(14) (15) (16) (17) (18) (19)
L. Lakritz, E. D. Strange, D. G. Bailey, and R . L. Stedrnan, Beitr. Tabakforsch.,8, 120 (1972). D. Hoffmann and E. L. Wynder, Cancer, 27, 848 (1971). H. W. Underwood, Jr., and W. L. Walsh, “Organic Syntheses, Collected Volume 11”, Wiley, New York, N.Y., 1943, p 553. D. Hoffrnann. M. Dono. and S. S. Hecht. J . Nati. CancerInst.. 58. 1841 (1977). D. Hoffmann, G. Rathkamp, and S. Nesnow, Anal. Chem., 41, 1256 (1969). I. Schrneltz, J. Tosk, and D. Hoffrnann, Anal. Chem., 48, 645 (1976). J. R. Newsome and C. R. Keith, rob. Sci., 9 , 65 (1965). W. C. Owen ??d M. L. Reynolds, Tob. Sci., 11, 14 (1967). T. S.Osdene, Reaction Mechanisms in the Burning Cigarette”, in “The Recent Chemistry of Natural Products Including Tobacco”, N. J. Fina, Ed., Philip Morris, Inc., New York, N.Y., 1976, pp 41-59. E. L. Wynder and D. Hoffmnn, “Tobacco and Tobacco Smoke”, Academic Press, New York, N.Y., 1967.
(20) L. Weil and J. Maher, Arch. Biochem. Biophys., 29, 241 (1950). (21) W. R. Johnson. R. W. Hale, S. C. Clough, and P. H. men, Nature(London), 243, 223 (1973). (22) I.Schmeltz, A. dePaolis, and D. Hoffmann, Beitr. Tabakforsch., 8, 21 1 (1975). (23) A. H. Thornson “Naturaiiy Occurring Quinones”, Academic Press, London and New York, 1971, p 368.
RECEIVED for review July 7 , 1977. Accepted August 29, 1977. This research was supported by the National Cancer Institute, Contract SHP-74-106. It was presented at the 30th Tobacco Chemists’ Research Conference, Nashville, Tenn., October 1976. No. XXXV. of “Chemical Studies on Tobacco Smoke”.
Analytical Aspects of Immobilized Enzyme Columns Richard S. Schifreen,’ D. Alan Hanna,2 Larry D.
bower^,^
and Peter W. Carr*’
Deparfment of chemistry, University of Georgia, Athens, Georgia 30602
The fundamental principles of operation of an lmmoblllzed enzyme flow analyzer have been studied. I n partlcular, models have been developed to explain the dependence of peak height, area, and half-width on sample concentration (0.1 to 2000 mM), sample volume (40-2500 pL), system flow rate (0.3-4.5 mL/min) and column size (0.4-0.9 mL). The system employed in this study Is an improved high speed thermochemical analyzer based on the use of the enzyme urease which is immobilized on porous glass by covalent attachment. A sample throughput of over 60 per hour can be achieved In small (0.5 mL) columns packed with approximately 1000 units of enzyme when operated at a flow rate of 2 mL/mln. I n general, we find that the dependence of the peak height, area, and wldth upon sample volume, flow rate, and column conflguratlon are analogous to the behavior of a concentration sensitive chromatographic detector.
Analytical methods based on the use of enzymes as reagents have been gaining popularity over the past decade (1-3). This is due to the fact that the inherent selectivity of enzymes is such that direct determination of a single species in a complex mixture is often possible without prior separation. In principle, enzymatic methods are sufficiently specific so that inherently nonspecific detection systems including pH-stats ( 4 , 5 ) , conductometers (6, 7 ) and enthalpimeters (8, 9) may be used to measure sample concentration. Many analytical chemists have been reluctant to use enzymes because of their expense and instability, as well as the difficulties experienced in attaining adequate precision in kinetic assays. Despite these problems many excellent techniques are available for the measurement of reaction rates (10-15). A fundamental limitation of kinetic analyses is their sensitivity to all those variables which can alter the reaction rate. Enzymatic reactions are particularly prone to irreproducibility and error due to pH and temperature changes as well as changes in the concentration of inhibitors and activators from sample to Present address, D e p a r t m e n t of Chemistry, U n i v e r s i t y of Minnesota, M i n n e a olis, Minn. 55455. Present a d g e s s , C h e m i s t r y D e p a r t m e n t , U n i v e r s i t y of N o r t h Carolina, C h a e l Hill, N.C. P r e s e n t afdress, D e p a r t m e n t of C l i n i c a l Pathology, U n i v e r s i t y of Oregon H e a l t h Science Center, P o r t l a n d , Ore.
sample. True end-point or equilibrium assays are generally not nearly as sensitive to slight changes in reaction conditions and are not a t all subject to small changes in the level of activators or reversible inhibitors. An often overlooked advantage of an end-point assay is the fact that the reaction is more complete than in a comparable kinetic assay; therefore there is a larger signal change and a concomitant increase in analytical sensitivity. Unfortunately, assays with soluble enzymes are often not allowed to reach equilibrium because this would require either excessive time or extravagant amounts of expensive enzymes. As indicated in two recent reviews (16, 17),the analytical advantages of immobilized enzymes are such that these reagents can overcome many of the limitations of soluble enzymes. In particular, it is readily possible to prepare several hundred active units of enzyme immobilized in a small (1 mL) column, thereby permitting equilibrium assays and circumventing many of the limitations of kinetic assays with soluble enzymes. Immobilized enzymes have been used in flow-through reactors of several configurations including: fixed-bed (18) and open tubular reactors (19),as well as on electrodes (20) and reagent pads (21). Continuous flow enzyme reactors have been reported for use in clinical (22-25) and environmental (26, 27) analysis. Commercial immobilized enzyme analyzers for urea (28) and a variety of sugars including glucose, sucrose, and fructose (29) are presently available. As mentioned above, the combination of an enzymatic reaction and a general detector is particularly attractive. Along this line, several groups including Mosbach and his co-workers, and ourselves, have developed thermochemical immobilized enzyme analyzers. The “enzyme thermistor” has been applied to a variety of analyses including trypsin (30-32), glucose (32-34), lactose (33),uric acid (33), cholesterol (33),penicillin G (32),and urea (32-34). One example which indicates the improvements afforded by enzyme immobilization is evident in our adaptation of the thermochemical hexokinase catalyzed phosphorylation method for serum glucose developed by Jordan and McGlothlin (35) to a flow analyzer by immobilizing hexokinase on a porous glass carrier (9). The flow system easily accommodated 30 samples per hour and avoided problems associated with the long equilibration time (5 min) of batch calorimeters and drastically reduced the consumption of hexokinase. A similar system has been developed for the assay of urea using immobilized urease (8). ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
1929
Flgure 1. Schematic description of four types of reactors. (A) Plug flow reactor. (B) Continuously stirred reactor, instantaneous conversion of substrate. (C)Continuously stirred reactor, zero-order conversion of substrate. (D) Axially dispersed plug flow reactor
A major practical drawback of many of the thermochemical immobilized enzyme analyses reported to date has been the low sample throughput and large volume of sample required. For example, most of the systems require well in excess of 10 minutes for a thermal peak to rise from and return to the baseline. This is in part due to the low flow rates necessitated by the compressibility of conventional gel type enzyme supports such as agarose as well as to the slow thermal response characteristics of the flow calorimeter. We have attempted to eliminate these problems by using non-compressible porous glass supports and small, fast thermistors as heat sensors. The purpose of the present work was to investigate the various mass and heat transfer processes involved in an immobilized enzyme enthalpi.meter so that these factors could be adjusted to optimize system sensitivity, throughput, and sample volume. The immobilized urease reactor was chosen for this study because it had been previously adapted to this system (B), is simple and inexpensive to prepare, requires no additional reagents, and has a relatively long lifetime, Le., in excess of one month. As will be seen, the basic principles reported here are appiicable to other enzymes and varieties of detectors such as colorimeters and electrochemical transducers.
THEORY OF IMMOBILIZED ENZYME THERMOCHEMICAL REACTORS T h e purpose of this section is to present a unified model of the behavior of an enzyme reactor incorporating a thermochemical sensor. Any immobilized enzyme flow analyzer can be considered as consisting of three stages of operations: first, enzymatic conversion of the analyte (the enzyme's substrate) to product; second, dispersion of the substrate and product as the sample moves through the analyzer; and last, detection of the product. In this particular case the product is considered to be a "pulse" of heat generated by the enzymatic reaction. Although differential equations can be written which rigorously describe the simultaneous conversion of sample to product and the dispersion of the sample and product, they are extremely difficult to solve. In the following model we will assume from the outset that the sample species is instantly converted to product; in fact, in the applications developed by us, an extremely large quantity of active enzyme (several hundred units) has been immobilized in a small (0.5 mL) reactor. Finally, for the sake of simplicity, we will assume that the detector responds very rapidly to the measured variable; in our case to the temperature of the fluid. It is important to consider the properties of two idealized limiting reactors, namely, the perfect plug flow reactor and the ideal continuously stirred reactor. An ideal plug flow reactor is one which is operated such that there is no axial mixing of the reactant plug with the fluid in front or behind it. The sample flows through the column or packed bed with an infinitely sharp front and tail. It is easy to show that the 1930
ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
extent of conversion in such a reactor is identical with that which occurs in a pure batch reactor in a period of time equal to the residence time in the flow reactor. Since there is no mixing of fluid, there is no dilution to consider. If complete conversion to product occurs, then the product concentration a t the outlet is stoichiometrically proportional to the concentration of substrate (analyte) injected into the inlet. Similarly, if there is no heat loss from the reactor and there are no heat generating processes other than the chemical reaction of interest, one can show that a rectangular temperature pulse will occur at the exit of the reactor (see Figure 1A) after some delay time, equal to the residence time in the reactor. The pulse will disappear when the entire plug is swept through the column. Based on the principle of conservation of energy and the assumption of no heat losses one can show by integration of the area under Figure 1A that
where AT,, refers to the height of temperature pulse ("(3). It is denoted as the maximum since this type of reactor will generate the greatest possible signal because there is no dilution of the sample. In Equation 1,C,, AH, and Cp, are used to designate the sample concentration (mol/L) injected into the reactor, the reaction enthalpy (cal/mol) and the specific heat of the mobile phase fluid (cal/EC-L).We will assume that the specific heat of a sample is identical to that of the mobile phase fluid. This will be valid for all but very concentrated aqueous solutions. It is interesting to note that in this case the predicted temperature change is dependent only on concentration, and is therefore independent of the total uolume of the system. This is also the case in direct injection enthalpimetry (36) and is a result of the assumption of no mixing (dispersion) of matter or heat in the flow reactor. The other extreme limit of behavior is the perfectly well mixed reactor. In this type of reactor, it is assumed that any sample or fluid entering the reactor is instantaneously mixed with all of the fluid in the reactor. Physically this is equivalent to an exponential dilution flask. The anticipated temperature-time curve for this type of reactor is shown in Figure 1B. If one assumes no heat loss through the reactor walls, complete thermal homogeneity in the reactor, as well as instantaneous conversion to product, then the temperature pulse which appears at the exit can be obtained by a simple heat balance on the reactor:
A T ( t ) =A T o e x p -
g [:; ~
.
I]
where A T ( t ) is the instantaneous temperature difference from the baseline, AT0 is the initial value of the temperature peak c p the mean specific heat of the reactor and its contents
(cal/OC-L),V,, the total volume of the reactor (L), F the fluid flow rate through the reactor (L/s), and t is time from the moment of arrival of the sample in the reactor. The initial temperature rise AT” is given as: A T O =
AHCaVa CPVtOt
For this ideal case the behavior of thermal peaks on the column will be dictated by all those processes which can act to disperse heat. This will include: axial dispersion and eddy diffusion as well as slow thermal equilibration of the fluid with the column packing and the liquid trapped in its pores. In addition, it is evident that the reaction will not occur instantly and the sample species will not enter and move through the column as an inf-itely narrow spike. Additional factors which can act t o broaden the measured peak are sluggish heat transfer to the detector, slow response of the detector, and slow electronic response of the measuring and recording system. It is interesting to note that the thermal diffusivity of water is almost the logarithmic mean of the mass diffusivities in liquids and gases, e.g. the thermal diffusivity of water is about 0.0014 cm2/s, i.e. heat is transferred by diffusion in water almost 100 times as fast as is a small molecule. Longitudinal thermal spreading therefore, should be significantly greater than in liquid chromatography, but inter-phase resistance to heat transfer should be much lower than its liquid chromatographic analog. The most important result of the “Gaussian” or chromatographic model of the peak is the prediction that the peak height (AT*)will depend upon the sample volume (VJ, the magnitude of the spreading or mixing factors (N), and upon the size of the reactor and those factors which act to retain heat ( VR). The retention volume will be exactly equal to the interstitial volume, Le., the dead volume (V,) if the heat does not equilibrate at all with the enzyme support particles. Assuming perfect equilibration with the stationary phase, the retention volume for a heat peak can be shown via the plate model to be (38, 39):
(3)
where V,is the volume of sample initially added and all other terms are defined above. In this case it is evident that the magnitude of the temperature rise depends upon the sample volume in marked contrast ta the behavior of a pure plug flow reactor. It is also interesting to note that the width of the signal derived from a plug flow reactor corresponds to the time required to process a volume of fluid equal to the added sample volume (V,)whereas the well mixed reactor time response depends on flow rate and the volume (Vtot) of the reactor. The other major qualitative difference in behavior of these two extreme cases is that the maximum temperature pulse for a well mixed reactor appears a t the outlet immediately after addition of the sample; however, the plug flow reactor pulse does not occur until the sample has been moved through the column. These two limiting models are valuable in the following regards. First, with any real reactor one cannot generate a temperature pulse greater than that which would occur in a plug flow reactor (Equation l),thus this sets the upper limit of the analytical sensitivity. The considerations leading to this apply to any other type of detector. Second, no matter how poorly designed the actual reactor is, its time response cannot be worse than that of a well mixed reactor (Equation 2). Clearly any real reactor lies between the above limits. To a good first approximation, one can model a packed bed reactor in terms of “reaction” plates rather than “separation” plates. Precisely the same mathematics which apply to chromatographic columns can be applied here. This approach has previously been applied to the analysis of a heat of adsorption detector (37). Subject to the assumptions that the sample is instantly converted to product, that there is no heat loss due to poor adiabaticity, that the sample zone is thermally homogeneous in the radial direction, and that the usual assuinptions involved in considering the plate model of a column apply, one can show that the temperature peak at a detector located at the exit (see Figure ID) of a column for an infinitely narrow sample input function will be given by:
A T ( t ) = A T * exp -
N ( t - t*)’ 2t*2
VD(1+ K ’ )
(4)
and
(5) where AT* is the maximum deviation from baseline that occurs at a time t* which is analogous to the retention time of a chromatographic peak, N is the number of “thermal” plates in the reactor, and VR corresponds to the volume of fluid required to “elute” the heat peak through the column. It is important to note that analogous equations could be written for any type of detector attached to the column outlet, e.g., a conductometer, photometer, or refractive index meter. In the case of a thermal det,ector, the signal is a physical entity rather than a chemical species; thus we have opted to write the equations directly in terms of temperature and consider the movement of the heat pulse through the reactor. If the system behavior is dictated by mass transfer rates, rather than heat transfer rates, then both N and V , will refer to the corresponding chemical species rather than heat.
\
I
where Cp,s is the specific heat (cal/”C-L) of the stationary phase, V , the volume of the stationary phase (L). The term K’ can be thought of as a thermal partition ratio. In most packed-bed enzyme reactors, the stationary phase is a highly hydrated gel or resin or an extremely porous inorganic material; thus the specific heats of the mobile and stationary phase will be nearly identical and the retention volume will be essentially equal to the entire geometric volume of the reactor if thermal equilbration is achieved. The results of D. Kunii (40) indicate that a 100-pm nonporous glass sphere should require less than 0.3 s to reach thermal equilibrium at the flow rates used in this study. Since the particles used were smaller and porous, we believe that almost perfect thermal equilibration occurs between t,he fluid and the enzyme support. It is evident that the Gaussian model applies only when the sample volume is so small that it does not perturb the peak shape. Equation 5 may be used to predict the magnitude of a thermal peak from experimentally measured parameters when the peak is Gaussian. The number of plates on a column may be related to the variance, for this case, in volume units:
(7) UL”,C
In the work reported here, the peak half-width was used as a measure of the signal variance. For a pure Gaussian peak, which will occur only when the sample volume is small relative to the column variance, it is easy to show that the functional relationship between column variance and half-width is given by Equation 8.
ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
1931
Substitution of Equation 7 and 8 into Equation 5 shows that:
AT* = 2J-
In 2 AHCaVa 71
.
(9)
CP,m.W1,2,c
I
X
which applies only for the case of pure Gaussian peaks and low sample volumes. This equation predicts that for a given ~ the height of the set of operating conditions ( o " , constant), peak will increase indefinitely in proportion to the added volume of sample. Clearly when the sample volume is large relative to the column variance an alternative equation must be used to relate AT* to V,. Sternberg (41)has derived the equations which describe the behavior of a system where the width of an input function is large relative to the variance of an intrinsically Gaussian column process. His results indicate that with a sufficiently wide input function, the system output is no longer Gaussian. Qualitatively, as the input distribution is made wider, the peak height increases to some maximum value, a plateau develops in the output curve, and the output peak width gradually corresponds to the inlet increases. With our system AT,, concentration in Sternberg's notation. AT@), which represents the instantaneous temperature at the column outlet, corresponds to Sternberg's outlet concentration. Sternberg's equation in terms of temperature and time may be written as follows:
a
-t
a
.a =-t
1
m W
I
1
- c.0
-5.c
00
5.0
I
13.0
5
DIMENSIONLESS TIME (1-t")
Figure 2. Theoretical signal-time curves and their dependence upon sample volume. All curves computed from Equation 10 with q C= 0.20 min and f ' = 1.0 min
where ut,crefers to the variance in time units due solely to the Gaussian column processes and 8 is the plug width, in time units, defined below:
One should note that in the limit as 8 approaches zero, i.e. as the sample volume decreases, one will obtain the equation of a pure Gaussian peak (Equation 4). The peak height (ATieak),i.e. the maximum deviation from baseline of a thermal peak is readily obtained from Equation 12.
AT;,
= AT,,
erf
(2&.
i
Sternberg has shown that the peak is symmetric about its maximum which will occur when: 0
t=t*+-
2
and that the peak variance is given by Equation 14: 77'7
For very large sample volumes, the peak half width becomes equal to V,, Le.:
w 1/ 2 , v
Va;when V
> 30,.
(15)
The effect of sample volume on the peak height and width is very strong as is illustrated in Figure 2, which depicts a series of theoretical curves calculated from Equation 10. These curves indicate that the peak height initially increases quite rapidly with sample volume but ultimately the height becomes independent of 8 when 8 is large. Because of the complexity 1932
ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
of Equation 10, a simple functional relationship between the peak half width, the column variance, and sample volume (V,) is not available. The results of a numerical analysis indicate that the behavior at low and high sample volumes agrees with Equations 8 and 15, respectively, and that Equation 15 is applicable when V , is greater than about 3 C T ~ , ~ . All chromatographic detectors can be divided into two general classes: concentration detectors and mass flow detectors. A property of concentration detectors is that the magnitude of the instantaneous signal is independent of flow rate but the peak area drops off as flow rate is increased (42). The thermochemical system described here may be assigned to the class of concentration sensors if one assumes that the transducer measures the instantaneous temperature of fluid which moves past it. The integral of all the peak shape equations (1,2, and 4) leads to the same final result:
where F is the volumetric flow rate (mL/min). Since the area under the curve decreases with increasing flow rate, the thermometric detector is evidently analogous to a concentration sensor. It is important to note that the peak area is independent of the number of plates in the reactor and therefore of changes in sample dispersion factors. The relationship between area and flow expressed in Equation 16 will fail when the flow rate is so high that the reaction is incomplete and also at very low flow rate if heat losses from the column are significant. A very important property of the area under a peak of a concentration detector is that it will be independent of any fiit-order slow response of the transducer. This mathematical property of the integral of a peak can be demonstrated by considering the convolution of any peak equation with a first-order low pass response (43). Thus far we have assumed that the conversion of substrate to product is instantaneous. This is an unrealistic assumption at high substrate concentrations. If one considers a pure plug flow reactor, it is evident that an incomplete reaction will not
_ -
/
i
/
Flgure 3. Peak half-width as a function of initial substrate concentration Theoretical Computed from Equation 20 for a zeroorder reaction. (-) curve. (0)Experimental points. Conditions: Column I, 120-hL samples, flow rate 1.22 mLlmin
affect the peak width. In the case of a well mixed reactor, the peak width is not a function of concentration if the reaction is first order, but the peak width will vary with concentration when the reaction is zero order. Solutions to the relevant partial differential equations which describe simultaneous axial dispersion and slow reaction are not readily available. Thus, we have chosen to use the well mixed reactor model to estimate the effect of a zero-order reaction on peak width. Assuming that a sufficient initial concentration of substrate, [SI, is injected into a well mixed reactor so that the reaction proceeds by a zero-order rate law, the response shown in Figure 1C will result. It can be shown by a mass balance approach that the product concentration after injection of substrate w ill first increase, then decrease. Mathematically, the peak half width in time units (At1/*) is readily shown to be:
A t , , , = r In (2
+
F)
k’is the enzyme activity per unit volume of reactor and T is the time constant for flushing the reactor ( V o / F ) . Figure 3 represents the increase in A t l / *with increasing [SIo for a reactor system of constant enzyme concentration, volume, sample size, and flow rate. Clearly once [SI,exceeds a certain value ([SI,= 1.3 k’ 71, peak spreading due to incomplete reaction becomes a major effect. This threshold value will be a function of total column activity, reactor volume, flow rate, and the K M of the enzyme. Since zero-order enzyme reactions generally accompany only saturating concentrations of substrate, spreading due to this mechanism should only be observed when the substrate concentration is sufficiently high so that complete conversion is no longer achieved. Once the concentration threshold is exceeded, one can no longer estimate w 1 p Cfrom the experimental peak width since the slow chemical reaction serves to increase the width above that caused by purely dispersive factors.
EXPERIMENTAL Reagents. Urease (No. U-2OO0, Lot 366-7340,Sigma Chemical Co., St. Louis, Mo. 63178) was immobilized on controlled porosity glass (CPG-10, 50-nm pore diameter, 200/400 mesh, Electronucleonics, Springfield, N.J. 07006) by means of a bifunctional silane reagent and glutaraldehyde cross-linking (11). Four liters of stock diluent (0.9% sodium chloride, 5 mM ethylenediaminetetraacetic acid (EDTA))were prepared by dissolving 36.0 g of sodium chloride (“Baker Analyzed”, J. T. Baker Chemical Co., Phillipsburg, N.J. 08865) and 6.0 g EDTA (“Baker Analyzed”, J. T. Baker Chemical Co.) in the appropriate volume of deionized water (Continental Deionized Water Service, Atlanta, Ga. 30309).
Figure 4. Schematic drawing of the flow enthalpimeter. (A) Reservoir, (B) pump, (C) pulse dampener-pressuregauge, (D) insulated water bath, (E) pre-equilibratiin coil, (F) sample injection valve, (G) equilibration coil, (H) reference thermistor, (I) adiabatic column, (J) reference thermistor, (K) overhead stirrer, (L) flowmeter, (M)waste receptacle, (N) ac phase-lock brdge-amplifier,(0) oscilloscope, (P) integrator, (Q) recorder
Solid pellets of sodium hydroxide (laboratory grade, Fisher Scientific Co., Fairlawn, N.J. 07410) were added to bring the pH within the range of 7.0 to 8.0. Two molar potassium phosphate stock buffer was prepared by diluting 60.5 g of potassium dihydrogen phosphate (Certified ACS, Fisher Scientific Co.) and 259.7 g of potassium hydrogen phosphate (“Baker Analyzed”, J. T. Baker Chemical Co.) to 1 L with stock diluent. Working phosphate buffer (0.500 M, pH 7.40) for the flow reservoir consisted of 250 mL of the stock phosphate buffer diluted to 1.ooO L with stock diluent. Stock 0.1OOO M urea standard was prepared by diluting 0.6006 g of urea (ACS specifications, Mallinckrodt Chemical Works, St. Louis, Mo. 63160) to 100 mL with stock diluent. Working standards were prepared by serial dilution of the stock urea standard with stock diluent and all standards were stored at + 4 OC for no longer than two weeks. A reagent kit based on the diacetyl monoxime condensation reaction (Harleco “Blood Urea Nitrogen Reagents and Standards Kit”, catalogue No. 635-6, lot No. 51 97 G, supplied by A. H. Thomas Co., Philadelphia, Pa. 19105) was used according to the package instructions in conjunction with a spectrophotometer (Spectronic 88, Bausch and Lomb, Rochester, N.Y. 14602) for colorimetric urea determinations. Instrumentation. The apparatus is shown in Figure 4. Phosphate working buffer is delivered from the reservoir A, through low flow rate fittings by a piston pump I3 (Model RPI SY/CSC, Fluid Metering Inc., Oyster Bay, N.Y. 11771). The buffer first passes through a pulse suppressor, C, consisting of a Tee connector (No. 200-22, Altex Scientific, Berkeley, Calif. 94710) with the third channel connected to a 1.5-m length of Teflon tubing (18 gauge, 0.107-cm Ld. X 0.157-cm 0.d. Bolab, Inc., Derry, N.H. 03038) whose free end has been sealed shut. The tubing is formed into a 1.5-cm coil and bound so the coils are free to flex with each pulse. After passing through a pressure gauge and pre-equilibration coil, E (30 cm, 0.076-cm i d . X 0.163-cm o.d. stainless steel tubing coiled on a 1.1-cm aluminum rod), the flow reaches the sample injection valve, F (Model SV 8031, Chromatronix, Berkeley, Calif. 94710), where the sample is introduced into the buffer stream. The flow buffer and sample plug then pass through Altex 0.03-cm i.d. tubing to the equilibration coil, G (95 cm, volume 194 pL 21 gauge, 0.051-cm i.d. X 0.081-cm 0.d. stainless steel needle tubing wrapped around a 1.1-cm 0.d. aluminum rod, Precision Sampling Corp., Baton Rouge, La. 70815). During its residence in the coil the sample is thermally equilibrated with the water in bath D (from a Model 4000 Heat of Absorption Detector, Varian Aerograph, Walnut Creek, Calif. 94598); stirred by a 5-cm 0.d. overhead stirrer, K, rotated at 600 rpm. After passing by a 10-KR reference thermistor, H (Model GB41M2, Fenwal Electronics, Framingham, Mass.), the sample is hydrolyzed by the reactor bed in the “adiabatic” region of the column, I (shown in Figure 6). The heated solution flows past a matched sensing thermistor, J, and through a flowmeter, L, (No. 11,Roger Gilmont Instruments, Inc., Great Neck, N.Y. 11021) to waste. Both themistors were ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
1933
A
c~~~~~~~~ Gloss ,-Teflon%
Insert5
0
Flgure 5. Adnbatic column assembly. (A) Thin walled vacuum jacketed cdumn, (B) reference thermistor assembly, (C) sensing thetmistor insert, (D) details of thermistor probe assembly
Table I. ymmobilized Enzyme Reactor Configurations‘ Volume (mL) Length (cm) Internal diameter (mm) Fraction active packing
I
I1
I11
IV
0.42 3.3 4.0
0.67
1.0
1.0
0.67 5.3 3.7 0.5b
0.85 12.0 3.0 1.0
5.3
3.7
a All columns are packed with 200-400 mesh controlled pore glass. Enzyme activity is approximately 1000 Reference (upstream) end of column is unitslg of glass. packed with 80-120 mesh silicone coated spherical solid glass particles.
etched with hydrofluoric acid to remove as much glass as possible and improve the response time characteristics. The temperature difference measured by the thermistors is converted to a disbalance voltage by a differential ax. phase lock bridge, N (44,45) (driven with a 1.0-V peak to peak 2-kHz sine wave signal). The slowest time constant in the electronic system is the 0.3-9 low pass filter on the output to the recorder. The amplifier is tuned using oscilloscope 0. The final d.c. output of the amplifier is integrated electronically by an operational amplifier, P (MP 1031, McKee Pedersen Instruments, Danville, Calif. 94526) and both the temperature peak and its integral are recorded simultaneously by a two-pen recorder, Q (Model 56, Perkin-Elmer Corp., Norwalk, Conn. 06856). The stirring motor chasis is connected directly to the ax. line ground and the water bath to amplifier common. This configuration minimizes noise pickup by the sensors from the stirrer and laboratory environment without perturbing the signal. Refractive index measurements were made by removing all components from the water bath and connecting a thermostated (33 “C, Model FE, Haake, Inc., Saddle Brook, N.J. 07662) low volume refractive index detector (8-kL cell, Model 1107, Laboratory Data Control, Riviera Beach, Fla. 33404) to the column outlet. Figure 5 shows the “adiabatic” column and thermistor assemblies in greater detail. When assembled properly, the sensing thermistor, C, just extends into the vacuum jacketed region of column A. The rest of the region is occupied by the immobilized enzyme bed. The end of the Teflon insert containing the sensing thermistor is flattened to allow the fluid to pass to the column outlet. Each of the various column configurations used in this study are described in Table I. It is absolutely necessary that all connectionsto the thermistor be water-tight before the unit can be submerged. In order to do this, the thermistor, its leads, and connecting wires are sealed in a length of Teflon tubing as shown in Figure 5D. The ends of a 1-m length of Teflon tubing (0.042-inchi.d. X 0.062-inch o.d., Bolab, Inc.) are pretreated with a solution (Chemgrip Treating Agent, Chemplast, Inc., Wayne, N.J. 07470) to make it bondable to epoxy. This tubing is placed over a length of miniature coaxial cable (No. 8700, Belden Corp., Chicago, Ill. 60644) from which the outer insulation has been removed. The leads of the thermistor are soldered to the cable, with the ground lead being insulated by a 1-cm length of thin Teflon tubing (0.022-inch i.d. X 0.042-inch o.d., Bolab, Inc.). The outer tubing is then placed two-thirds of 1934
ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
the way up the body of the etched thermistor and sealed with epoxy (EPO-TEK 360, Epoxy Technology,Inc., Watertown, Mass. 02172). This unit can then be epoxied into a treated Teflon insert or a ‘/16-inchi.d. connector (No. 200-00, Altex Scientific, Inc.). The reference sensor, as shown in Figure 5B, is made by screwing the connector assembly into a “Tee” fitting (No. 200-22, Altex Scientific, Inc.) which has had the thermistor channel drilled out to about 0.24 cm in diameter. Procedure. The stirring motor and pump were turned on 5 min before initiating the first analysis in order to assure full thermal equilibration as indicated by a flat baseline. Flow rate was set to a pre-calibrated mark on the flowmeter and. where indicated, determined by measuring the time to fill a vessel of known volume. Samples were prepared by mixing three parts urea standard with one part of 2.00 M working phosphate buffer, yielding a final phosphate concentration of 0.500 M. The sample was then drawn into the sampling valve and injected into the flowing buffer stream. Complete conversion was verified colorimetrically under a wide variety of conditions including both high and low flow rates and high sample concentrations, and sample volumes. Unless otherwise indicated, the system was operated at a flow rate of 1.22 mL/min. Temperature change was calculated as the product of the measured resistive disbalance of the thermistors and their approximate thermal coefficient of -40 il/OC. Peak width at half and peak maximum time were converted maximum height (w1I2) from the measured time units to volume units via the measured flow rate. Peak area was calibrated based on the observed temperature change and peak width of a flat-topped peak and Jespersen’s (46) value of -14.7 kcal/mol for the AH of the hydrolysis reaction in phosphate buffer at a pH of 7.5. Determination of the K Mof Immobilized Urease. Buffer was prepared by diluting the stock 2.0 M potassium phosphate buffer to 0.02 M with stock diluent and adjusting the pH to 7.40 with hydrochloric acid and potassium hydroxide. Reaction rates were measured in a 25-mL thermostated cell at 33 “C by monitoring the pH change with time (Model 801 with Model 751 digital printer, Orion Research, Cambridge, Mass. 02139). Initially, 15.00 mL of the 0.02 M phosphate was pipetted into the stirred, thermostated cell followed by the addition of approximately 1 mL of wet immobilized urease. The reaction was initiated by injecting the appropriate volume of a 1.00 M urea solution prepared in the 0.02 M phosphate buffer. Volumes of 60,150,300, and 600 pL, corresponding to cell urea concentrations of 2,5, 10, and 20 mM, respectively, were introduced. After each determination, the pH in the cell was restored to 7.40 by addition of dilute hydrochloric acid. The initial rate was measured over the first 90 s of reaction and the KM determined through a Lineweaver-Burke plot. Substrate inhibition of urease by ammonium ion has been well documented (47). In this case, however, replicate analyses at the 20-mM level were reproducible. This indicates that effects due to product inhibition or loss of enzyme activity were not significant.
RESULTS AND DISCUSSION Preliminary experiments were carried out during the development of the previously reported urea and glucose (45) analysis systems. We had found that the principal factors influencing the system sensitivity were the sample volume and flow rate. At optimum flow rate, the peak temperature changes for 0.12-mL samples of urea amounted to about 12% of that based on a pure plug flow model (Equation 1) when Jespersen’s value for the heat of hydrolysis of urea (AH= -14.7 kcal/mol ( 4 6 ) ) was used despite the fact that the reaction proceeded to completion. Even with much larger volumes of sample, a flat-topped thermal peak did not occur. Although the analytical sensitivity of the system was acceptable, it was difficult to increase the sample throughput t o above 40 per hour without running the risk that peaks would overlap. The slow thermal time response of the measuring sensor was due to the thermistor being mounted in a “Tee”. Upon introducing a thermistor axially into the end of the column, the peak
Table 11. Estimation of Sources of Sample Dispersiona
System component Sample valvef Connection tubing Thermal equilibration coil Reference thermistor junction Columng Total Thermal system'
Component geometric kolumeb
___
0.03 0.20 0.08 0.42h
-__
___
Total apparent volumebsc 40 p L d 120 @Le 0.275 0.320 0.649 0.655 1.092 1.092 0.95
0.183 0.275 0.534 0.573 0.96 0.96 0.84
Calculated com onent half-width! 40 pLd 120 pLe 0.14 -0
0.19 -0 0.24 0.34' 0.31
0.15 -0 0.18 -0 0.23 0.33' 0.32
Calculata All measured with a low dead volume refractive index detector at a flow rate of 1.22mL/min. 0 All in mL. Measured with a 40-pL sample volume. e Measured with a ed from time to peak maxima and the measured flow rate. Total volume 120-pL sample volume., f This includes the detector., g Column I packed with 200-400 mesh porous glass. of unpacked column. Total measured half-width. J Same conditions as refractive index detector. half-width decreased by almost a factor of two, flat top peaks were obtained with a 0.75-mL sample and peak heights increased by approximately a factor of 3. Sources of Dispersion. In order to determine the sources of residual spreading, a refractive index detector was used to carry out the series of measurements presented in Table I1 in which the contribution of each component of the system to the observed half-width was quantitated. The most important observation was that the peak half-width, shape, and peak maximum time were almost equal to that obtained with a thermistor as the detector. This fact alone indicates that mass dispersion is the dominant factor in the entire system and that heat transfer between phases within the reactor and a t the thermistor is relatively fast. The spreading due to each component of the system was calculated on the assumption that half-widths are additive in accord with the square rule for peak standard deviations. A problem in an exact analysis of the data in Table I1 is the anomalous effect of the very low sample volume (40 pL) on the apparent retention volume and half-width. Since the peaks obtained from the system are definitely non-Gaussian, the peak maximum did not coincide with the center of gravity of the peak and retention volume is not a true measure of system volume. The time corresponding to the peak maximum should increase as the volume injected increases; this (see Equation 13) was observed to be the case with volumes greater than 120 p L but as indicated in Table I1 and Figure 8, the opposite trend was observed at very low volume. It is probable that the very narrow tubing used to construct the 40-pL loop caused a momentary decrease in flow rate, thereby delaying the peak maximum. It is evident from Table I1 that the two major sources of dispersion are the thermal equilibration coil and the column per se. The length of the thermal equilibration coil cannot be decreased significantly without adversely affecting the completion of thermal equilibration of the sample with the bath and a concomitant increase in noise. Table 11, however, indicates that even if the broadening in the equilibration coil could be eliminated, we would still have significant broadening in the column. Further changes in the equilibration coil to increase throughput would not justify the increase in noise which would result. It is interesting to compare the observed retention volumes with the geometric volume of the unpacked column. Assuming a column fractional dead volume of about 0.40 (38),the interstitial volume of column I will be about 0.17 mL. The estimated internal porosity of the glass is 0.33 as calculated from the packing density and specified pore volume per gram; thus the total volume available to the sample would be ?.bout 0.24 mL. For the thermal peaks a retention volume in the column of about 0.27 mL and 0.30 mL was found for 120-pL and 40-wL samples, respectively. The higher retention volumes
observed with the refractive index detector may be due to dead volume between the column and dehctor. These comparisons indicate that the analyte and its products almost completely permeate the porcus glass particles (34-75 pm). Assuming this to be the case, then heat, which has a much higher diffusivitity than mass, does indeed equilibrate thoroughly with the fluid trapped on the pores. We estimate that about 0.2 s is needed for thermal equilibration of the enzyme particles with a heated sample plug. Since heat does diffuse faster than matter, it is interesting to estimate the magnitude of the contribution of longitudinal heat diffusion to the half-width. Using a value of 8.002 cm2/s for the diffusivity of heat in water, we estimate longitudinal diffusion could amount to no more than 0.10 mL, which is small compared to the other dispersion factors. One can conclude that the thermal detection system peak width is controlled by mass dispersion in the valve, equilibration coil, and column. A priori estimation of the contribution of the sample size, dispersion in the tubing and column is possible. For a 120-pL sample, a h d - w i d t h of 0.08 mL is obtained from Sternberg's equations for pure plug flow (41). Using the Golay equation for open tubes (48)) one estimates a half-width of about 0.25 mL for dispersion in the tubing prior to the column. This is slightly less than the observed value (see Table 11). Dispersion in the column is not so readily estimated because the particles are porous and our assumption that the sample is instantly converted to products is not precisely correct. Assuming the rule of thumb in liquid chromatography that the optimum H E T P will be no less than about three times the particle diameter (49)) the half-width due to column dispersion will be at least 80 pL, which is a factor of three better than our observed values. This is not at all surprising since we could not pack the columns by optimum techniques and the fact that the ratio of column to particle diameter is about 100 which is several times the optimum value used in high performance liquid chromatography (50). Effect of Sample Volume on System Behavior. A series of studies on the effect of sample volume on the measured peak height and half-width was carried out at two concentrations of urea (2.0 and 20.0 mM). The 2.0 mM concentration was chosen because it falls near the bottom of the normal serum urea concentration range and therefore the kinetics of the enzymatic reaction should be first order. The 20 mM concentration was chosen because it is about equal to the Michaelis constant ( K M= 19 mM for soluble urease a t pH 7.0 in phosphate (51)).The immobilized urease used in this work had a Michaelis constant of about 27 mM at pH 7.4 in 0.01 M phosphate buffer. The difference in Michaelis constant for the soluble and immobilized materials is typical (52). The results of this study are presented in Table I11 and Figures 6 and 7. Figure 6 compares a normalized peak height ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
1935
Table 111. Effect of Sample Volume on Observed Peak Half-Widtha Peak half-widthb Column IV Sample volume. mL
Column I urea concn, mM
Column I1 urea concn, mM
urea
concn, mM
2.0
20.0
2.0
20.0
20.0
0.040 0.12 0.25 0.50 0.75 1.00 2.50
0.31 0.32 0.46 0.70 1.01 1.35 2.85
0.29 0.27 0.43 0.68 0.98 1.31 2.91
0.42 0.40 0.47 0.69 1.02 1.35 2.84
0.44 0.41 0.48 0.69 1.02 1.35 2.82
0.38 0.40 0.51 0.74 1.09 1.41 3.02
SlopeC
1.07
1.09
1.02
1.01
1.10
Flow rate was 1.22 mL/min in all experiments. Width of peak at the half maximum signal (mL). This is the least square slope measured from a volume of 0.50 to 2.50 mL.
- -
r""--j'
i=
A 5
SAMPLE
?:
?-
VOLUME ( m l )
Figure 6. Effect of sample volume on peak height. Condkions: Column I, flow rate 1.22 mL/min, peaks normalized by dividing by height of h@ volume peak. 2 mM urea Concentration (0). 20 mM concentration (A).Theoretical curve (-, Equation 12)
for two concentrations of urea as a function of sample volume with all other conditions being identical. The peak heights were normalized by dividing the measured temperature change by that obtained for a "steady-state'' peak. The theoretical curve is calculated based on Equation 12. The steady-state peak heights were 15.9 and 15.5 m O C for the 2.0 and 20 mM urea samples, respectively. These values correspond to about 66% of the value estimated for pure plug flow based on Equation 1 (vide infra). T h e results for the 2 mM and 20 mM samples are similar despite the fact that the two concentrations lie in the firstand nearly zero-order kinetic domains. This indicates that the rate of product generation is controlled not by the kinetics of the enzyme reaction but by mass transfer of the substrate to the surface of the carrier or by diffusion within the porous glass. Since the effect of sample volume on the peak height is mainly due to the sample dispersion considerations, the effect of the size and configuration of the column was tested (see Figure 7 ) . Steady-state (flat top) peaks were obtained with sample volumes of about 1.0 mL. The major difference 1936
ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
Z C
SAMPLE
VOLUME ( m l )
Figure 7. Effect of sample volume and column design on peak height. Conditions: 20 mM urea concentration, flow rate 1.22 mL/min. Column I, experimental (0). Cdumn 11, experimental (0).Column 11, theoretical (--, Equation 12, u " , = ~ 0.3 mL). Column IV, experimental (A). Column IV, theoretical (-, Equation 12, u V c= 0.3 mL)
between the three columns is a difference in the maximum temperature change. The effect is most pronounced for column IV which was the narrowest, longest column used. We believe that this may be accounted for by heat leakage from each reactor due to poor adiabaticity. This effect will obviously be greatest for the reactor with the highest ratio of surface area to total volume. The steady-state peak heights for 20 mM samples analyzed with columns I, 11, and IV are 6870,68%) and 49% of that calculated for plug flow. The theoretical curve shown in Figure 6 is based on Equation 12 and our estimate of the half-width (wllz = 0.30 mL, see Table 111) of the system. Overall, the agreement of the theoretical curve with the experimental points is good. The maximum deviations occur a t low volume and are due to the fact that the actual peak height depends most strongly on the model for the column per se when the sample volume is small. Since Equation 12 is based on the assumption that the column behavior is inherently Gaussian, which is not the case even for very small samples, these deviations are reasonable. The data shown in Figure 7 are quite similar to those of Figure 6. The theoretical curves in Figure 7 represent the function calculated from columns I1 and IV from Equation 12 and the measured w I l 2 appearing in Table 111. The agreement is similar to that seen in Figure 6 which shows that the changes observed in dispersion due to different column configurations are, as expected, reflected in the measurement of W l j 2 . The effect of sample size on the peak half-width for three columns at two urea concentrations is shown in Table 111. The data follow the general trend shown in Figures 6 and 7. When the injected volume is low, the half-width is essentially due to physical dispersion. This table indicates that the higher sensitivity with larger samples is obtained a t the expense of a wider signal and a concomitant decrease in sample throughput. The dependence of half-width (mL) upon injected volume was determined via least squares analysis of the data at a sample volume in excess of 0.50 d. The results (Table 111) indicate a slope close to unity in accord with Equation 15. Sternberg (41)has shown that peak half-width is not a simple linear combination of the half-width due to the column and the half-width due to sample size. This results because the conversion factor from variance to half-width
Column I, O . l 2 0 m l , 2 O m ~ Refroctide lrdex
Columr I , O.l20ml, 2 0 m M
0.4
t
-
LL
0.2; 1
LI.
LL 3
rr
A
-
0.2 B Q3 u 3 1 2 3 4 5
TIME
D
Flgure 8. Experimental response curve as a function of sample volume.
Conditions: Column I, 20 mM urea concentration, Row rate 1.22 mL/min. Curve A , 40 pL. Curve B, 120 pL. Curve C, 250 pL. Curve D, 500 pL. Curve E, 750 pL. Curve F, 1000 pL depends upon peak shape. Agreement of the data of Table I11 with Equation 14 is also shown by comparing the curves in Figure 8, which are recorder tracings of a sample volume study, with the theoretical curves plotted in Figure 2. Sample throughput is a major concern in automated analysis just as resolution is a central issue in chromatography. An optimum system is one which provides sufficient sensitivity to do the analysis while simultaneously minimizing sample volume and peak half-width. Peak half-width (9) can be decreased by increasing the flow rate but (vide infra) this will decrease the sensitivity. The peak width in volume units could also be decreased by using a smaller reactor. As indicated by the data in Table 111, larger columns produce somewhat greater spreading. One should note that both high flow rates and small columns result in decreased residence times and may lead to incomplete conversion. Furthermore, the useful lifetime of an immobilized enzyme reactor, all else being equal, depends upon the total initial amount of enzyme, which is proportional to the reactor volume. T h e use of very small particles would present several advantages. First, the peak width could be decreased by optimizing the enzyme support size, particle size distribution, and packing procedure. Second, the larger surface area to volume ratio would increase the rate of external mass transport. Third, internal diffusion time could be decreased. Both of these mass transfer effects would increase the catalyst's effectiveness factor (53, 5 4 ) . Such studies were not done here because 200-400 mesh glass is the smallest controlled pore material available at this time. It is also evident from Table I11 that a decrease in sample volume will decrease the peak width thereby resulting in improved throughput and a proportional loss in analytical sensitivity. It should be remembered, however, that this technique will only be successful at sample volumes where the variance is predominantly a function of the injection width, rather than column dispersion (see Equation 14). Once this limit is reached, no further advantage can be accrued as can be seen by comparing the data for 40-pL and 120-pL sample volumes (Table 111). Effect of Flow Rate on Peak Height and Width. The volumetric flow rate has a major effect on the absolute peak height ("C) and on the peak width in time units. Peak height as a function of flow rate was studied for several column configurations. The results, which were normalized by dividing each temperature change by the largest one in any given series of experiments, are summarized in Figure 9. The major feature of all the thermal curves is a pronounced roll-off in peak height at low flow rates. It is important to note that the
FLGW RATE (mi/min) Flgure 9. Dependence of normalized peak height on flow rate. (A) Column I , sample 120 pL of 20 mM urea, refractive index detector. (6)Column I, sample 120 pL of 20 mM urea. (C) Column 11, sample 120 pL of 20 mM urea. (D) Column IV, sample 120 pL of 20 mM urea. (E) Column 111, sample 120 pL of 20 mM urea. (F) Column I, steady state peak height for 20 mM urea sample
signal from the refractive index detector did not drop at low flow rate. The marked contrast between the behavior of a temperature sensor and a matter detector indicates that the roll-off at low flow must be due to heat transfer effects either within the column or to the detector; or heat losses from the column. Heat losses are the most likely source of the phenomena since the heights of the steady-state peaks (see Figure 9) decreased. Equation 16 indicates that the product of peak area and flow rate should be constant and therefore independent of dispersive effects in the column. Although the data are not presented, we have found that a plot of peak area times flow rate vs. flow rate resembles the plot of peak height vs. flow rate. That is the quantity (area x flow rate) increases very rapidly as the flow rate is increased from zero. In contrast to the behavior of the peak height ploh (Figure 9), the roll-off a t high flow rate is not nearly as steep. The decrease at low flow can only be accounted for by incomplete reaction or loss of heat from the column. Since we have verified that the analyte is completely converted to product, we believe that the decrease in both peak height and area is due to heat loss from the column. This is further supported by the fact that a flow rate of 1.2 mL/min., column IV, which has a higher surface area, produced a much smaller peak than did either of the other columns. In addition, it appears that column IV has a slightly higher optimum flow rate than any other column configuration. All of these observations are consistent with heat loss from the column. Before attempting a detailed analysis of the proposed heat loss phenomena, it is necessary to consider the high flow rate behavior of the reactor. For this case, Figure 9 indicates that both detector systems show an approximately equal linear ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
1937
Table IV. Effect of High Flow Rate on Peak Height and Half-Widtha
Column
Ib
IIb
IIIb IVb
I-RIC
Sample concn, mM
Flow rate, mL/min
Peak height, 10-3 o c
Half-width, mL
2 2 2 20 20 20 2 2 2 20 20 20 20 20 20 20 20 20 20 20 20 20
2.35 3.11 4.56 2.54 3.44 4.45 1.89 2.69 4.68 1.89 2.69 4.68 1.90 2.64 4.98 2.39 3.13 3.74 0.33 1.30 2.22 3.95
9.66 8.90 8.10 65.36 66.25 60.71 4.53 4.39 3.94 45.13 43.25 38.63 48.44 45.31 39.56 48.68 46.43 44.08 11.90d 11.50d 11.05d 10.80d
0.32 0.31 0.34 0.38 0.50 0.43 0.40 0.47 0.50 0.40 0.47 0.50 0.38 0.43 0.50 0.42 0.47 0.47 0.31 0.36 0.34 0.37
Peak height x half-width, “ C mL 3.09 2.76 2.73 24.8 26.5 26.1 1.81 2.06 1.97 18.1 20.3 19.3 18.4 19.5 19.8 20.4 21.8 20.7 4.40d 4.1 4d 3.76d 4.00d
a All sample volumes are 0.120 mL. Data obtained with the thermal detector. Data obtained with the refractive index detector. These data are in arbitrary units of cm recorder deflection or (cm.mL).
decrease with flow rate for small samples (120 p ) . Large sample volumes, which correspond to steady-state peaks, however, do not roll off nearly as rapidly. This indicates that the phenomenon may be due to peak width increases (broadening) as the flow rate increases. Equation 9, which applies for small sample volumes and approximately Gaussian peaks, suggests that the peak height should decrease inversely with an increase in peak half-width ( w 1 p c ) . We did observe small but significant increases in the half-width (in volume units) as the flow rate increased. These measurements are summarized in Table IV. Even though each peak height decreased as flow rate increased, the last column of this table indicates that the product of peak height with half-width for both detectors is reasonably random and is much more constant than are either the peak height or the half-width. We feel that the increased sample and product dispersion satisfactorily accounts for these observations. This broadening, which increases with flow rate, corresponds to resistance to mass transfer, in both the mobile and stationary phases, which is observed a t high flow rates in chromatography. The effect is approximately equal with both types of detectors and since heat transfer between phases is much more rapid than mass transfer, the decrease in peak height and increase in width can, therefore, be attributed to a mass transfer related phenomenon. Considerable difficulty was encountered in our attempt to determine the magnitude of heat losses from the thermal reactors. It is evident that the dispersive phenomenon, will affect the data a t low flow rate. Secondly, a t very low flow rate the signals decrease to quite low values decreasing the signal to noise ratio accordingly. Finally, at low flow rate the piston pump utilized cannot be reproducibly set to deliver at a pre-determined rate. Consider the movement of a plug of heat through a packed column. As pointed out above, heat transfer from the fluid to the small porous glass particles is quite fast so we need not consider radial gradients. Heat can be lost from the flow calorimeter either by axial transport to the non-insulated regions or radially across the glass walls and through the “vacuum” jacket. Axial transport to the entrance end of a column was qualitatively eliminated as a possibility by the 1938
ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
experiments with columns I1 and 111. As indicated in Table I, the entrance end of the column was packed with non-active glass so that no heat was generated until the sample moved through about 50% of the whole volume of the column. Comparison of the results for columns I1 and I11 (see Figure 9) indicates no substantial difference. Axial transport to the exit end of the column will not lead to heat losses insofar as the thermistor detector is concerned since it will see the heat before it leaves the column. Radial heat losses at any instant can occur only from the segment of column occupied by the heated fluid pulse. Obviously a narrower column will have a greater area per unit volume of sample slug than a wider column and should therefore lose more heat. This is evidently in accord with the results shown in Figures 7 and 9. The heat leakage modulus of small, isoperibol calorimetric vessels has been measured by Hansen (55). He found that for a series of vessels of similar construction, but progressively decreasing total volume, the heat leakage modulus increased dramatically a t volumes less than about 20 mL. Since our flow calorimeters (0.5-0.8 mL) are considerably smaller than Hansen’s batch calorimeters and are structurally poorer, i.e., thicker walls, lower vacuum, and nonspherical geometry, one would expect considerableheat loss even at the short residence times (0.5 to 2 min) which correspond to the flow rates employed to obtain the data in Figure 9. Crude measuremenh from the data at low flow rate in Figure 9 indicate heat leakage constants of 0.33 to 1 min-’. In view of the simplicity of our calorimetric design, we feel that these estimates are in good agreement with the results of Hansen. In order to conclusively demonstrate the fact that heat losses are the cause of the decrease in peak height at low flow rate, the two series of experiments whose results are shown in Figure 10 were run. The data shown in this figure were obtained by carrying out a run with column IV and then placing a tight fitting (6 mm thick) Teflon insulating jacket over the column taking care not to disturb the column packing. The data indicate an increased peak height at all flow rates. The similarity of the slopes at high flow rate show that the packing was not disturbed and the increased peak height clearly demonstrates that there is substantial heat leakage
(5) R . E. Karcher and H. L. Pardue, Clin. Chem. ( Winston-Salem, N.C.),
35
..-.. ?O 0 0
E +
25
I
z ic w I
Y
5
Q W
a
IC
9 L
3
1
2
3
1
1
4
5
FLOW RATE (rnl/min)
Figure 10. Effect of improved adabaticity on peak height as a function of flow rate. Conditions: Column IV, sample 120 pL of 20 mM urea. Column without Teflon jacket (0). Column with Teflon jacket (0)
from the columns. We believe that at best, use of a perfectly adiabatic column could improve the sensitvity by only about 50%. Concentration Studies. Peak height, area, and width were studied as a function of sample concentration over the linear dynamic range of the instrument. As was observed by Bowers (8, 451, peak height and area are both linear up to approximately 200 mM with a sample volume of 120 pLI. Examination of Figure 3 shows that peak volumetric half-width is constant over that range. Above concentrations of 200 mM, complete conversion of the urea sample is not achieved and the calibration curve becomes nonlinear. Examination of Figure 3 shows that incomplete conversion is also accompanied by an increase in peak half-width. The failure of the enzyme column to completely convert the substrate indicates the enzymatic reaction has passed into a primarily zero-order kinetic regime. In a stirred, soluble enzyme system this would necessarily be due to exceeding the KM of the enzyme per se. In an immobilized enzyme reactor such as the one described, any of several steps may be rate limiting: the diffusion of substrate from the solution phase to the external surface of the support particles, the diffusion of the substrate into the pore where the active enzyme is immobilized, the rate of enzymatic conversion of substrate to products, and the rate that the products diffuse into the flowing solution. Since mass transfer processes are first order, we believe that in the system employed here the amount of enzyme is rate limiting at a very high substrate concentrations. As noted above, a simple first-order reaction will not lead to an increase in peak width as a function of sample concentration. Characterization of the reactor, at sample concentrations greater than 200 mM, as a zero-order system suggests that peak widths can be described by Equation 17. The similarity of the theoretical curve and experimental points in Figure 4 shows the validity of this assumption.
LITERATURE CITED (1) G. G. Guilbault, Anal. Chem., 42, 334R (1970). (2) H. U. Bergmeyer, Ed., “Methods of Enzymatic Analysis”. Academic Press, New York. N.Y., 1975, Vol. 1-4. (3) G. G. Guilbault, “Enzymatic Methods of Analysis”, Pergamon Press, New York, N.Y., 1970. (4) R. E. Adams, S.R. Betso, and P. W. Can, Anal. Chem., 48, 1989 (1976).
17, 214 (1971). (6) R. A. Messing, Biotechnol. Bioeng., 16, 525 (1974). (7) R. A. Messing, Biotechnol. Bioeng., 16, 897 (1974). (8) L. D. Bowers, L. M, Canning, C. N. Sayers, and P. W. Carr, Clin. Chem. ( Winston-Salem, N . C . ) , 22, 1314 (1976). (9) L. D. Bowers, P. W. Carr, and R. S. Schifreen. Clin. Chem. (Winston-Salem, N.C.), 22, 1427 (1976). (10) H. V. Malmstadt, C. J. Delaney. and E. A. Cordos, Anal. Chem.,44 (12), 79A (1972). (1 1) H. V. Maimstadt, C. J. Dehney, and E. A. Cotdos, C f t . Rev. Anal. Chem., 2, 559 (1972). (12) S. R. Crouch, Anal. Chem., 41, 880 (1969). (13) G. E. James and H. C. Pardue, Anal. Chem.. 40, 796 (1968). (14) H. L. Pardue in “Advances in Analytical Chemisw and Instrumentation”, C. N. Reilley and F. W. McLafferty, Ed., Interscience, New York, N.Y., 1969, Vol. 7. (15) H. V. Maimstadt and S. R. Crouch, J . (:hem. Educ., 43, 340 (1966). (16) H. H. Weetall, Anal. Chem., 46, 602A (1974). (17) L. D. Bowers and P. W. Carr, Anal. Chem., 48, 544A (1976). (18) D. T. Bostick and D. M. Hercules, Anal. Chem.. 47, 447 (1975). (19) W. E. Hornby, J. Campbell, D. J. Inman, and D. L. Morris in “Enzyme Engineering”, E. K. Pye and L. B. Wingard, Ed., Plenum, New York, N.Y., 1974, Vol-2, p 401.. (20) G. G. Guilbault and J. G. Montalvo, Jr., J . Am. Chem. SOC.,92, 2533 (19701. (21) J. W. Kuan. K. Y. Lau and G. G. Guilbautt, Clin. Chem., ( Winston-Salem, N.C.), 21, 67 (1975). (22) G. P. Hicks and S. J . Updike, Anal. Chem., 38, 726 (1966). (23) M. K. Weibei. W. Dritschilo, H. J. Bright, and A. E. Humphrey, Anal. Biochem., 52, 402 (1973). (24) H. J. Kuntz and M. Stastny. Clin. Chem. ( Winston-Salem, N.C.), 20, 1018 (1974). (25) R . A. Messing, Biotechnol. Bioeng., 16, 525 (1974). (26) D. R. Senn, P. W. Carr, and L. N. Kiatt, .4nal. Chem., 48, 954 (1976). (27) L. H. Goodsen and W. E. Jacobs, “Enzyme Engineering”, E. K. Pye and L. 8. Winogard, Ed., Plenum, New York, N.Y., 1974, Vol. 2, p 393. (28) B. Watson and M. H. Keyes, Anal. Len., 9, 713 (1976). (29) J. A. Burns. Cereal Foods World. 21, 594 (1976). (30) A. Johansson, J. Lundberg, 8 . Mattiasson, and K. Mosbach, Biochim. Biophys. Acta, 304, 217 (1973). (31) K. Mosbach and B. Daniek.cn, W h i m . Biophys. Acta, 364, 140 (1974). (32) K. Mosbach, B. Danielsson, A. Eager&, and M. Scott, Bicchim. Biophys. Acta, 403, 256 (1975). (33) E. Mattiasson, B. Danielsson. and K. Mosbach, Anal. Lett., 9, 217 (1976). (34) H. L. Schmidt, G. Drisam, and G. Grenner, Biochim. Biophys. Acta, 429, 283 (1976). (35) C. D. McGiothlin and J. Jordan, Anal. Chem., 47, 786 (1975). (36) J. C. Wasiiewski, P. T. S. Pei, and J. Jordan, Anal. Chem., 38, 2131 (1964). (37) R. P. W. Scott, J . Chromatogr. Sci., 11, 349 (1973). (38) A. B. Linlewood. “Gas Chromatography”, 2nd ed.,Academic Press, New York, N.Y., 1970, Chapter 5. (39) B. 6. Karger, M. Mrtin, and G. Guiichon, Anal. Chem., 46, 1640 (1974). (40) D. Kunii and J. M. Smith, AIChE J . , 7, 29 (1963). (41) J. C. Sternberg, Adv. Cbromatogr., 2, 206-270 (1966). (42) A. B. Linlewood, “Gas Chromatography”, 2nd ed.,Academic Press, New York, N.Y.. 1970, Chapter 8. (43) A. E. Littlewood, Reference 42, Chapter 6,p 197. (44) E. B. Smith, C. S.Barnes, and P. W. Carr. Anal. Chem., 44, 1663 (1972). (45) L. D. Bowers, Ph.D. Dissertation, The University of Georgia, Athens, Ga., 1975. (46) N. D. Jespersen, J . Am. Chem. SOC.,97, 1662 (1975). (47) J. E. Varner in “The Enzymes”, P. D. Boyer. H. Lardy, and K. Myrback, Ed., Academic Press, New York. N.Y., 1960, Voi. 4, Chapter 13. (48) M. J. E. Gohy in “Gas Chromatography 1958. Proceedings of the Second Symposium Amsterdam, May, 1958”, D. H. Desty, Ed., Academic Press, New York, N.Y.. 1958, p 36. (49) J. Knox in “High Pressure Liquid Chromatography in Clinical Chemistry”, P. F. Dixon, C. H. Gray. C. K. Lim, and M. S. Stoll, Ed., Academic Press, New York, N.Y., 1976, Chapter 1. (50) R. N. Kelley and F. W. Billrneyer, Anal. Chem., 41, 874 (1969). (51) F. J. Reithel in “The Enzymes’ , P. D. Boyer, Ed., Academic Press, New York, N.Y., 1971. (52) 8. K. Hamiiton, C. R. Gardner, and C. K. Cotton, AICbf J., 20, 503 (1974). (53) 8. Atkinson and D. E. Lester, Biotechnoi. Bioeng., 16, 1299 (1974). (54) M. Moo Young and T. Kobayaski, Can. J. Chem. Eng., 50, 162 (1972). (55) L. D. Hansen, T. E. Jensen, S. Mayne, D. J. Eatough, R. M. Izatt, and J. J. Christensen. J . Chem. Thermodyn.. 7, 919 (1975). 1
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RECEIVED for review March 22, 1977. Accepted August 26, 1977. This work was supported by the National Institutes of Health Grant GM 17913, a University of Georgia Graduate Assistantship awarded to R.S.S. and a National Science Foundation Undergraduate Research Participation Grant award for support of D.A.H. This work is from the Ph.D. dissertation of R.S.S. Parts were presented a t the 173rd National Meeting of the American Chemical Society, New Orleans, La., March 1977.
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