Anal. Chem. 1982, 5 4 , 2618-2620
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Defermination of Diffuslon Coefficients by Flow Injection Analysis Greg Gerhardt and Ralph N. Adams" Department of Chemlstty, Universlty of Kansas, Lawrence, Kansas 66045
The accurate determination of diffusion coefficients for small- and medium-sized organic molecules in realistic media of interest to chemists is not a trivial experimental problem. The classical approaches using open capillary or boundary diffusion cells with radiotracer or fluorescent detection have been applied to only a few organic species (1-3). Chronoamperometric and other voltammetric methods are excellent for many inorganic ions, but interpretation of the results with organic compounds is plagued by adsorption and other uncertainties in the response of electrode surfaces (2,4). Recently it has become possible to measure diffusion coefficients of ions and relatively small organic species in brain extracellular fluid. It is important to have reliable solution diffusion coefficients of these species to serve as benchmarks against which to assess the influence of the complex brain milieu. T o get such data we turned to modern flow injection analysis (FIA) which involves diffusion-convection-controlled dispersion of samples in a flowing stream (5-7). Inherent in the dispersion equations is the ability to determine experimental coefficients as pointed out by Vanderslice et al. (6). Here we report a simple and versatile FIA procedure which is capable of high precision and accuracy in determining diffusion coefficients for a variety of systems of chemical and neurobiological interest.
PRINCIPLES The procedure involves the base line to base line peak dispersion equation of Vanderslice et al. (6) (eq 1). L is the
distance between the injection port and the detector in centimeters, q is the flow rate in milliliters per minute, D is the diffusion coefficient, f is a concentration and detector sensitivity factor, and At, is the peak width in seconds. Experimentally one can keep a, L, f , and q = constant and eq 1 reduces to
x is a calibration factor which contains all of the parameters of the flow system. One can determine a series of calibration factors for preset flow rates by using standards for which the D value in a given medium is well characterized. Once the calibration factors are determined, an unknown D value can be calculated by eq 3. At,' = peak width of unknown. The D, =
(-&)""
(3)
validity of eq 3 requires that all flow system parameters used for the standards be duplicated for the unknowns, as reemphasized later.
EXPERIMENTAL SECTION Instrumentation. A basic block diagram of the FIA system is seen in Figure 1. Our apparatus was composed of a commercial FIA system (Bifok FIA-05), which consists of a peristaltic pump, autoinjector, and flow module system. A Beckman Model DB UV/vis spectrophotometerfitted with an 8-pL flow cell (Precision Cell, Inc., Model 8820) was used as the detector. A fixed-wavelength (254 nm) LC detector was also used in place of the spectrophotometer for some of the measurements. , A strip chart recorder (Fisher Recordall, series 5000) was used to record all of the peak dispersion data. The detector signal output-to-recorder 0003-2700/82/0354-2618$01.25/0
interface consisted of a simple voltage divider for easy modification of the recorder sensitivity. The system flow path consisted of 0.5 or 1.0 mm diameter coiled (5-10 cm diameter coils) sections of Teflon or polyethylene tubing. Flow path lengths ranged from 300 to 500 cm. Reagents. All flow solutions were prepared by using double-distilled water and ACS grade chemicals. The standard and unknown solutions were prepared by dissolving quantities of the commercially obtained compounds in the flow stream solutions. The concentrations of the unknown solutions were chosen to match those of the calibration standards. All flow solutions were deoxygenated prior to preparation of the standards and unknowns to decrease air oxidation of the solutions. Procedure. Inherent in this method is the necessity for measuring the diffusion coefficients (D values) of one or more internal standards under identical experimental conditions used for the unknown. The internal standards chosen for this were 1-5 mM solutions of potassium ferrocyanide and potassium ferricyanide in 1 or 2 M potassium chloride. The D values of ferrocyanide and ferricyanide ions in these media were originally determined by von Stackelberg et al. (8)and have been repeatedly verified over a 30-year period by many workers ( 4 , 9, IO). Potassium chloride solution was continuowly pumped through the system and the detector was turned on at least 1 h before actual measurements were made. Flow rates were varied by adjusting pump speed and ranged from 0.40 to 1.25 mL/min. All sample volumes injected were 40 pL. The sensitivities of the recorder and detector were adjusted to produce peak heights of ca. 6 in. Peak widths (At,) were measured for the standard solutions as a function of preset flow rates. Calibration factors were then calculated based on the literature D value (von Stackelberg) and the measured peak widths. In practice, both ferro- and ferricyanide were used to obtain an average calibration factor for a preset flow rate. Experimentally, these two factors were either identical or very close in value. With the calibration factor determinations complete, the flow solution was changed to the medium of interest. Two experimental conditions must now be met: (1) the flow rates used for the standards are duplicated for the unknown system; (2) the detector and recorder sensitivities must be adjusted so as to produce recorded peak heights which are within 5% of those recorded with the standards. This matches the elusive concentration and detector sensitivity factor, f , of eq l. The unknown D value can then be calculated from the recorded peak widths and corresponding calibration factors according to eq 3. All data reported are the mean of repeated determinations together with the standard deviation of the results.
RESULTS AND DISCUSSION The validity of the proposed method was initially explored by cross-checking the data for ferro- and ferricyanide ions. Solutions of both were used to obtain calibration factors. Then the calibration factor for ferricyanide ion was used to calculate an experimental D value for ferrocyanide and vice versa. The results of these measurements are shown in Table I. The experimental D values for ferro- and ferricyanide ions in 1and 2 M KC1 are those determined by the FIA procedure. It is clear that they are in excellent agreement with the widely accepted von Stackelberg data. This attests to the reliability of the present procedure, provided the precautions mentioned above are strictly used, The ferricyanide ion values in sodium hydroxide also show good agreement, but we were unable to do a large number of these measurements since sodium hydroxide corroded the flow system tubing. To illustrate that the FIA method is applicable to a fairly wide range of D values, we measured Tl(1)in 1 M KC1 (after 0 1982 American Chemlcal Society
ANALYTICAL CHEMISTRY, VOL. 54, NO. 14, DECEMBER 1982
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Figure 1. Basic block diagram of the FIA system used for diffusion coefficient measurements.
Table I. Comparison of Literature and Experimental Diffusion Coefficients no. of Dlit;, Dexptl, deter10 105 compounda medium cmZ/s c"/s minations 14 0.76,b 0.74, i 0.023 K,Fe(CN), 1M KCl 14 0.63,b 0.64, f 0.022 K,Fe(CN), 1 M KCl 14 K,Fe(CN), 2 M KC1 0.75,b 0.76, i 0.025 20 0.62,b 0.61, i 0.025 K,Fe(CN), 2 M KCl 3e K,Fe(CN), 1 M NaOH 0.45,c 0.47, f 0.025 TlNO, 1M KC1 1.55d 1.49 f 0.09 10 a Temperature = 25 i 1 "C; concentrations of K,Fe(CN),, Reference 8. K,Fe(CN),, and TlNO, were ca. 1-5 mM. Reference 9. References 8 and 10. e Problems with NaOH, see text.
the usual standardization vs. ferri- and ferrocyanide). Thallous was chosen since its diffusional rate is ca. 2.5 times faster than ferri- or ferrocyanide and there are reliable electrochemical values for it (8, IO). The mean value of (1.49 f 0.09) X cm2/s determined by FIA, is within 4% of the literature data. These Tl(1) determinations were made after the apparatus had been unused for about 1month. It was pumped with KCl for several hours and t h w the standardizations and Tl(1) determination were run. This is mentioned just to illustrate the apparent reliability of the technique to intermittent determinations-realizingy of course, that each use does involve the restandardization. The latter process is no more timeconsuming than the usual blank determinations in analytical practice. Our major interest was in determining reliable D values for a variety of biogenic amine neurotransmitters, their metabolites, and related substances of neurochemical interest. These were all measured in 0.1 hl phosphate buffer, pH 7.4, and are tabulated in Table 11. To the best of our knowledge, there are no experimental D values in the literature for the neurotransmitter-related substances. However, compounds 1 and 16, dopamine and its anabogue 4-methylcatechol, have been measured by chronoamperometry-their electrochemical D value in the same mediurn is -0.60 X cm2/s, in good agreement with the present results. There are only small differences in the D values of the amine neurotransmitters, dopamine, norepinephrine, epinephrine, 5-hydroxytryptamine, and their various metabolites (1-9, Table 11). Ascorbic acid (compound lo), a species present in high concentration in mammalian brain, shows a solution diffusion rate in this same range. The putative transmitter leu-enkephalin (compound ll), a pentapeptide has, (as could be expected, a somewhat slower diffusional rate. Tlhe related drugs phencyclidine and ketamine (13and 14) show interesting differences in D values which, from the precision of the determinations, can be assumed to be quite real. A11 the values of Table I1 can be corrected to physiological temperature of 37 OC by applying the standard correction of + 2 % / O C (11). It is interesting to compare the D value for 1-naphthalenesulfonic acid (15) of 0.66, f 0.016 to a recently rleported value of 0.76 f 0.12 which was determined in agar gel, p H 7.4 a t 37 OC: (12). Agar gels normally decrease solution diffusion coefficients by ca. 10%
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Table 11. Diffusion Coefficients of Biogenic Amine Neurotransmitter-Related Compounds' no. of deterD X lo5, minano. compound cmz/ls tions 1 DA (dopamine) 0.60, f 0.025 1 9 2 DOPAC (dihydroxy0.59, i: 0.017 11 phenylacetic acid) 3 HVA(homovanil1ic 0.59, i 0.033 7 acid) 4 NE (norepinephrine) 0.55, f 0.026 7 5 DOPEG (dihydroxy0.58, f 0.027 8 phenylethyleneglycol) 6 VMA (vanillomandelic 0.59, * 0.040 7 acid) 7 E (epinephrine) 0.51, i 0.028 8 8 5-HT (5-hydroxy0.54, i 0.021 16 tryptamine) 9 5-HIAA (5-hydroxy0.55, f 0.031 1 5 indoleacetic acid) 1 0 AA (ascorbic acid) 0.53, i 0.026 14 11 leucine enkephalin 0.41, i 0.014 6 12 &hetamine 0.61, * 0.012 8 13 PCP (phencyclidine) 0.47,f 0.027 9 14 ketamine 0.56, i 0.026 9 15 1-naphthalenesulfonic 0.66, i. 0.016 9 acid 16 4-methylcatechol 0.65, f 0.028 9 ' Temperature = 25 f 1'C, all in 0.1 M, pH 7.4 phosPCP was supplied by the National phate buffer. Institute on Drug Abuse, Research Triangle Institute, NC.
(13). If one increases the FIA value to its 37 O C counterpart and allows for the difference between agar and pure solution, the results are in very good agreement. As in most FIA systems, we coil the flow path to decrease the space required for the large lengths of tubing. It was noted that there was a change in the measured peak widths as the degree of coiling of the tube was varied. This has been observed by other laboratories (6, 14) and is attributed to enhanced secondary flow resulting from the coiled tubing (7). This observed effect on the peak widths does not seem to alter the validity of our procedure. The use of 5-15 cm diameter coiled sections and also straight sections of tubing gave similar diffusion coefficients using the standardization procedures. Unlike other diffusion coefficient methods, the present procedure does not suffer from limitations imposed by a specific type of detector. Visible or UV detection was used herein but other detectors such as refractive index, fluorescence or electrochemical can easily be used in the present analysis scheme. Reproducible diffusion coefficients can be measured in as little as an hour once the flow system is calibrated. This is in marked contrast to capillary diffusion methods which require several days for the measurements. The reproducibility is easily seen from the n values and the standard deviations of the measured diffusion coefficients. Compounds such as dopamine, which were redetermined independently over periods of several weeks, still have small standard deviations. LITERATURE CITED (1) Miller, T. A.; Lamb, 8.; Prater, K.; Lee, J. K.; Adams, R . N. Anal. Chem. 1954, 36, 418-420. (2) Miller, T. A.; Prater, B.;Lee, J. K.;Adams, R. N. J. A m . Chem. SOC. 1965, 87, 121-122. (3) Bacon, J.; Adams, R. N. Anal. Chem. 1970, 4 2 , 524-525. (4) Adams, R. N. "Electrochemistry at Solld Electrodes"; Marcel Dekker: New York, 1969; pp 214-231. (5) RDZiEka, J.; Hansen, E. H. "Flow Injection Analysls"; Why: New York, 1981; pp 6-50. (6) Vanderslice, J. F.; Stewart, K. K.; Rosenfeld, A. G.; Higgs, D. J. Talanta 1981, 2 8 , 11-16. ( 7 ) TlJssen,R. Anal. Chim. Acta 1980, 114, 71-89.
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von Stackelberg, M.; Pilgram, M.; Toome, V. Z . Elektrochem. 1953, 57, 342-350. Elsenberg, M.; Tobias, C. W.; Wllke, C. R. J. Elecfrochem. SOC. 1954, 101, 306-320. Levich, V. G. ”Physicochemical Hydrodynamlcs”; Prentice-Hall: Engla wood Cllffs, NJ, 1962; p 326. Meltes. L. “Polarographic Techniques”, 2nd ed.; Interscience: New York, 1965; p 140. Nicholson, C.; Phllllps, J. M. J. Physiol. 1981, 311, 225-257. Laitinen, H. A.; Kolthoff, I. M. J. Am. Chem. SOC. 1939, 6 1 , 3344-3449,
(14) Palnton, C. C.; Mottola, H. A. Anal. Chem. 1981, 53, 1713-1715.
RECEIVED for review June 23,1982. Accepted August 18,1982. The support of this work by NSF (Neurobiology Section) via Grant BNS 7914226 and NIH via Grant NS 16364 is gratefully acknowledged. G.G. also received partial support from an Analytical Division Fellowship from the American Chemical Society.
Determination of Temperature Rise Time and Temperature Profiles for Three Commercial Pyrolyzer Sample Holders John J. R. Mertens‘ VUB-Cyclotron, Vrije Unlversiteit Brussel, Plelnlaan 2, 1050 Brussels, Eelgium
Eddy Jacobs, Andr6 J. A. Callaerts, and A. Buekens Dlenst Industriele Scheikunde, Vrue Unlverslteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium
The importance of various physical parameters in pyrolysis gas chromatography (Py GC) has been mentioned by several authors (1-5) but has only been investigated by a few who developed a pyrolysis system (6-9). Wells et al. (10) report the heating profile curves obtained for a CDS Pyroprobe ribbon pyrolyzer (Chemical Data Systems, Inc., Oxford, PA). This paper describes a simple method of determining the temperature rise time (TRT) and the temperature profile of the three types of sample holders of this commercially available CDS Pyroprobe pyrolyzer, both in the presence and absence of sample (polystyrene). The Pyroprobe system is provided with electronic feedback control of the preset temperaturs which corrects for all heat effects, e.g., the heat consumed by endothermic thermal degradation processes. In this setup it is no longer possible to measure a “true pyrolysis temperature” neither by means of a thermocouple, as described by Levy et al. (6), nor by monitoring the T R T on that place of the filament where the sample has been applied, as described by Wolf at al. (7). The pyrolysis time and temperature thus are to be measured indirectly.
EXPERIMENTAL SECTION The temperature of the heated sample holder is measured by means of a phototransistor provided with a focusing lens mounted on a movable set. The sensor-head is directed perpendicular to the axis of the coil (or strip). The correct position of the phototransistor along this axis can be adjusted with a micrometer probe incorporated in the setup. The coil (or strip) is inserted intoa Pyrex-glasstube with the same dimensions as the pyroprobe interface chamber. Both the tube and the nitrogen gas flowing through the tube are heated at 200 OC to simulate the temperature contribution due to heat flux from the filament toward the wall of the interface chamber. The intensity of the wire radiation is measured as a voltage over a 1 kn resistance in series with the phototransistor and recorded on a high impedance input X.B. recorder (Kipp & Zonen-BD11) or a storage oscilloscope (Tektronix). The part of the coil taken into account by the phototransistor is one winding, so that small displacementa to the left or the right result in a clear drop in output voltage. For both the ribbon and coil, the manufacturer provides a correction factor tabulated as a function of the preset temperature. The sensitivity of the phototransistor is given as a plot of the output voltage vs. the equilibrium temperature (Figure la). The calibration curve originaly used was a straight line fitted on the
logarithim of the voltage as a function of the preset temperature in the region 420-800 OC. At higher temperatures a slight deviation from linearity is observed, probably due to the change of the light frequencies in the emitted spectrum and/or saturation of the phototransistor at higher intensities. A lower temperatures (
