Anal. Chem. 1991, 63,16-20
16
ARTICLES
Chromatographic Approach to the Measurement of the Interstrand Distance for Some Chiral Bonded Phases William H. Pirkle* and Robin S. Readnour School of Chemical Sciences, University of Illinois, Urbana, Illinois 61801
A series of homologous N,N’-bis(2,4-dinltrophenyl)-a,w-diaminoaikanes (bis-DNP’s) was chromatographed at various temperatures on r-basic chirai stationary phases derived from N-(2-naphthyl)aianine in order to determine the enthalpy and entropy of adsorption. The number of methylene groups in the bis-DNP’s influences the abiiHy of the terminal r-acMlc groups to interact simultaneously with neighboring strands of stationary phase, a process termed “bridging”. When the number of methylene groups is optimal for bridging, the enthalpy of adsorption is most exothermic. The length of the bis-derivative required for optimal bridging is related to the interstrand distance. Optimal bridging occurs for the bis-DNP’s havlng five methylene groups regardless of the extent of surface coverage of the sliica for the surface coverage range lnvestlgated. Thls suggests that the strands are not randomly spaced on the silica, with lnterstrand distance being infiuenced only by surface coverage, but are instead clustered, the clusters having similar distributions of interstrand distances. Adsorption is more exothermic for phases of high surface coverages than for low. If Interstrand spacing is independent of surface coverage but surface coverage affects the enthalpy of adsorption, then surface coverage must influence the cluster size, which then influences the average extent of solvation of a strand of bonded phase.
INTRODUCTION Chromatographers have extensively studied the nature of the surface of both derivatized and underivatized silica gel (I, 2). Much of the earlier work in this regard deals with the determination of total silanol group density but provides little understanding of the actual distribution of silanols on the surface. More recently, Lochmdler and co-workers (3-5)have investigated the distribution of the strands of bonded phases by luminescence studies and found evidence for a “patch model” in which the strands of the bonded phase are “not evenly distributed but rather clustered into regions of high density”. A similar conclusion is drawn from the body of chromatographic data presented herein. We previously have shown that one can markedly enhance the enantioselectivity of a chiral stationary phase (CSP) by converting the analyte enantiomers into bis-derivatives of the general class Z(CH,),,Z (6). Here, Z represents a moiety the 0003-2700/9 1/0363-00 16$02.50/0
chirality of which is “recognized“ by the CSP. If the moieties at either end of the bis-derivative interact independently with neighboring strands of the CSP, the binding energy of each enantiomer of the bis-derivative is approximately doubled relative to that of the corresponding enantiomer of a monoderivative, Z(CH2),H. This approximately doubles the difference in binding energy of the enantiomers of the bis-derivative, enhancing the observed enantioselectivity. The enantioselectivity noted for the members of a homologous series of racemic bis-derivatives depends upon the number of methylene groups, n, in the spacer chain. Retention is afforded by a blend of processes that involve interaction of the bis-derivatives with either one strand or two strands of bonded phase. The contribution of each process to the total retention is dependent upon the dimensions of the bis-derivative. What might be termed “the Goldilocks Effect” is operative, for the “bridging” process produces the greatest enthaplic contribution to retention when the bis-derivative is neither too long nor too short but is, rather, just right. This is illustrated in Figure l a where straight lines represent low-energy conformations of methylene chains and bent lines (Figure l b ) represent higher energy conformations. Other bridging modes might occur, but these would be less effective if they were to require energetically costly conformational changes in the phase and/or the analyte (Figure lb). It seemed likely that a homologous series of achiral bisderivatives might be used to probe the distribution of strand spacings of appropriately functionalized bonded phases, chiral or otherwise. In essence, the bis-derivatives are to be used as “molecular rulers”, and the quality of their fit (i.e., bridging ability) is to be determined from retention data.
EXPERIMENTAL SECTION Chromatography was performed by using either a Beckman Model lOOA pump, Altex 210 injector, Altex Model 152 detector (254 nm), and Kipp and Zonen BD 41 recorder or a Rainin Rabbit HPX pump, LDC UV Monitor D detector (254 nm), Reodyne injector, and a Altex Model C-RIA integrating recorder. The constant-temperature bath was made in-house and consists of an insulated vessel with stirrer, heater, and an electronic temperature controller (7). Approximately 1 m of 1/16-in.0.d. stainless steel tubing was used between the injector and the column, being coiled about the column as a heat exchanger. The flow rate of the pump was maintained at 1 mL/min to ensure thermal equilibration of the mobile phase before it reached the immersed column. The mobile phase in all experiments was a mixture of v/v 2-propanol in hexane prepared by using volumetric techniques. The time 0 1990 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 63, NO. 1, JANUARY 1, 1991
17
point were determined from the standard deviation of slope and intercept for AH and AS, respectively,in accordance with a 95% confidence level of the Student’s t test (IO). Data were collected at six or more temperatures from 0.00 to 80.00 “C.
too short
just
right
too long
RESULTS AND DISCUSSION To be employed successfully, the bridging technique described herein requires that the functionality on either end of the bis-derivative interact a t some specific site in each strand of bonded phase. Owing to our interest in CSP’s,the columns employed in this study are derived by hydrosilylation of enantiomerically pure N-(2-naphthyl)alanine 10-undecenyl ester with trichlorosilane, this material ultimately being bonded to 5-wm silica particles in varying amounts. The generalized structure of the bonded phases, shown in structure 1, oversimplifies the mode of linkage of the trifunctional silanes
/
W Flgure 1. Goldilocks Effect.
required, to,to pass a void volume of solvent through the column was measured at each temperature with dodecane used as a nonretained elution marker. The elution time of dodecane, to, decreases linearly with temperature, as would be expected from the greater differential thermal expansion of column, packing, and mobile phase. Because of the thermal expansion of the mobile phase, the linear flow rate within the column increases as the column temperature increases. The capacity factor, k’, of the analytes was evaluated by using the t o for each temperature. Chromatographic columns derived from 11-(triethoxysily1)-1undecanyl N-(2-naphthyl)alaninate were prepared by the reported varying amounts of the chiral silane being bonded procedure (8), to the silica. The columns studied are designated as I,, (0.30 mmol/g) and 1, (0.08 mmol/g) respectively of the (S)-N-(2naphthy1)alanine undecanyl ester chiral stationary phase bonded to 5-pm Spherisorb silica gel, affording surface coverages of 1.36 and 0.36 pmol/m2, respectively. All loadings were determined from elemental analysis performed by Tom McCarthy and associates, University of Illinois. After each column was packed, end capping was accomplished by pumping 10 mL of hexamethyldisilazane in 50 mL of methylene chloride through the column. Additional chromatographic columns derived from trichlorododecylsilane were prepared in the following manner. Rexchrome 5-pm silica gel (5 g) (Regis Chemical Co.) was dried through azotropic removal of water by refluxing benzene for 12 h. To the now dried mixture of silica gel and benzene, either 0.3 g or 1.0 g of trichlorododecylsilane (Aldrich Chemical Co.) was added dropwise with agitation. The slurry was allowed to stand for 1 h under a slow nitrogen purge. The derivatized silica gel was collected by filtration, washed thoroughly, and dried under vacuum. By elemental analysis, the silica portions are loaded with 0.08 and 0.15 mmol/g of the dodecylsilane, respectively. Each of the modified silicas was packed as a methanol slurry into a 4.6 X 250 mm column and end-capped as described above. The N,”-bis(2,4-dinitrophenyl)-a,w-diaminoalkane (bis-DNP’s) analytes used in this study are known from immunoassay research (9). Synthesis involves addition of excess l-fluoro-2,4-dinitrobenzene to dichloromethane solutions of commercial (Aldrich Chemical Co.) a,w-diamines of carbon chain length from 2 to 12. Each reaction mixture was washed with aqueous base to remove hydrofluoric acid and any phenols that may have been produced. Each crude product was filtered through silica to remove solids or highly polar impurities. The same procedure was followed for the preparation of the N-(2,4-dinitrophenyl)-n-alkylamines (mono-DNP’s) using the corresponding n-alkylamines of carbon chain lengths 1, 2, 3, 4, 6, 10, and 14. Data analysis was carried out on an IBM PC, using a basic linear regression program to determine AH, AS, and the correlation coefficients for the various In k’vs 1/T plots. Error bars for each
1 lh
(R)N2N
Ala. Und. (1.36 pmol/m2)
11
(2)N2N
Ala. Und. (0.36 pmol/m2)
to silica, these leading to some degree of polymeric bonding. The achiral analytes, N,N’-bis(2,4-dinitrophenyl)-cu,w-diamines, structure 2, are obtained by the action of 2,4-dinitrofluorobenzene on linear a,w-diamines.
2 Bridging ability is best determined not from retention alone but by study of the enthalpic and entropic components of adsorption energy. If a homologous series of bis-derivatives is chromatographed at several temperatures, the enthalpy, AH, and entropy, AS, of adsorption for each member of the series can be evaluated from a linear van’t Hoff plot of In k’vs 1/T (eq 1). Although one cannot dissociate AS from In (a is In k’= - A H / R T
+ A S / R + In
(1)
the phase ratio), when a series of analytes is chromatographed on the same column, the phase ratio is invariant and the shape of the A S vs n (the number of methylene groups in the bisderivative) curve is not affected. The curve is simply displaced vertically by the value of In a. The AH‘S and AS’S so determined are composite values influenced by the relative contributions of the bridging and nonbridging processes. The former will make the greatest contribution at a value of n such that the bis-derivative is able to interact simultaneously with adjacent strands of the bonded phase without enthalpically costly conformational changes in either the phase or the analyte. There is a distribution of interstrand spacings between near neighbors, so the shape of the plot of A H vs n is expected to reflect this distribution to some extent. Equation 2 was used to extract the desired thermodynamic parameters from the raw data. Here, AG, AH, and AS are
AG = -RT[ln k‘ + In @] = AH - T A S
(2)
18
ANALYTICAL CHEMISTRY, VOL. 63, NO. 1, JANUARY 1, 1991 -3
Table I. Thermodynamic Data for Mono-DNP's and Bis-DNP's"
Nb 1 2 3 4 6 10 14
mono-DNP's AH' AS^ -4.74 -4.47 -4.27 -4.21 -4.17 -4.14 -4.07
-12.0 -12.0 -12.0 -12.1 -12.3 -12.7 -12.8
7
-41
bis-DNP's nb
AHc
ASd
2 3 4 5 6 7 8 9
-6.80 -7.81 -8.28 -8.50 -8.47 -8.39 -8.29 -8.34 -8.14 -7.99
-13.2 -16.2 -17.7 -18.7 -19.1 -19.2 -19.3 -19.7 -19.4 -19.3
10
12
" Using the (R)-N-(2-naphthyl)alanine(0.30mmol/g) column, bNumber of methylenes in analyte chain. CIn kcal/mol. (cal/mol)/K.
,
io:
2
0
. , . , . ,
, . , .
4 6 8 10 12 n (Number of Methylenes)
1
Figure 2. AH vs n for bis-DNP's chromatographed on phases 1, and 1, with 20% v/v 2-propanoVhexane. lh.
the free energy, enthalpy, and entropy of adsorption, respectively, R is the gas constant, T i s the temperature, k'is the capacity factor, and is the phase ratio. From this equation, it follows that doubling the free energy of adsorption results in the squaring of the capacity factor (6). This is approximately the case when the capacity factors of weakly adsorbed monoderivatives, Z(CH2),H, are compared to those of the corresponding bis-derivatives. The usual observation is that the experimental value is greater than that expected from squaring the value observed for the monoderivative. The ability to "square" k ' depends on the bis-derivative's ability to bridge so as to double the energy of adsorption relative to a comparable monoderivative. More rigorously, AG can be expected to more than double through successful bridging. While AH doubles, A S does not since less entropy is lost with the secondary bridging interaction than with the initial docking. The enthalpy of adsorption of a bridging bis-derivative is essentially double that of the corresponding monoderivative (Table I). The maximum (negative) value of AH occurs for the bis-DNP's when n = 5. The ratio of this AH to that of the analogous N-(2,4-dinitrophenyl)aminoalkane,hereafter termed mono-DNP's is 2.03 (extrapolating between the butyl and hexyl analogues). This ratio is reduced as the length of the bis-derivative decreases. At n = 2, the ratio is 1.52, signifying a lesser ability of the shorter bis-derivatives to bridge. The same trend is not observed for A S because the initial adsorption of but one end of a bis-derivative entails a greater entropy loss than does the second bridging interaction. One must bear in mind that the AH and A S values being determined encompass all changes that attend the adsorption of the analyte. These changes involve the stationary phase as well as the analyte. Changes in the extent of solvation of a strand of stationary phase upon interaction with a bis-derivative are presumably about the same regardless of whether that strand is involved in the initial docking or the secondary bridging interaction. Hence, changes in the extent of solvation of the stationary phase during interaction with the analyte will shift the AH vs n curves vertically but will presumably have little affect upon the shape of the curve. A similar but less justifiable assumption concerning entropy loss leads one to conclude that changes involving the stationary phase will again shift the A S vs n plots vertically but will have little affect upon the shapes of the curves. The changes in the extent of solvation of a DNP group on interaction with a strand of bonded phase is presumably about the same for the initial docking as for the secondary bridging interaction. Figure 2 shows the plots of AH vs n for the bis-DNP's as determined on columns 1 h and 11,which differ only in the amount (0.30, and 0.08 mmol/g, respectively) of the silane
2 3 --
0
2
4
6
8
1 0 1 2 ' 4
n (Number of Methylenes)
Figure 3. A S vs n for bis-DNP's chromatographed on phases 1, and 1, with 20% v/v 2-propanoVhexane. bonded to the silica. By use of an initial surface area of ca. 220 m2/g, the surface coverage of 1 h is 1.36 pmol/m2 and that of 1, is 0.36 pmol/m*. Both columns were end-capped with hexamethyldisilazane after packing. The mobile phase used to generate the data in Figure 2 was hexane containing 20% v/v %propanol. From both AH vs n curves ( 1 h and l l ) , one sees that AH is most exothermic when n = 5 and that the exothermicity of adsorption is greater for column l h . Figure 3, the A S + In @ vs n plots, shows that entropy loss is also maximized a t n = 5 but changes little thereafter. What mechanistic inferences can be drawn from these data? From the similarity of the shapes of the AH vs n plots, one infers that the most probable interstrand distance is essentially the same for both of the columns. This seemingly supports the existence of Lochmiiller's "patches" and indicates that the strands are not spread evenly over the surface. Otherwise, the phase of lowest surface coverage would have its strands furthest apart, and optimal bridging would require a longer bis-derivative. Further, the fact that both columns show optimal bridging with the same bis-derivative indicates that the difference between phases of different surface coverages is possibly the number and certainly the diameter of the otherwise similar patches. If the patches have similar distributions of strand spacings, why does AH depend upon surface coverage? One possible reason is that differing surface coverages lead to a different blend of mixed mode retention by the silane strands and the residual silanols on the surface. To investigate this, two columns, 31and 3,,, differing in the amounts of trichlorododecylsilane bonded to silica (0.08 and 0.16 mmol/g, respectively) were used to represent, as closely as possible, the type 1 phase without the chiral moiety at the end of each strand. Thus, the contribution to analyte retention from the residual silanols in the type 3 columns should model that of the residual silanols in type 1 columns. Table I1 provides retention data for the bis-derivatives on 31,3h, 11, and 1 h at 25.0 OC. From the retentions noted on 3] and 3h, it can be inferred that analyte retention by residual silanols on the 1 h phase is insignificant, leading to less than 0.5% of the total retention.
ANALYTICAL CHEMISTRY, VOL. 63, NO. 1, JANUARY 1, 1991
19
Table 11. Chromatographic Data for Bis-DNP’s” k’ nb
31
3h
11
lh
2 3 4 5 6 7 8 9 10 12
0.56 0.53 0.67 0.62 0.55 0.43 0.28 0.19 0.15 0.13
0.44 0.50 0.52 0.49 0.45 0.26 0.23 0.14 0.11 0.06
5.18 6.30 6.41 5.54 3.95 3.82 3.19 2.70 2.38 2.02
137.2 170.1 175.2 151.8 120.9 96.9 80.1 69.5 59.6 48.5
-6 0
Table 111. Thermodynamic Data for Bis-DNP’s” 11
3h
lh
nb
AH
AS
AH
AS
AH
AS
AH
AS
2 3 4 5 6 7 8 9 10 12
-3.95 -4.83 -5.97 -6.09 -6.55 -7.94 -6.60 -6.85 -6.73 -6.48
-13.8 -17.6 -21.1 -21.8 -23.4 -29.0 -24.8 -26.3 -26.5 -26.3
-4.24 -5.15 -6.20 -6.57 -6.96 -8.07 -6.44 -6.56 -6.75 -6.57
-15.8 -18.9 -22.2 -23.7 -25.2 -30.0 -24.7 -25.9 -27.0 -27.5
-3.60 -5.67 -6.10 -6.39 -6.38 -6.36 -6.26 -6.11
-8.9 -15.5 -16.9 -18.2 -18.5 -18.8 -18.9 -18.7 -18.5 -18.2
-6.80 -7.81 -8.28 -8.50 -8.47 -8.39 -8.29 -8.34 -8.14 -7.99
-13.2 -16.2 -17.3 -18.8 -19.1 -19.3 -19.3 -19.8 -19.4 -19.3
-6.00
-5.79
4 6 8 10 1 2 14 16 18 n (Number of Methylenes)
Figure 4. AH vs n for mono-DNP’s chromatographed on 1, and 1, using either 10% or 20% v/v 2-propanollhexane as a mobile phase.
“All chromatographic data collected at 25 O C with 20% v/v 2propanol/hexane Number of methylenes in analyte.
31
2
a All chromatographic data collected with 20% v/v 2-propanol/ hexane. Number of methylenes in analyte.
For phase 11, the contribution to the overall retention by residual silanols cannot exceed ca. 9% of the total. Can such a modest contribution to the total retention significantly influence the observed AH‘S for column ll? To better understand this point, retention data for the bis-derivatives were collected by using phases 3] and 3h a t several other temperatures. The thermodynamic values calculated from this retention data are presented in Table 111. Interestingly, the AH values for the two dodecyl columns are quite similar, differing by less than 10% for a given bis-derivative, and fall between the corresponding values noted for phases lIand l h . The relatively similar AH‘S noted on phases lIand 31 allow one to conclude that even if ca. 9% of the retention of the bis-derivatives stems from residual silanols in phase 11,the overall AH will be little affected. Hence, one concludes that the substantial differences (ca. 2.2 kcal/mol) in the AH‘S observed on 11 and l h do not have their origins in retention by residual silanols. Another plausible explanation for the vertical offset of the AH vs n plots is that AH is influenced by the size of the patch. We know that phase &, cannot differ from lIby simply having a greater number of identical patches. If so, there would be no offset in the AH plots. Phase 1 h must have larger patches and these have a higher proportion of interior strands than do small patches. Because adjacent strands tend to buttress one another, solvation by the mobile phase is expected, for steric reasons, to occur more extensively for exterior strands than for interior strands. Strands in small patches will, on average, be more extensively solvated, and adsorption of an analyte will entail more extensive desolvation. This is energetically costly and leads to a reduction in both the exothermicity and entropy loss observed for analyte adsorption. The shape of the AS vs n plots for columns 1 h and 11,Figure 3, are quite similar and are as might be anticipated. Optimal bridging leads to the maximum loss of entropy. Although the
bis-derivatives of n > 5 bridge less effectively, they lose more entropy when they do bridge simply because they are longer. Hence, the comparative invariance of the A S values for the bis-derivatives having n = 5 or more is rationalized. The vertical displacements of the curves stem at least in part from the different values of In +, from differing extents of solvation, and from “buttressing” by neighboring strands. A larger patch of bonded phase, having a greater proportion of interior strands, is expected to be more organized and rigid. Hence, an analyte docking a t a “rigid” site would lose more degrees of freedom than one docking a t a “flexible” site. Moreover, larger patches, being less effectively solvated than small patches, undergo less desolvation on analyte adsorption and return less 2-propanol to the bulk mobile phase. This means that the overall entropy loss associated with analyte adsorption is expected to be greater for phases having large patches than for phases having small patches of bonded phase. Earlier, it was suggested that the greater exothermicity of bis-derivative adsorption on 1 h than on 11 stems from less desolvation during analyte adsorption owing to the lower level of solvation of l h . If correct, this argument would require similar chromatographic behavior for other analytes. Accordingly, a series of N-(2,4-dinitrophenyl)alkylamines (mono-DNP’s) was examined. Figure 4 shows the AH vs n plot obtained by using 1 h and 11 with 10% and 20% v/v 2-propanol/hexane. The AH vs n plots show that, as n increases, there is a marked decrease in exothermicity for the first several members of the series but little change in exothermicity for the later members. The point a t which the inflection occurs is influenced somewhat by the surface coverage as are the values of AH. The shapes of these curves suggest that the alkyl portion of the analytes interacts sterically with neighboring strands of bonded phase. These interactions become more severe until n reaches ca. 4-5 but change little thereafter, presumably because the additional methylene groups are now deflected away from the stationary phase into the bulk mobile phase. These steric encounters are more likely to occur during interaction with interior strands than with exterior strands, thus causing the sharper inflection in the phase having the greatest surface coverage owing to its higher proportion of buttressed interior strands. In the 20% 2-propanol/hexane mobile phase, the AH values from the 1 h curve are 1to 1.5 kcal/mol more exothermic than those of lI. This displacement is about half of that noted for the dianalytes and is again attributed to differences in the average extent of solvation of the two phases. If desolvation effects are responsible for the reduced exothermicity noted on column l h , one would expect the major portion of this effect to come from the 2-propanol rather than the hexane. Accordingly, the mono-DNP’s were reexamined when 10% rather than 20% 2-propanol is used in the mobile phase. The relevant AH vs n plots are also shown in Figure 4. Little change in AH occurs for the 1 h phase with the reduction in 2-propanol concentration, consistent with a modest
20
ANALYTICAL CHEMISTRY, VOL. 63,NO. 1, JANUARY 1, 1991 10,
T
- 16
0
2
T
I
1 1 6 S 10 12 1 4 1 6 18 n (Number of Methylenes) 4
AS vs n for mono-DNP’s chromatographed on 1, and 1, using either 10% or 20% v/v 2-propanol/hexane as a mobile phase.
Figure 5.
degree of solvation of the buttressed strands in either mobile phase. However, reduction of the 2-propanol concentration causes the enthalpies of adsorption on l1to become significantly more exothermic, consistent with a greater extent of solvation relative to phase l h . The reduction in 2-propanol concentration could also reduce the extent of solvation of the mono-DNP’s, thus reducing the extent of their desolvation upon adsorption. This would increase the adsorption exothermicity for both stationary phases, but this increase in exothermicity is expected to occur to roughly the same degree for both phases. Hence, the changes in enthalpy noted in decreasing the 2-propanol concentration are principally attributed to the differing extents of solvation of the differently sized patches of bonded phase present in 1 h and lI. Figure 5 displays the plots of A S vs n for the mono-DNP’s using both 10% and 20% 2-propanol in the mobile phase for phases 1 h and lI. Note that the two curves for the lhphase undergo but a modest vertical shift as the 2-propanol concentration is reduced. However, the two curves for the l1phase are substantially shifted. The 1, phase undergoes little change in the extent of analyte-promoted desolvation when the 2propanol concentration is reduced since it is relatively less solvated in either case. However, the 1, phase, being less solvated by 10% 2-propanol than by 20%, undergoes less analyte-promoted desolvation in the former instance. The
lesser desolvation increases the loss of entropy upon analyte adsorption, thus accounting for the change in the relative positions of the two curves. In order to apply the finding that the most probable strand spacing corresponds to that optimal for bridging by a bis-DNP having five methylene groups, one needs to know the conformation of the bis-derivative during bridging. Is it extended with coplanar rings or is it flexed with some dihedral angle between the rings? In the former case, the distance between the centers of the rings is ca. 12.4 A when n = 5. This represents the upper limit for the effective length of this bis-DNP, and conformational changes of the bis-DNP’s could reduce this distance. Clearly, the use of more rigid “molecular rulers” or more rigid connecting arms for the stationary phase would aid in answering questions of conformation during bridging. Since the interstrand distance, which actually influences the experimental data, is the distance between the functionalized ends of the strands and not the distance between their points of attachment to silica, the use of phases having connecting arms of differing lengths may also provide useful information concerning the “stiffness” of the bristles of a brushlike phase.
ACKNOWLEDGMENT We are grateful to C. H. Lochmuller and G. Vigh for helpful discussions.
LITERATURE CITED Synder, 13.;Ward, J. J. Phys. Chem. 1068, 70, 3941. Berendsen, G. E.: de Gaian, L. J. Llq. Chromatogr. 1078, 7 , 403. Lochmuller, C. H.; Colborn. A. S.: Hunnicutt, M. L. Anal. Chem. 1083, 5 5 , 1344. Lochmuller, C. H.; Hunnicvtt, M. T. J. Phys. Chem. 1086, 90, 4318. Lochmuller, C. H.; Kersey, M. T. Anal. Chem. 1088, 60, 1910. Pirkle, W. H.: Pochapsky, T. C. Chromatographia 1988, 2 5 , 652. Anderson, R. W. J. Chem. Educ. 1967, 44, 569. Pirkle, W. H.; Pochapsky, T. C.; Mahler, G. S.; Corey, D. E.; Reno, D. S.: Alessi, D. M. J . Org. Chem. 1988, 57, 4991. Valentine. R. C.; Green, N. M. J. Mol. Biol. 1087, 2 7 , 615. Davis, R. B.; Thompson, J. E.: Pardue, H. L. Clin. Chem. 1078, 2 4 , 611.
RECEIVED for review July 2, 1990. Accepted October 8, 1990. This work has been supported by a grant from the National Science Foundation.
