Anal. Chem. 1994,66, 211-215
Analysis of Mixtures Based on Molecular Size and Hydrophobicity by Means of Diffusion-Ordered 2D NMR Kevin F. Morris,+ Peter Stiibs,’v* and Charles S. Johnson, Jr.’it Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, and Department of Physical Chemistry, Royal Institute of Technology, S- 700 44 Stockholm, Sweden Diffusion-ordered 2D NMR spectroscopy (DOSY) has been applied to the analysis of aqueous mixtures. Pulsed field gradient NMR (PFG-NMR)experiments were performed with special provisions for minimizing the effects of pulseinduced eddy currents and with sample spinning during the data acquisition period. The PFGNMR data sets were processed with the data inversion program SPLMOD to resolve and identify the solutes on the basis of diffusion coefficients that normaUy are related to molecular size. Contour plots were then constructed in which conventional 1D NMR spectra were displayed in one dimension and diffusion spectra in the other. Complete resolution of molecular species was obtained except when two components had essentially identical diffusion coefficients. The addition of surfactants at concentrations above their critical micelle concentrations permitted solutes to be resolved on the basis of their degree of solubilizationin the micellesformed. Do6Y is shown to be a powerful tool for the study of equilibria involvingbinding, absorption,and partitioning in more complex systems than previously considered accessible by conventional PFG-NMR methods. Diffusion-ordered 2D N M R spectroscopy (DOSY) combines the selectivity of high-resolution N M R with characterization on the basis of molecular diffusion c~efficients.l-~ When DOSY is applied to a mixture, the conventional N M R spectrum is displayed in one dimension while the “diffusion spectrum” is displayed in the other dimension. The diffusion spectrum consists of peaks whose positions and widths indicate the diffusion coefficients and their estimated errors, respectively. This amounts to resolution of N M R spectra on the basis of molecular sizes since according to the Stokes-Einstein equation the tracer diffusion coefficient of a molecule is inversely proportional to the molecular r a d i u ~ .There ~ is a wealth of physicochemical information available from pulsed field gradient N M R (PFG-NMR) experiments (see ref 4), and the main purpose of DOSY-like methods is to extend the applications to more complex systems. The essence of DOSY is the display of all of the chemical shifts and diffusion constants for a mixture simultaneously so that species with different sizes can be identified. At a given chemical shift the experimental data set is identical to that obtained in a state-of-the-art PFG-NMR experiment. The complete 2D data set is obtained with no additional cost in University of North Carolina. Royal Institute of Technology. (1) Morns, K.F.; Johnson, C. S.,Jr. J . Am. Chem. Soc. 1992,114,3139-3141. ( 2 ) Morris, K.F.; Johnson, C. S.,Jr. J. Am. Chem. Soc. 1993, 115,42914299. (3) Hinton, D.P.;Johnson, C. S.,Jr. J. Phys. Chem. 1993, 97, 9064-9072. (4) Stilbs, P. Prog. N u c l . Magn. Reson. Specrrosc. 1987, 19, 1-45. t
0003-2700/84/0366021 I$04.50/0 Q 1894 Amerlcan Chemlcal Soclety
time, and the transformation of the diffusion data into diffusion spectra then gives “at-a-glance” recognition of the nature of complex mixtures. Thus, DOSY provides a map of the chemical shift/diffusion domain that reveals regions requiring more detailed study. The “engine” in DOSY is the PFGN M R experiment, and the transformation of N M R signal intensities versus gradient pulse areas into diffusion spectra is based on standard, widely available computer algorithms. We expect that the PFG-NMR experiment will be improved and that the transformation algorithms will be upgraded, but the basic idea of an automated experiment with data inversion to produce a DOSY display will continue to be useful. Thus, DOSY extends rather than replaces PFG-NMR. We have found that DOSY is especially useful for the study of systems involving assemblies such as micelles, microemulsion droplets, and vesicles. It should be noted that, even though DOSY has some ability to resolve different size components a t the same chemical shift, it is especially accurate and powerful for analyzing unknown mixtures when all peaks are resolved on the chemical shift axis. The peaks are then ordered on the basis of molecular size, and molecular aggregation and assembly is revealed. Without DOSY, the assignment of even well-resolved peaks in a complex mixture is not always obvious. In DOSY, the diffusion spectra are obtained by approximate inverse Laplace transforms (ILT) of data sets from PFG-NMR experiments. Unfortunately, the ILT is an illconditionedtransformation, and even under the best conditions, the amount of information that can be obtained is limited. If the N M R intensity at a given chemical shift results from a single molecular species, the diffusion coefficient can usually be determined within a few percent. However, when the intensity contains contributions from two or more molecular species, accuracy decreases and the analysis may become intractable. In particular, experience shows that diffusion coefficients differing by a factor of less than 2 cannot reliably be resolved even with high signal-to-noise ratios, and analyses reporting three or more diffusion coefficients are subject to large errors.* In spite of these limitations, DOSY turns out to be very useful because of the extreme selectivity of the N M R experiment. Consider two types of mixtures. The first contains a number of ionic or molecular solutes in a solvent of low viscosity. We refer to this as a discrete mixture since a small set of concentrations and diffusion coefficients suffices for its description. Even though the diffusion coefficients for the different species may be closely spaced, it is possible that complete resolution in the N M R dimension will remove the necessity for complicated data analyses, Le., only singleAnalyticel Chernbtry, Vol. 66, No. 2, January 15, 1994 211
exponential fits will be required. The second type of mixture contains polydisperse components with a wide range of sizes. This type of mixture requires continuous distributions of diffusion coefficients rather than discrete values for its description. Most of our attention has focused on this area.2*3 Examples are polymer solutions and supramolecular mixtures containing aggregates, e.g., micelles, microemulsion droplets, and vesicles. In the case of phospholipid vesicles, the size distributions obtained with DOSY were shown to compare favorably with the results obtained by electron microscopy and dynamic light ~ c a t t e r i n g . Note, ~ however, that fast chemical exchange processes may cause such systems to appear monodisperse, as shown below for micelles. DOSY often succeeds for polydisperse samples because of the wide range of diffusion coefficients and theavailability of powerful analysis program~.~s59~ The experimental methods and details of the analyses for both discrete and continuous distributions of diffusion coefficients have been described in detail elsewhere.2 For both discrete and continuous distributions, computer programs have been devised that contain data analysis algorithms as well as information theoretic rules for rejecting questionable solutions. When unknown samples must be analyzed, the recommended procedure is to assume continuous distributions of diffusion coefficients. A computer program based on CONTIN,5,6a regularized least squares analysis, can then be used to generate the 2D DOSY display. However, when there is reason to believe that only discrete components are present, algorithms such as SPLMOD can be used to determine sets of solutions consistent with the data.7-8 As described below, this necessitates the implementationof rejection criteria to avoid artifacts arising from the ill-conditioned nature of the solutions. The purpose of this report is to demonstrate the effectiveness of DOSY in the analysis of discrete mixtures involving chemical equilibria. Thesystemschosen for this demonstration exhibit solubilization equilibria that have been extensively studied by FT-PFG-NMR, the immediate predecessor to DOSY.4 Previous work on solubilization has recently been r e ~ i e w e d Thedata .~ reported here areconsistent with previous work; however, the point of this paper is not the quantification of solubilities. We use the recently developed stop-and-go spinner system to enhance resolution in the PFG-NMR experiments in order to minimize overlap of signals from different species.I0 Also, the hydrophobicity of the solutes is used as a handle to tune their effective diffusion rates. This is effected through the introduction of the surfactants, sodium dodecyl sulfate (SDS) or dodecyltrimethylammonium bromide (DTAB), that form micelles. The various solutes partition into the micelles according to their relative solubilities in water and hydrocarbon media, but undergo rapid exchange between the bulk solution and the interior of the micelle. Under such conditions, PFG-NMR experiments report only the time~
~~~
( 5 ) Provencher, S . W. Comput. Phys. Commun. 1982, 27, 213-227. (6) Provencher, S.W. Comput. Phys. Commun. 1982, 27, 229-242. (7) Provencher, S.W.; Vogel, R.H. In Numerical Treatment of Inverse Problems in Differnetial and Integral Equations; Deuflhard, P., Hairer. E., Eds.; Birkhauser: Boston, MA, 1983; pp 304-319. ( 8 ) Vogel, R. H. SPLMOD Users Manual, Technical Report DAOb; European Molecular Biology Laboratory: Heidelberg, 1983. (9) Stilbs, P. In Solubilization; Christian, S . H., Scamehorn, J. F., Eds.; Marcel Dekker: New York, 1994. (IO) Wu, D.; Woodward, W. S.;Johnson, C. S.,Jr. J.Magn. Reson., Ser. A 1993, 104. 231-233.
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averaged diffusion coefficient for each species. Therefore, for the j t h solute the observed diffusion coefficient Dj is described
+
Dj = pjDjmiC ( 1 -pj)DJf'ee
wherepj is the degree of solubilization and D,miC and Df, are the tracer diffusion coefficients for solubilized and free molecules, respectively. It is important to note that the radius of the micelle is much smaller than the diffusion distance in the PFG-NMR experiment so that diffusion within the micelle is not detected; Le., Djmicis equal to the diffusion coefficient of the micelle." Since the concentration of the surfactant is much greater than the critical micelle concentration (cmc), DjmiC is also equal to the diffusion coefficient of the surfactant. According to eq 1, the apparent diffusion coefficient of a solute can be varied by changing the concentration of the surfactant and thus the degree of solubilization. Our focus here is the resolution of mixtures; however, the DOSY experiment can also be used to determine simultaneously the degrees of solubilization of a number of solutes. It thus extends the field of application of FT-PFG-NMR solubilization experiments4Jl to more complex systems. We note that there is also an N M R paramagnetic relaxation approach to the study of micellar s o l ~ b i l i z a t i o n .N~M ~ R relaxation methods give data sets that can also be analyzed and displayed in 2D. However, the various resonances for a single species will not have the same relaxation times and will not line up to give a 1D N M R spectrum as in DOSY. We emphasize that the DOSY experiments reported here provide complete resolution of mixtures and permit the partitioning of a number of solutes to be evaluated in a single experiment. This is expected to be of value in the study of a variety of "smart" polymers that are designed to selectively incorporate 1iga11ds.l~In general DOSY provides a convenient method for the study of equilibria involving binding, absorption, and partitioning.
EXPERIMENTAL ASPECTS Materials and Sample Preparation. Anhydrous methyl alcohol and analytical grade isopropyl alcohol were obtained from Mallinckrodt, and ACS grade toluene and benzyl alcohol were supplied by Fisher Scientific. Sodium dodecyl sulfate (SDS) (98%), dodecyltrimethylammoniumbromide (DTAB), 1-pentanol (99+%), neopentyl alcohol (99%), and tetraethylene glycol (TEG, 99%) were obtained from Aldrich. 2-Methyl-2-propanol (98%) was purchased from E M Science, and Aaper Alcohol and Chemical Co. provided ethyl alcohol (95%). All chemicals were used without further purification, and samples were prepared gravimetrically in deuterium oxide (99.9% D) purchased from Cambridge Isotope Laboratories. PFG-NMR Spectrometer. The DOSY experiment has also been described in detai1.2J A Bruker AC-250 spectrometer with a custom-built I 0-mm probe (Cryomagnet Systems, Inc.) was used in all of the N M R experiments. The probe was ( 1 1) Stilbs, P.J . Colloid Interface Sci. 1982, 87, 385-394. ( 1 2 ) Johnson, C. S..Jr. J . Magn. Reson., Ser. A 1993, 102. 214-218. (13) Gao, 2.; Wasylishen, R.E.; Kwak, J. C. T. J . Phys. Chem. 1989, 93, 219&
2192. (14) Newkome,G.R.;Young,J.K.;Baker,G.R.;Potter,R.L.;Audoly,L.;Cooper, D.; Weis, C . D.; Morris, K. ; Johnson, C . S . , Jr. Macromolecules 1993, 26, 2394-2396.
Flpure 1. (a) Radio frequency pulses and free induction decay (FID) for the LED pulse sequence. and (b) matched gradient pulses and the sample spinning rate. The gradient pulses shown in (b) represent the last two pulses in a train of five matched and equally spaced pulses. Phase cycling and sometimes homospoil pulses during T. are used to suppress secondary echoes
equipped with an actively shielded gradient coil15having a coil constant of 0.156 T m-I A-I and designed to minimize eddy currents. The gradient driver, which provides gradient pulses with areas reproducible to 1 part per million, has been described elsewhere.16 Also, the magnet was equipped with a computer-controlled sample spinner system so that the sample could be held stationary during the critical diffusion time A and then spun at approximately 20 Hz during the data collection period as shown in Figure 1 . l o This resulted in a 5-fold decrease in N M R line widths (from 3 to approximately 0.5 Hz) in the PFG-NMR experiments and permitted resolution of most of the signals from mixtures in this study. The gradient pulses disturbed the deuterium lock signal, and the slow reacquisition of the lock signal accounts for most of the remaining line width. All measurements were made a t (25 i 1) o c . Data Acquisition and Conversion. All experiments were performed with the longitudinal eddy current delay (LED) pulse sequence to avoid artifacts resulting from residual eddy Figure I illustrates this sequence and defines the important parameters. For each DOSY data set, the timing parameters r, A, and T. were held constant and the PFGNMR experiment was repeated for various values of K = 786, where y is the magnetogyric ratio and g and 6 are the gradient pulse amplitude and duration, respectively. The FIDs were acquired with an Aspect 3000 computer, and the complete set of 30-50 FIDs was transferred to a Silicon Graphics 4D-25 orINDIGO(MIPSR4000) WorkstationviaEthernet by means of the transfer program BRUKNET. Apodization, Fourier transformation, phasing, and polynomial baseline corrections were performed with the N M R software package FELIX 1.1 (Hare Research, Inc.) to give a data set of the form
where Aj(u) is the one-dimensional N M R spectrum of the j t h diffusing species when K = 0 (taking into account transverse and longitudinal relaxation), Dj is the associated tracer diffusion coefficient, and NAis the number of components required for the fit. The analysis consists of determining the best set of Aj. Dj values for those regions of the spectrum where the intensity ~~~
(1S)Gibba. S. J.; Morris, K. F.; Johnson. C.S.,Jr. J. Ma@. Rcson. 1991, 94,
exceeds a predetermined threshold. This was accomplished with the data inversion program SPLMOD, which permits parallel processing of Nd data sets.’.8 Spectral regions containingmore than IOOadjacent pointsabove the threshold were divided prior to analysis into smaller regions each with an equal number of points. Each point in the N M R spectrum is associated with 2&30 intensities acquired with different values of K and 6. Note that the ill-conditioned nature of this problem means that it is not sufficient to fit the data! One must also make intelligent use of all available information to select the most likely solution. This includes prior knowledge thattheamplitudesanddecayconstantsin theLEDexperiment are nonzero and that the decay kernels have an exponential dependence on R. We also know the range of physically acceptable diffusion coefficients, the range of diffusion coefficients accessible to the PFG-NMR experiment, and the resolving power of the SPLMOD analysis. Thus, the current set of acceptability criteria includes the following: ( I ) Diffusion coefficients must be feasible and experimentally accessible. (2) Standard errors in diffusion coefficients reported by SPLMOD must be less than 30%. (3) Diffusion coefficients of components at the same chemical shift must differ by a factor of more than two. These rules have evolved through trial and error with simulated data and with experimental data sets. They are conservativeandaredesigned to reject frequently occurring artifacts. The analysis proceeds as follows. The user specifies an integer Nwhich is thelargest permittedvalueofNA, thenumber of exponential components in the fit. SPLMOD then returns N sets of solutions that include the best fit based on N exponential components, the best fit based on N - I components, etc. If the fit with Ncomponents fails to meet the criteria, it is rejected and the tit with N - 1 components is tested. This continues until either an acceptable solution with Nhcomponents is found or all solutions are rejected. In particular, this procedure guards against the proliferation of componentssince theaddition ofa component usually improves the fit but a t the price of violating the third criterion. Even with these precautions spurious lines are sometimes encountered, as for example in the “cross-talk” effect.2 However, that complication is usually associated with analyses involving threeor morecomponents,andinthepresent work,a maximum of two components was permitted. The list of criteria can, of course, be expanded to make use of other obvious features of NMRspectra. Forexample,complicated molecules havemore than one resonance line, and an isolated or unaccompanied line a t a specific diffusion coefficient is therefore suspect. Once a solution meeting the above criteria has been found in each spectral region, the DOSY display is generated with normalized Gaussians having center positions and intensities equal to the diffusion coefficients and amplitudes determined by SPLMOD, respectively. Therefore, the DOSY plot has the form NA
F(D.4 = c A j ( W j ( D )
(3)
j=1
where
165-169. (16) Bocrncr. R. M.;Wmdward. W. S.3. Mag”. Reson., SI,.A, in pms. (I7)Gibbs. S. J.; Johnran, C. S.. Jr. J. M a p . Reson. 1991, 93. 30s-402.
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Here uj is the standard deviation reported by SPLMOD plus the estimated systematic error for the complete data set, typically 4% of the diffusion coefficient. Inclusion of the extra line width is necessary because analyses of different NMR multiplets for the same diffusing species give slightly different diffusion coefficients but usually within 4% of the average value. The extra or minimum line width permits smooth projections to beobtained on thediffusion axisand realistically reflects errors in the measured diffusion coefficients.
RESULTS AND DISCUSSION As the first example, we consider a mixture containing 5.0 mM methanol, 10.0 mM ethanol, and 10.0 mM n-pentanol in DzO. The DOSY parameters were 6 = 1 ms, 7 = 3.5 ms, A = 100 ms, and T, = 50 ms, and 22 spectra were collected with K values ranging from 209 to 3.94 X IO3 cm-I. The analyses were performed with N = 2, and the resulting DOSY display is shown in Figure 2a. The four components resolved at the diffusion coefficients 1.80 X 1.34 X 1.02 X and 7.30 X IOd cm2s-l are assigned to HOD,methanol, ethanol, and n-pentanol, respectively. The diffusion coefficients here are so closely spaced that the resolution of any pair would be difficult if they contributed a t the same chemical shift. The advantage of high resolution is illustrated in Figure 2b, which shows an enlargement of the spectral region 3.2-3.6 ppm where ethanol and n-pentanol contribute. Complete resolution in the diffusion dimension is possible since there is little overlap. If any pair of lines overlapped here, criterion three would ensure a singlecomponent fit at a diffusion coefficient between the true values. This isolated value would conflict with the other values and could be discounted. We also note that the integrated intensities in narrow bands centered on the dotted lines in Figure 2a give 1D NMR spectra for the various components. The coupling patterns can be identified and the spectra assigned, but the relative intensities of the lines may be altered 214
AnalyticalChemlsrry, Vol. 66, No. 2, January 15, 1994
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by transverse relaxation during the time intervals 7 and longitudinal relaxation during T + T,. In Figure 2 the diffusion coefficients alone suffice to distinguish all of the components. That is not always the case, and Figure 3a shows an example in which nearly identical diffusion coefficients preclude the resolution of 2-methylpropanol and neopentanol. This mixture contains 5.0 mM methanol, 10.0 mM 2-propanol, 10.0 mM 2-methylpropanol, and 10.0 mM neopentanol in DzO, and the DOSY data set was collected with the same parameters used in the previous experiment. The SPLMOD analysis gives diffusion coefficients at 1.89 X 1.32 X 8.74 X lod, and 7.40 X 10" cm2s-l, which we assign to HOD, methanol, 2-propanol, and 2-methylpropanol/neopentanol,respectively. Complete resolution of this mixture was effected by the addition of 0.150 M DTAB as shown in Figure 3b. The DOSY parameters were the same as in the previous experiment except that 6 = 1-2 ms and 28 spectra were collected with K values ranging from 208 to 8.34 X lo3 cm-I. Also shown in Figure 3b are values o f p for methanol (0.1 l ) , 2-propanol ((0.18), 2-methylpropanol (0.23), and neopentanol (0.53) obtained by the solution of eq 1, In this calculation the values of DPW were obtained from the DTAB-free solution (Figure 3a), and the values of D,miC were set equal to the diffusion coefficient measured for DTAB. The presence of DTAB micelles is ensured by the concentration of DTAB and is verified by the measured diffusion coefficient. Parts a and b of Figure 4 show DOSY displays for a mixture containing 10.0 mM toluene, 10 mM benzyl alcohol, and 10 mM tetraethylene glycol in D20 without and with 0.150 M SDS, respectively. The DOSY parameters and K values for Figure 4a,b were the same as those for Figure 3a,b, respectively.
reversal in the order of the diffusion coefficients when SDS is added. In particular, in the presence of SDS the diffusion coefficient for toluene shifts to 1.29 X 10-6cm2s-l while benzyl alcohol and TEG undergo modest changes to 3.00 X 1odand 3.95 X 10-6 cm2 s-I, respectively. This is of course a consequence of the varying degrees of solubilization of the solutes. We find the p values to be 0.33, 0.67,and 0.92 for benzyl alcohol, toluene, and toluene, respectively. In conclusion, DOSY with sample spinninggives automated resolution of most simple mixtures and identification of solutes on the basis of molecular size alone. The addition of a surfactant above its critical micelle concentration can increase the separation of the average diffusion coefficients for solutes having different solubilities in the micelles. Thus, molecules can also be resolved on the basis of their hydrophobicities. We find that DOSY is a powerful tool for the study of complex reaction mixtures where reactants must partition into micelles. This work taken with DOSY studies of polydisperse samples suggests that DOSY has analytical significance. Flguro 4. (a) DOSY display processed with SPLMOD for a mixture COntalning 10.0 mM toluene, 10 mM benzyl alcohol, and 10 mM tetraethybne glycol h D20and (b)DOSY display for the same solute concentrations plus 0.150 M SDS.
The SPLMOD analysis for the SDS-free mixture gives 1.87 X l k 5 , 1.02 X l k 5 , 8.02 X 10-6, and 5.63 X 10-6 cm2 s-l, corresponding to HOD, toluene, benzyl alcohol, and TEG, respectively. A point of interest in this illustration is the
ACKNOWLEDGMENT This work was supported in part under National Science Foundation Grant CHE-9222590 (C.S.J.), North Carolina Biotechnology Grant 9212-ARG-0901 (C.S.J.), and the Swedish National Research Council, N F R (P.S.). Received for review August 23, 1993. Accepted October 29, 1993.' Abstract published in Adoance ACS Absrrocts, December 1 , 1993.
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