of fragment ion loss from diatomic and triatomic metal parent ions, we have not measured any noticeable broadening in arrival time spectra. One of the initial applications of reflectron instruments was in the study of metastable ion decay ( 2 , 5 , 6 ) .These experiments used the slow overall time scale for ion drift in the first flight tube, deceleration, and reacceleration to probe microsecond metastable lifetimes. Unimolecular dissociation lifetimes are another common problem in photodissociation studies of large molecules. In the configuration described above, however, irradiated ions remain in the turning region for up to 3-4 p s (mass dependent) before reacceleration. This instrument is therefore sensitive to “slow” unimolecular fragmentation processes. It should be emphasized that the present system is not yet fully optimized for the study of large molecules. The system described in Figure 1is in fact equivalent to two low-resolution spectrometers connected by the reflection/dissociation region. Mass selection of parent ions and mass analysis of fragment ions are both limited to unit resolution a t about m / z 200 (typical for a simple linear TOF). However, the same PbI7+ ion can be detected without photodissociation by its time of flight through the full reflectron instrument with a resolution of about 1OOO. To incorporate this general idea into the design of a genuine high-mass/high-resolution instrument, then, it should be possible to include a reflectron for high-resolution analysis prior to mass selection and another reflectron after the dissociation region for high-resolution analysis of fragments. This “triple reflectron” instrument would not be simple geometrically, but designs based on the linear reflectron (3, 18) concept could be used to achieve a more compact system. The general design philosophy described here may have significant applications for the study of large molecules, particularly for biological systems. Kinematic effects associated with large mass differences between parent ions and collision partners make collisionally activated dissociation less attractive than high-energy laser dissociation for these systems (19,20). In the reflectron configuration the timing problems associated with laser experiments are effectively eliminated, and the benefits of essentially unlimited mass range can be realized without sacrificing resolution. Additionally, the pulsed nature of these laser experiments lends them naturally to coupling with recently developed laser desorption sources (21-25) for the study of involatile species. These and other
applications of reflectron systems are under current investigation in our laboratory.
ACKNOWLEDGMENT We thank Fred McLafferty and Jon Amster for helpful discussions about these experiments. LITERATURE CITED (1) Mamyrin, B. A.; Karataev. V. I.; Shmikk. D. V.; Zagulin. V. A. Zh. Eksp. Teor. Fiz. 1973, 64,82. (2) Boesl, U.;Neusser, H. J.; Weinkauf, R . ; Schlag, E. W. J . Phys. Chem. 1982, 86,4857. (3) Lubman, D. M.; Bell, W. E.; Kronick, M. N. Anal. Chem. 1983, 55, 1437. (4) Kuehlwind. H.;Neusser, H. J.; Schlag, E. W. Int. J . Mass Spectrom. Ion Phys. 1983, 51,25. (5) Kuehlwind, H.;Neusser, H. J.; Schlaa. E. W. J. Phys. Chem. 1984. 88,6104. (6) Kuejlwind, H.;Neusser, H. J.; Schlag, E. W. J. Phys. Chem. 1985, 89, 5600
(7) Hadden, W. F.; McLafferty, F. W. J. Am. Chem. SOC. 1988, 90, 4745. (8) Hadden, W. F.; McLafferty. F. W. Anal. Chem. 1969, 41,31. (9) Stults, J. T.; Enke, C. G.; Holland, J. F. Anal. Chem. 1983, 55,1323. (10) Glish, G. L.; Goeringer, D. E. Anal. Chem. 1984, 56,2291. (11) Cooks, G. L. 11th International Mass SDectrometw Conference, Bordeaux, 1988. (12) Geusic, M. E.; Jarrold, M. F.; McIlrath, T. J.; Freeman, R. R.; Brown, W. L. J . Chem. Phys. 1987, 8 6 , 3862. (13) Brucat. P. J.; Zheng, L. S.; Tittel. F. K.; Curl, R . F.; Smalley. R . E. J . Chem. Phys. 1988, 84,3078. (14) Liu, Y.; Zhang, Q. L.; Tittel, F. K.; Curl, R . F.; Smalley, R . E. J. Chem. Phys. 1988, 85,7434. (15) LaiHing, K.; Wheeler, R . G.; Wilson, W. L.; Duncan, M. A. J . Chem. Phys. 1987, 87,3401. (16) Alexander, M. L.; Levinger, N. E.;Johnson, M. A,; Ray, D.; Lineberger, W. C. J . Chem. Phys. 1988, 88. 6200. (17) Posey, L. A.; Johnson, M. A. J. Chern. Phys. 1988, 89,4807. (18) El-Sayed, M. A.; Tai, Tsong-Lin J. Phys. Chern. 1988, 92,5333. (19) Neumann, G. M.; Sheil, M. M.; Derrick, P. J. 2 .Naturforsch. 1984, 39a,584. (20) Kiplinger, J. P.: Bursey, M. M. Org. Mass Spectrum. 1988, 23, 342. (21) Grotemeyer, J.; Boesl, U.; Walter, K.; Schlag, E. W. J. Am. Chem. Sac. 1988, 108. 4233. (22) Ternbreull, R . ; Lubman, D. M. Anal. Chem. 1986, 58, 1299. (23) Engelke, F.; Hahn, J. H.; Henke, W.; Zare, R. N. Anal. Chem. 1987, 59,909. (24) Tembreull, R.; Lubman, D. M. Anal. Chem. 1987, 59, 1082. (25) Spengler, B.; Karas, M.; Bahr, U.; Hillenkamp. F. J. Phys. Chem. 1987, 9 1 , 6502.
K. LaiHing P. Y. Cheng T. G. Taylor K. F. Willey M. Peschke M. A. Duncan* Department of Chemistry School of Chemical Sciences University of Georgia Athens, Georgia 30602 RECEIVED for review December 2, 1988. Accepted March 21, 1989.
Polishable Modified Carbon Fiber Composite Electrodes Containing Copolymers of Vinylferrocene or Vinylpyridine in a Cross-Linked Polystyrene Matrix Sir: The carbon fiber composite electrodes described herein are polishable, random arrays of polymer-modified ultramicroelectrodes. These electrodes illustrate two new general approaches for obtaining modified electrodes that have renewable surfaces, but with electrochemical properties resem0003-2700/89/0361-1460$01.50/0
bling those of their nonrenewable polymer-film counterparts. These new types of electrodes may be designed and fabricated to have the selectivity, sensitivity, and detection limit of surface-modified electrodes, the signal-to-charging-current ratio and steady-state behavior of ultramicroelectrodes ( I , 21, 0 1989 American Chemical Society
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Figure 1. Cross sectional view of cylindrical modified carbon fiber composite electrodes. The black disks represent carbon fibers (7.2-gm
diameters; not drawn to scale). (a) Matrix-modified electrode. The white area represents a copolymer of vinylferrocene or vinylpyridine with cross-linked polystyrene. (b) Ring-modified electrode. The rings surrounding the disks represent a coating of cross-linked poly(viny1ferrocene) (also not to scale). The matrix (whAe area outside rings) is cross-linked polystyrene. and the geometric current density and polishability of solid electrodes. Electrocatalysts may be incorporated into the composite matrix as well. Both types of electrodes rely on bundles of carbon fibers dispersed in a cross-linked polystyrene matrix; the fibers are collinear within the cylinder that comprises the composite electrode. Carbon fiber microelectrodes (3-6) and arrays (7, 8) of carbon fibers have been used widely by electrochemists because of the useful physical properties of the carbon fibers themselves. Commercially available carbon fibers are typically less than 10 pm in diameter, are flexible, have electrical resistances from 1.0 to 4.0 kQ/cm (3),and are inexpensive. Modification of the carbon fiber electrodes was accomplished by one of two means: matrix modification or ring modification. Matrix-modified electrodes were prepared by copolymerizing vinylferrocene or vinylpyridine along with the styrene and divinylbenzene (DVB) that formed the composite matrix. For ring-modified electrodes, individual fibers in a bundle were coated with cross-linked poly(viny1ferrocene) by electrocopolymerization of vinylferrocene and DVB. The coated fibers were then incorporated into a cross-linked polystyrene matrix as described above. A diagram of the cross section of the cylindrical electrodes is shown in Figure 1. The general concept of ring-modified electrodes was modeled after the work of Subramanian (9) and of Bell and coworkers (10, 11), who used electropolymerization to form polymeric interlayers on carbon fibers used in epoxy composites, for improved mechanical properties. Recently we reported carbon particle composites containing solids (12), vinylferrocene (13), and vinylpyridine (14) as modifiers. Also, Wang and co-workers used commercially available epoxy-bonded graphite to prepare bulk-modified electrodes containing a cation-exchange resin, poly(viny1pyridine), or cobalt phthalocyanine (15). Both particles and fibers have advantages as the conductive components of the composite, depending upon the application. The advantages of fibers used in electrodes described herein include improved conductivity, enhanced mass transport properties, and especially, ease of miniaturization (16). In addition, the uniform size of the microelectrodes will be easier to treat mathematically. EXPERIMENTAL SECTION Materials. Hercules AS4 carbon fibers were provided to us by James P. Bell, University of Connecticut. The fibers were packaged as a 3000-fiber bundle around a spool, and individual fibers had nominal diameters of 7.2 pm. Scanning electron microscopy showed that these fibers have uniform, circular cross sections. Styrene, divinylbenzene (DVB), and vinylpyridine were purchased from Aldrich Chemicals and were vacuum-distilled. Vinylferrocene was also purchased from Aldrich and was purified
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by sublimation. Dimethylformamide (DMF), obtained from Baker Chemicals, was distilled and dried over activated alumina. Water was purified by using a Millipore reverse osmosis-ion-exchange system and had a measured resistivity of 18 MQ cm. All other chemicals were of reagent grade and used as received. Methods. Matrix-modified electrodes were prepared by mixing the modifying monomer (vinylferrocene or 4-vinylpyridine) with styrene,DVB, and azobis(isobutyronitrile) (AIBN)radical initiator and sonicating for 15 min to ensure dissolution of the AIBN and complete mixture of the monomers. An example composition for the vinylferrocene copolymer matrix-modified electrode was 67.8% styrene, 2.4% vinylferrocene, 26.9% DVB, and 2.9% AIBN. To minimize swelling (see below), while maintaining a high capacity for binding, the following composition was used for copoly(vinylpyridine) composites: 39.1 % styrene, 39.9% vinylpyridine, 19.0% DVB, and 2.0% AIBN. The carbon fibers were inserted into open-ended glass tubes (inner diameters of 1-5 mm). The tubes were placed upright in glass vials and were filled with the monomer mixture. After sonication for an additional 5 min, the vials were sealed with screw caps and heated in an oven at 65 "C for 3-10 h. Vinylferrocene ring-modified composite materials were prepared by first electrocopolymerizing vinylferrocene and DVB to form films of the copolymer on individual fibers. This process was accomplished by maintaining a nominal potential of -2.5 V versus a Ag/Ag+ (0.01 M) reference electrode for 30 min with carbon fiber bundles used as working electrodes in dry DMF solution that contained 10 mM vinylferrocene, 2 mM DVB, and 0.1 M tetrabutylammonium perchlorate (TBAP) (I 7). Alternatively, 64% dimethylacetamide (DMAC) in aqueous 0.1 M sulfuric acid was used as the solvent. Here, the minimum amount of DMAC was used to keep the solution clear, indicating dissolution of monomers. This approach minimized the solubility of oligomers and polymers produced at the surface of the electrode and allowed growth of thicker films. After the electropolymerization process, the fibers were rinsed thoroughly with dry DMF, spread out, and hung to dry in an oven at 40 "C for 1h. These modified fibers were placed in open-ended glass tubes that were filled with a solution of 70-78% styrene, 28-20% DVB, and 1-2% AIBN (weight percent) and sonicated for 5 min to disperse the fibers. After sonication, the tubes were placed in an oven and heated at 65 "C for 2-5 h. The composite cylinders were sealed into glass tubes with epoxy and prepared for use as electrodes by first grinding with successively smaller grit (320,400, and 600 grit) silicon carbide paper (3M Company). Polishing was performed with 6-pm and 1-pm diamond paste followed by 0.05-pm y-alumina (all from Buehler). The electrodes were rinsed thoroughly with acetone and water after each successive polishing step. Glassy carbon electrodes were polished according to the same procedure. Instrumentation. Scanning electron microscopy (SEM) and energy dispersive X-ray analysis were performed by using an Amray-1000 SEM instrument with an EDAX-9100 attachment. Fourier transform infrared (FTIR) spectra were obtained with a Mattson Cygnus 100 FTIR spectrometer. All electrochemical experiments were performed with a BAS-100 electrochemical analyzer. Electroanalytical experiments were carried out in aqueous 0.1 M KC1 using a Ag/AgCl reference electrode unless noted otherwise. RESULTS AND DISCUSSION Preparation and Characterization of Composite Materials. Composites as Materials. The composite cylinders formed after polymerization of the matrix were hard and appeared dark and glasslike. In the case of ring-modified electrodes, the carbon fibers, normally quite flexible, became very rigid upon formation of the cross-linked poly(viny1ferrocene) film via electrocopolymerization. In order to estimate the thickness of the polymer films, electropolymerization was carried out using bundles of fibers as working electrodes under conditions similar to those described in the Experimental Section. The fibers were then dried in a vacuum oven at 40 "C for 15 h. The weight gained by the fibers was consistent with coatings in the range of 0.034.7 pm thick; the thicker coatings were obtained by using
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Flgwe 3. Scanning electron micrographs of polished matrix-modified composne electrode: (a) after 1 min of sonication, magnified 1000 times: (b) after 15 min 01 sonication. magnified 1100 times. The polishing procedure is described in text; bars represent 10 pm. Figure 2. Scanning electron micrographs of cross section of vinyl-
ferrocene-modified ComposRes. (a) Matrix-modified carbon fiber Ccmposne electrode magnified 480 times. Bar represents 20 pn. (b) Ringmodified carbon fiber composne electrode magnified 2600 times. Bar represents 2 Fm. the mixed solvent system (dimethylacetamide/su!furic acid). Evidence that the fihremained intact upon incorporation into the cross-linked polystyrene composite is given below. The electrodes were evaluated as materials by using scanning electron microscopy. Bulk properties, i.e. adherence of the cross-linked polystyrene matrix to coated and uncoated fibers, and properties of the electrode surface after cleavage, polishing, and ultrasonication were of interest. Figure 2 shows scanning electron micrographs of cross sections of the matrix- and ring-modified vinylferrocene composite materials. The samples were prepared by placing the composite cylinder in liquid nitrogen for 30 8 and then breaking the material in two. The fractured surface of the matrix-modified electrode shown in Figure 2a shows that fibers protruding from the surface were oriented in a similar direction with respect to the fractured surface, and the fibers themselves were not evenly dispersed throughout the composite. Energy dispersive X-ray analysis (EDX) showed that iron from the ferrocene moieties was located throughout the polymer matrix, as expected. The cross section of the vinylferroeene ring-modified fiber compasite is shown in Figure 2h. This composite material was very similar to the matrix-modified electrode: the fibers were unevenly distributed and had a nearly uniform orientation with respect to the surface of the material. Energy dispersive X-ray analysis showed that roughly 20 times more iron was located on the poly(viny!ferrocene) coating on the fibers than on ends of the carbon fibers: iron was not detected within the
cross-linked polystyrene matrix of this composite. The sides of the poly(vinylferrocene)-coa~ring-modified carbon fibers appeared much smoother in the SEM images than did those of uncoated fibers from the same batch (IO,11). These data suggest that the electropolymerized vinylferroeene coating was indeed cross-linked by copolymerization with DVB and remained intact, rather than dissolving in styrene and divinylbenzene used to form the surrounding matrix. There was a marked difference between the degrees of fiber pull-out for the two materials. There appeared to be a strong bond between the uncoated fibers and cross-linked polystyrene that allowed fihen to pull out of the matrix only very slightly upon breakage of the composite rod. However, fibers coated with poly(vinylferrocene)pulled out much further and showed poorer binding between the polyfvinylferrocene)film and the surrounding cross-linked polystyrene matrix. The poor bonding led to improved mechanical strength since the fibers could slip within the matrix, hut occasional fissures appeared as well (revealed upon polishing as discussed below). Electrode Polishing. The procedure used to polish electrodes (described in the Experimental Section) left large amounts of alumina on the surface of the matrix-modified electrodes as shown hy scanning electron microscopy (Figure 3a) and EDX. The surfaces of the carbon fibers were not directly visible anywhere on the surface of the composite, probably h e c a w they were obacured by alumina and diamond particles and polymeric debris that adhered to the ends of the carbon fibers and the polymer matrix surrounding them. Ultrasonication for 15 min removed the debris and revealed the ends of the carbon fibers (Figwe 3h). The fibers protruded from the surface of the electrode, thereby increasing the active surface area of the electrode. Close inspection of the micrograph shows that even after sonication, some particles were
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I EILQTI Figure 5. Cyclic voltamqram of 5 mM hexamminerulhenium(II1) chloride haquears 0.1 M KCI electrolyte soMlon on t incarbar fiber composite ekctrode containing 3000 fibersin a geometric area of 0.0707 om2. Scan rate was 50 mVh.
EIUOLTI Figure 6. Cyclic voltammograms of vlnylferrocen~lliedc a b n Rber compwne electrodes (0.0314-cm2 geometric area) In bknk electrolyte (0.1 M KCI) solution at scan rates of 100 mVIs: (a) matrix-modified electrode, 3000 fibers: (b) rlng-modlfied electrode. 6000 fibers.
Figure 4. Scanning electron micrographs of polished ring-modified carbon fiber composite electrode: (a) after 1 min of sonication, magnified 1000 times; (b) after 15 min of sonication, magnified 1040 times; (c) same as b, different location on surface. Bars represent 10 fim.
still imbedded within the electrode's surface. The polished surface of a poly(vinylfemne) ring-modified electrode is shown in Figure 4a. EDX analysis again showed a large signal for aluminum, a result of polishing with alumina particles. The particles themselves are also visible. EDX analysis also showed that iron was distributed evenly across the surface as a result of polishing (recall that iron was associated only with the fibers when a cross section of the electrode was examined). Although sonication for 15min cleaned the surface of the electrode considerably, there were still many alumina and diamond particles imbedded in the surface of the electrode (Figure 4h). As discussed above, the poly(viny1ferrocene)coated fibers did not bind strongly to the composite matrix; this led to formation of rare fissures such a~ the one shown in the polished electrode in Figure 4c. Electrochemical Behavior of Carbon Fiber Composite Electrodes. Unmodified Composite Electrodes. Unmodified
carbon fiber composite electrodes were prepared to evaluate synthetic procedures and electrochemical performance of fihrous composite electrodes. Figure 5 shows a cyclic voltammogram for an aqueous solution containing 5 mM hexammineruthenium(II1) chloride and 0.1 M KN03 on an unmodified m h o n fiber composite electrode. This electrode had a diameter of 3 mm and contained 3000 fibers, which is 42000 fihers/cm2. The shape of the voltammogram suggests that both time-dependent planar diffusion and steady-state radial diffusion were important components of mass transport to the random array of microelectrodes. The voltammogram's shape is similar to that expected at a single microelectrode. However, the voltammogram was obtained with conventional instrumentation since the current was the sum of responses for 3000 carbon fibers. Poly(uiny1ferrocene) Composite Electrodes. Previous work on modified particulate carbon composite electrodes showed that vinylferrocene could be incorporated into a composite material containing carbon black and that ita properties were similar to thhse of poly(vinylferr0cene)fh on solid electrodes (13). Figure 6 shows cyclic voltammograms for (a) a matrix-modified poly(viny1ferrocene) composite (3% vinylferrocene, 78% styrene, 18% DVB, 1%AIBN) and (h) a ring-modified poly(viny1ferrocene) composite in blank electrolyte solution. The peak current densities were 0.7and 0.6 mA/cm2, respectively (geometric surface areas of all fibers were added to calculate current density).
ANALYTICAL CHEMISTRY, VOL. 61, NO. 13, JULY 1, 1989
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Square wave voltammograms of (a) poly(viny1ferrocene) ring-m6dified carbon fiber composite (same electrode as in Figure 6b) in acetate buffer solution, pH 3.0, and (b) same solution as a with 2 mM ascorbic acid added. Conditions: composite electrode (- - -) and glassy carbon electrode with geometric surface area of 0.0855 cm2 (-); square wave amplitude, 25 mV; frequency, 15 Hz; step potential, Flgure 7.
4 mV.
Peak current density can probably be increased dramatically by improving the conditions under which the polymer film is formed. For example, a peak current density of 6.1 mA/cm2 was obtained for ferrocene moieties at 50 mV/s for a singlefiber ring-modified electrode (16) prepared as follows. The fiber was held at -1.5 V vs SCE for 16 h in a solution containing 41 mM vinylferrocene, 11 mM DVB in 74% DMAC in 2% (v/v) sulfuric acid before fabrication of the single-fiber electrode. The ring-modified electrodes allow higher concentrations of ferrocene centers a t the surface of the electrode than do matrix-modified electrodes because incorporation of too much vinylferrocene into the matrix yields a crumbly polymer. Composite electrodes made without vinylferrocene showed no evidence of faradaic current in the range of potentials attributed to ferrocene moieties in modified electrodes. A Fourier transform infrared (FTIR) spectrum of a KBr pellet containing pulverized fibers coated with vinylferrocene copolymer showed peaks at 995,815, and 1080 cm-', which have all been attributed to poly(vinylferrocene);the latter two peaks have been assigned to the cyclopentadienyl rings in the ferrocene moieties (18). No extraneous peaks that would have to be attributed to breakdown products of ferrocene were observed. Electrode surfaces prepared by freezing the matrix- and ring-modified composite rods and then cleaving them showed electrochemical characteristics qualitatively similar to those of surfaces that were polished. However, peak currents were 2.2 and 3.7 times larger, respectively, which probably can be attributed to cleaner surfaces presented to electrolyte solution and the resulting increase in active electrode area. The electrochemical behavior of these materials as modified electrodes for catalytic applications was investigated by using
W EIWLTI
Cyclic vobmmograms of 0.3mM ferricyanide. The currents increase over time on vinylpyridine-modified carbon fiber composite electrodes: (a) 0 and 1 h at pH 3.0; (b) 0 and 1 h at pH 2.0; (c) 0, 1, and 2.5 h at pH 1.0. Scan rate was 250 mV/s. Flgure 8.
the the ferrocene moiety for oxidation of ascorbic acid (19, 20). Figure 7 shows square wave voltammograms for (a) a ring-modified poly(viny1ferrocene) fiber composite electrode in blank electrolyte solution (pH 3.0) and (b) the oxidation of ascorbic acid on a glassy carbon electrode and on a ringmodified composite electrode at pH 3.0. A summary of peak potentials and peak currents appears in Table I. The peak current density a t a ring-modified poly(viny1ferrocene) composite electrode increased by a factor of 21 when 2 mM ascorbic acid was added to the pH 3.0 buffer solution. The peak potential was about 170 mV less positive in the presence of electrode-bound ferrocene, relative to an unmodified glassy carbon electrode. The improved efficiency of mass transport to the carbon fibers was largely responsible for the 32-fold increase in current density, relative to that for glassy carbon. Poly(uiny1pyridine) Composite Electrodes. Matrix-modified composite electrodes were made with fiber densities of 83000 fibers/cm2 in a polymer matrix containing 40% vinylpyridine, 39% styrene, 19% DVB, and 2% AIBN. These electrodes yielded clean background signals and good electrode responses for methyl viologen, hexammineruthenium(III), and ferricyanide in solutions buffered at pH 7. However, at more acidic pH values, the pyridine moieties within the polymeric matrix caused the polymer to swell via protonation and changed the electrode response toward ferricyanide, as reported for particulate carbon composite electrodes containing copoly(viny1pyridine) (14). A series of voltammograms was recorded that illustrates the responses of a vinylpyridine copolymer electrode at different pH values as a function of time. The responses of this electrode for the reduction of 0.3 mM hexacyanoferrate(II1) with pH buffered at values of 3.0, 2.0, and 1.0 are shown in
Anal. Chem. 1989, 6 1 , 1465-1466
LITERATURE C I T E D
Table I. Sauare Wave Voltammetric Data for Oxidation of Ascorbic Acid
Anderson, J. E.; Tallman, D. E.; Chesney, D. J.; Anderson, J. L. Anal. Chem. 1978. 50, 1051-1058. Weisshaar, D. E.; Tallman, D. E. Anal. Chem. 1983, 55, 1146-1151. Dayton, M. A.; Brown, J. C.; Stutts, K. J.; Wlghtman, R. M. Anal. Chem. 1980, 52, 946-950. Ponchon, J. L.; Cespuglio, R.; Gonon, F.; Jouvet, M.; Pujol, J. F. Anal. Chem. 1979, 57,1483-1486. Wightman, R. M. Anal. Chem. 1981, 53, 1125A-1134A. Edmonds, T. E.; Guoliang, J. Anal. Chim. Acta 1983, 757,99-108. Lipka, S.M.; Cahen, G. L., Jr.; Stoner, G. E.; Scribner, L. L., Jr.; Gileadi, E. J . Electrochem. SOC.1988, 135, 368-372. Caudill, W. L.: Howell, J. 0.;Wightman, R . M. Anal. Chem. 1982, 54, 2532-2535. Subramanian, R. V.; Crasto, A. S. Polym. Compos. 1986, 7 , 20 1-218. Bell, J. P.; Chang, J.; Rhee, H. W.; Joseph, R. Polym. Compos. 1987, 8 , 46-52. Chang, J.; Bell, J. P.; Shkolnik, S. J . Appl. Polym. Sci. 1987, 3 4 , 2105-2124. Shaw, 6.R.; Creasy, K. E. J . Electroanal. Chem. Interfacial Electrochem. 1988, 243,209-217. Shaw, 8. R.; Creasy, K. E. Anal. Chem. 1988, 60, 1241-1244. Park, J.: Shaw, 6.R. Anal. Chem. 1989, 67, 848-852. Wang, J.; Golden, T.; Varughese, K.; El-Rayes, I. Anal. Chem. 1989, 61, 508-512. Creasy, K. E.; Wang, C. L.; Shaw, 6.R. Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Atlanta, GA, March 6-10,1989. Shaw, 6.R.; Haight, G. P., Jr.; Faulkner, L. R . J . Nectroanal. Chem. Interfacial Electrochem. 1982, 140,147-153. Aso, C.; Kuhitake. T.; Nakashima, T. Makromol. Chem. 1989, 724, 232-240. Petersson, M. Anal. Chim. Acta. 1986, 787, 333-338. Cox, B. G.; Jedral, W.; Palou, J. J . Chem. Soc., Da/ton Trans. 1988, 733-740.
peak peak current potential, density, mV mA/cm2
conditionsn glassy carbon electrode; 2 mM ascorbic acid ring-modified poly(viny1ferrocene) composite electrode; blank electrolyte, pH 3.0 ring-modified poly(viny1ferrocene) composite electrode; 2 mM ascorbic acid, pH 3.0
529
0.2b
391
0.3”
362
6.4c
Other conditions are as in Figure 7. Current density was calculated by using geometric surface area. CCurrentdensity was calculated by using the combined surface areas of all fibers. Figure 8. Both charging and faradaic currents increased over the 1-2.5-h time periods shown. The changes over time were more dramatic a t lower pH’s because as the hydronium ion activity increased, swelling of the pyridine-containing electrode surface became more extensive and occurred more rapidly. The higher charging currents indicate that increased active surface area was created as time passed. Since the faradaic current rose much more rapidly than the charging current, it is evident that the polymer, positively charged due to pyridine protonation, concentrated the highly charged ferricyanide ions. ACKNOWLEDGMENT We thank Jongman Park for advice on vinylpyridine copolymer matrices, Chia Lin Wang for data on the single-fiber ring-modified electrode, Andrew Garton for assistance with FTIR spectroscopy, and James P. Bell, Angel Wimolkiatasak, and Jemei Chang, Department of Chemical Engineering and Institute of Materials Science, for useful discussions related to electropolymerized interlayers in composites. Expertise in scanning electron microscopy offered by Carol Blouin, Institute of Materials Science, is acknowledged gratefully.
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*
To whom correspondence should be addressed.
Kenneth E. Creasy B r e n d a R. S h a w * Department of Chemistry U-60 University of Connecticut 215 Glenbrook Road Storrs, Connecticut 06269-3060 RECEIVED for review July 5, 1988. Revised March 24, 1989. Accepted March 27,1989. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, to the Research Corporation, and to support by the National Science Foundation under Grant NO. CHE-8707973.
A Statistical Justification Relating Interlaboratory Coefficients of Variation with Concentration Levels Sir: One of the most intriguing empirical relationships in modem analytical chemistry was published by Horwitz in 1980 (1, 2); see for example Figure 1 of ref 2. The graph results from an examination of over 50 interlaboratory collaborative studies conducted by the Association of Official Analytical Chemists on various commodities for numerous analytes over the last 100 years. Individual methods are tested by a t least half a dozen laboratories on a series of blind samples. The results are analyzed for bias and interlaboratory variability. The graph relates the interlaboratory coefficients of variation (CV) found during proficiency testing with the concentration levels at which those particular analyses need to be carried out. The smooth relationship accomplishes this with no respect for the quite different methodologies and instrumentation used for the various analyses. We have taken the liberty of labeling the graph as the “Horwitz Trumpet”. The trumpet has profound implications for the level of detection and the precision that can be ex-
pected in setting legal controls in health-related legislation. The statistical techniques were developed to detect significant deviations from predetermined quality requirements and to provide a warning when this was no longer being fulfilled. The classical expectation of quality assurance is the production of identical interchangeable articles. However when an analytical laboratory produces results on a foodstuff, the results are not a series of identical measurements. The foodstuff varies in composition and there is no predetermined, absolute reference point from which to measure. Frequently a consensus value is established by adding a constituent and then recovering it. This somewhat artificial process is the closest that is obtained to a reference. We now present a very simple theory that accounts very well for the experimental observations. Let us postulate the following origin of the “trumpet curve”. Suppose each laboratory result were the summation of many simple yes/no binomial components, each estimating the
0003-2700/89/036 1-1465$01.50/0 0 1989 American Chemical Society
