(12) G. W. Hepner, Gastroenterology, 67, 1250 (1974). (13) J. D. Welsh, 0. M. Zschiesche, V. L. Willits, et al., Arch. htern. Med., 122. 315 11968). (14) D. P. Bose and J. D. Welsh, Am. J. C/in. Nutr., 26, 1320 (1973). (15) D. J. Finney, “Statistical Methods in Biological Assay”, Charles Griffin and Co., Ltd.. London, 1964. (16) E. J. Purceli, “Calculus with Analytical Geometry”, Meredith Publishing Co., New York. 1965. (17) C. H. Hartmann and K. P. Dimick, J. Gas Chromatogr., 4, 163 (1966).
(18) D. H. Calloway, E. L. Murphy, and D. Bauer. Am. J. Dig. Dis., 14, 811 (1969).
RECEIVED for review March 28, 1975. Accepted October 9, 1975. This research was supported in part by Public Health services contract N ~ 505 . R R ~ and ~T~~Nutrition ~ ~ ~ Foundation, Inc., New York, Grant No. 468.
Reconciliation of Gas-Liquid Chromatographic and Nuclear Magnetic Resonance Measurements for Association Constants of Organic Complexes Daniel E. Martire Department of Chemistry, Georgetown University, Washington,D.C. 20057
Association constants derived from the usual GLC approaches are larger than those determined by NMR for the same supposed complexing systems. Thermodynamic tqodels have been proposed to account for these apparent discrepancies. Equations are derived to permit a more sensitive experimental test of two of these models: the local immiscibility model and the additive contribution model. The latter model is more compatible with available GLC and NMR data. The former model is quantitatively inconsistent with the data. A possible explanation of the seemingly excellent correlation claimed for the immisclbillty model is offered in light of !he derived equations: insensitivity of the method of data testing.
During the past ten years, there has been much activity in the development and utilization of gas-liquid chromatography (GLC) for the precise measurement of association constants for 1:1 organic complexes stabilized (to some extent) by charge-transfer or hydrogen-bonding interactions (1-22). Recently, however, the significance of GLC-derived “association constants” has been brought into question (18, 19, 23, 24). Where comparative studies have been made (5, 7, 14, 15, 18, 19, 23-25), the values from nuclear magnetic resonance spectrometry (NMR) and/or ultraviolet-visible spectrophotometry (UV/V) were found t o be smaller than the “GLC association constants” for the same complexes. Such systematic differences have also been observed between other thermodynamic (Le., non-GLC) and spectroscopic results (26, 27). A model has been proposed (18) and successfully applied (17, 18, 25) t o account quantitatively for these apparent discrepancies. T h e basic proposition of the additive contribution model (18) is that the GLC method yields values which are a measure of the total effect of donor-acceptor interactions (chemical plus physical), whereas values determined spectroscopically reflect only chemical interactions, Le., specific complex formation (28-30). Another, less conventional, point of view has been put forth recently by Purne11 and Vargas de Andrade (23, 24). Utilizing a model based on local immiscibility of the additive (donor or acceptor, whichever is present in excess of the other) and inert solvent mixture, they seemingly reconciled GLC and NMR data for several supposed complexing systems, while 398
claiming that other models, e.g., (18), were incompatible with their data. Accordingly, their equations and the equations derived previously (18) are recast or extended here to permit a more definitive experimental test of the two models. Since the details of the models and derivations are described elsewhere (18, 23, 24), only the salient assumptions and equations are given below.
LOCAL IMMISCIBILITY MODEL (23,24) Consider a locally immiscible mixture of a n involatile additive (A) and an inert solvent (S)to which is added a volatile solute (D), where the condition CA >> CD obtains, C; referring to the concentration of component i. Formal thermodynamic treatment of D partitioning between the gas phase and two immiscible, involatile, liquid phases yields the following GLC equation:
where K R is the observed infinite dilution partition coefficient of D between the “mixture” of A and S of volume fraction $A and the gas phase, and Kkr,k)and K&sj are the solute partition coefficients with pure A and pure S, respectively. Also, & = 1 - 4 ~and, , with zero volume of mixing, $t = C, V,, where V , is the molar volume of component i. With the additional assumption that the transfer of D between regions of A and S in the mixture is rapid (on the NMR time-scale), the following equation relating NMR (lhs) and GLC (rhs) quantities is derived:
where A() is the chemical shift difference (6: - 68), the zero superscript designating the shift in the pure liquid, and A is the difference (6 - a:), 6 being the measured shift a t volume fraction $A. Also, the chemical shifts refer t o those associated with a nucleus (generally a proton) of D. Equation 2 may be rearranged to give: (3) where AK{ = K $ ( &-, KW,sj. T h e above equations would apply if “there is not random mixing in A S mixtures, but rather a high degree of
ANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976
+
-
Substituting K from Equation 6 into Equation 10 and collecting terms, one finds:
aggregation such that the local concentration of A is always that corresponding t o pure A" (23). T h e testing of Equation 2 with data for supposed AD complexing systems (see later) led the authors to suggest "either t h a t these systems exhibit no complexing (in t h e usual definition of this phenomenon) or as is much more likely that, if they do, it cannot be mathematically described in conventional terms associated hitherto with totally random distribution of reactants in solvrnt" (2.1).
which reduces to Equation 2 only when CY = 0. Alternatively, working with the inverse of Equation 12, or substituting K from Equation 6 into Equation 11, one obtains:
A D D I T I V E C O N T R I B U T I O N MODEL (18) Consider a random mixture of a n electron acceptor additive ( A ) and an inert solvent (S)to which is added a volatile electron donor solute (D), where the usual condition C.4 >> Cr, applies. Assume that interactions between A and D consist of' long-lives. specific. 1:l AD complex formation (the "chemical" contribution) and/or short-lived, loose, A-D interactions (the "physical" contribution). Also assume that A and S form an ideal solution and t h a t the concentration of A , D complexes ( x 2 2) is negligibly small. T h e following G1.C equation is derived:
where, again, UC; - K&A) = K ~ ( Aand ) , where Equation 13 reduces to Equation 3 only when CY = 0.
DISCUSSION
where K is the true 1:l AD association constant, cy (a positive quantity) is a measure of the effect of noncomplexing A-D interactions, and where the sum ( K n ) will be referred to as the "GLC association constant" or K " ' A ~(23, 2.i). LVhen the assumed conditions are met experimentally, Klt should he a linear function of C.4 over the entire concentration range. as has been observed for many systems (6.1.3, 2.1).Thus. with pure A
+
K;:, 1, = K\\,.,[l + ( K + fi)V,i']
(5)
or
K=--
V.4 1K
;;
N (6) KY;,,, .shere (',I = k';' for pure A. Combining Equations 4 and 5 and assuming zero volume of mixing, one obtains Equation
1.
L'tilizinp the above assumptions and allowing for three distinct chemical shifts of D: unperturbed as in pure S (a?), perturbed h y 1:l A D complex formation (6.~11).and per, folturbed hy noncomplexing AD interactions ( h , ~ - r > )the lowing NhIH equation is derived:
_1 ---
1 1 K1,C4
1 + -A,
where 1 = (6 - 6;). ci being the measured shift at Cq, and
\\here 1,i i t o n c e n t r a t r o n - ~ n d e p ~ n dwith ~ n ~ 141) , = (611, - 6:) and A x 1) = 6a 1) - 6 :. When the assumed conditions are realized. 1 I should be a linear function of C;' over the entire concentration range ( 2 4 ) .Then: 1 - VA _ -
1"
1 + KA, A
+ (--)V A+ K A+K
Ci'
(11)
For many supposed complexing systems, including the large number treated in Reference 23, both Equations 1 and 4 fit the GLC data within experimental error over the entire concentration range. Also, as shown previously (23) and indicated above, they are formally identical equations. Hence, on the basis of GLC measurements alone, it is hardly possible to choose between the two models. For this reason, NMR and/or UV/V studies have been conducted on the same systems in attempts t o establish the significance of "GLC association constants" and the validity of proposed models (14, 17-19,23-25). Purnell and Vargas de Andrade (23,24)tested their local immiscibility model by analyzing 1 (from N M R ) as a function of ~ A / K R (from GLC). Equation 2 predicts that 1 should vary linearly with ~ A / K Ryielding , a slope Kg,41An. Yet, inspection of Figures 2-4 of Reference 24 reveals some upward curvature with increasing ~ A / K Rparticularly , for the systems containing the solute 1,2-dichloroethane. Nevertheless, it is claimed that the "computer calculated slopes" and the product K~:,A,A' are in agreement (see Table 11 of Reference 24), albeit at low 4 A / K R for one system. T h a t the immiscibility model is, in fact, quantitatively inconsistent with the experimental data is indicated by the analyses below. T h e authors find that their NMR results fit a n equation of the form of Equation 7 over the entire concentration range ( 2 4 ) . Hence, their NMR data must be consistent with Equation 10, where, at this point, K may even be regarded as some concentration-independent parameter. They also find t h a t their GLC data obey Equation 1. However, it is clear that Equation 2 can be quantitatively consistent with both Equations 1 and 10 only i f :
Since their experimental results (taking experimental error into account) show that K';Lc > K , self-consistency is precluded. Before proceeding to another manifestation of this inconsistency, it should be noted that, contrary t o a statement made otherwise ( 2 4 ) ,the additive contribution model 1 s formally compatible with the observed experimental behavior. From Equation 12 we see that: (a) A can only be a linear function of @JKH (with slope K:,a,A')) when a = 0, i.e , when K',' c = K , and (b) when K'JLdC> K (i.e., when CY > 01, the A vs. d a / K ~plot should be curved upward, where the extent of curvature depends on the value of
ANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976
399
Table I. Analysis of Representative GLC and NMR Results at 30 C Di-n-octyl ether (A)/n-Heptadecane (S) Solutes (D) KGLCU Kb Cic
1. Chloroform
2. 1,2-Dichloroethane
0.407 0.215
0.305 0.036
0.102 0.179
Table 11. Test of the Models:
md
0.146 0.351
Di-n-butyl tetrachlorophthalate (A)/Squalane (S)
3. 4. 5. .6. 7.
Chloroform 0.640 0.590 0.050 0.051 1,2-Dichloroethane 0.131 0.614 0.579 0.745 o-Xylene 0.698 0.510 0.188 0.178 m-Xylene 0.521 0.345 0.176 0.202 p-Xylene 0.580 0.545 0.035 0.037 a From Table Iof Reference 23 (there listed as K , (exptl)). b From Table I of Reference 24 (NMR Results). C CY = K G L C - K . Units of 1. mol-’. d m = a K ’ ~ ( s/ V A K O R ( A computed from values given in Table I of deference 28;
systema
Local immiscibility model, Equation 3 Slopeb
Intercept
vs. Ci’
AO/A
U M R data, Equation 1 1 Slopeb
Intercept
1.427 0.568 1.646 1.959 0.407 2.954 1.019 0.677 1.102 4 0.942 0.701 2.232 5 0.945 0.700 1.209 6 1.147 0.636 1.510 7 1.071 0.660 1.160 a Systems numbered according 1.-’. 1 2 3
Additive contribution model, Equation 1 3 Slopeb
Intercept
1.670 0.494 3.017 0.087 1.074 0.659 2.234 0.291 1.149 0.635 0.521 1.437 0.544 0.632 1.113 0.646 t o Table I. b Units of mol 0.502
0.106 0.650 0.292 0.617
K&A,Ao= 14 470 (24) and m = 0.579 (Table I). However, there appears to be an inconsistency. According to EquacUKi:,SI/VAKiIAj(see Table I, particularly the 1,2-dichlorotions 2 and 12 (and consistent with the NMR experiment), ethane systems). a line drawn between the two end points in the 3 vs. ~ A / K R Equation 12, which is also quantitatively consistent with plot (see Figure 3 of Reference 24) must have a slope equal the data (see later), sheds some light on why seemingly exto K$,&!A0.Given the extreme curvature for this system, cellent agreement was found between the “computer calcuthe limiting slope ( ~ A / K R 0) should then be far smaller lated slope” (linear least-squares) and the product K;(A,AO than K$,4130.Rough graphical analysis of the experimental (24). Differentiating Equation 12, one obtains the following curve suggests that a value in the range 5000-7000 would expression for the slope of the A vs. ~ A / K plot R a t a given be more appropriate. This is in agreement with a limiting ~AIKR: slope of 6100 computed for this system from Equation 16. A more sensitive and clearer quantitative test of the local immiscibility model can bs made by examining A o / 3 as a function of C;]. The model leads to Equation 3, while the experimental NMR data must follow Equation 11. From L‘ K R - VA J the GLC and NMR data (23, 24), the slopes and intercepts according to Equations 3 and 11 were computed for several A t the two extremes of concentration, CA = 0 (or @A/KR= representative systems. As can be seen in Table 11, the 0 ) and CA = V i 1 (or ~ A / K = R l / K & A I )Equation , 15 reducagreement is good in cases where KGLCis close to K (i.e., es to for small CY,see Table I), but poor otherwise. In all cases, the predicted slopes are too small and the predicted intercepts too large. On the other hand, comparing Equations 13 and 3, and noting that CY 1 0 and that KEi4)> AK;, it is clear that the additive contribution model moves in the right direction, i.e., it must lead to larger slopes and smaller intercepts. Thus, formally and quantitatively (see Table where m = [CYK~,~,/V.~,K:,.~,]. Thus, according to the above II), the additive contribution model is more compatible equations, if m is not small with respect to unity, the slopes with the experimental data. a t the two concentration extremes should be measurably different, and curvature should be readily observable (e.g., The excellent quantitative correlation of the data via Equation 13 (or Equation 12) is not surprising. I t should be 1,2-dichloroethane systems). On the other hand, if m is small, curvature may not be apparent in the A vs. ~ A / K R apparent, in fact, that there would be perfect agreement except for the slight difference between KG1)Cfrom Equaplot, and a linear least-squares fit of the data might contion 4 (used for the calculations in Tables I and 11) and ceivably “split the difference” between the slopes given by KGLc from V.t,AK~/K~,,!(23). A more convincing quantiEquations 16 and 17, to yield a slope quite close to K!,A,AO. tative test of the applicability of the additive contribution T o test this hypothesis, 3 values were generated through model to these systems would involve independent experiEquation 12 for five equally-spaced values of ~ A / K R bemental determination K or CY,or theoretical estimation of m = 0.2 (see Table I for typitween 0 and l / K & A )choosing , cal m values). The generated “data points” were then a . Unfortunately, except for the aromatic (D)/di-n-octyl ether (A)/n-heptadecane (S)systems, for which K = 0 and subjected to a linear least-squares analysis which yielded a KGLc = cy (23, 24), theoretical estimates would be too crude trivial negative intercept (24) and a slope of 0.998 Ki,p\Jo, with a linear correlation coefficient of 0.998. Even for as to be a t all meaningful. However, several studies may be cited where such theoretical treatments were possible ( I 7, large a value as m = 0.3, this procedure yields a linear 18, 31 ), and where the additive contribution model proved least-squares slope of 0.995 K&AIAo.Moreover, if there are relatively more data points a t the high 4~ end of the scale to be quantitatively and physically consistent with GLC and spectroscopic data (16-18,25). (23, 24), the linear least-squares slope could come even Since the weight of experimental evidence (albeit largely closer to the product K&A+O. Therefore, it seems likely that the remarkable agreement inferential) supports descriptions consistent with the additive contribution model or variations thereof, emphasis has cited in Reference 24 is merely an artifact of the insensitive been placed here on testing the more recent theory. The method of data testing used (see later). Interestingly, the local immiscibility model is novel, thought-provoking, and above procedure cannot account for the claimed agreement a t least semi-quantitative in its correlative ability. It is cona t low ~ A / K for R the system 1,2-dichloroethane (D)/di-nceivable that its failure to fit the data for the several sysbutyl tetrachlorophthalate (A)/squalane (S),for which
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400
ANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976
tems considered could be a result of anomalous behavior of the systems or the inherent crudeness of a first-generation model. I t appears, for example, that the model should fit the data for systems where KGLC= K = KNMR,such as is likely for aliphatic alcoholln-electron donor hydrogenbonded complexes (16). T h a t , in itself, would be noteworthy. Nevertheless, in addition to the inconsistencies described above, it presently lacks the support of independent experimental evidence (even inferential) for the existence of local aggregates of A and S in the mixed solvent, or separate clustering of A and S about D when solute is added. A similar two-phase thermodynamic model has been used to interpret solute activity coefficients in nematic liquid-crystalline solvents (32). In t h a t case, however, there was some supporting evidence for solvent clustering from x-ray and light scattering experiments. In short, more experimental evidence and additional refinement are needed before a compelling case can be made for the model.
ACKNOWLEDGMENT Stimulating discussions and correspondence with J. H. Purnell are gratefully acknowledged.
LITERATURE CITED (1) J. H. Purnell, "Gas Chromatography: 1966". A. E. Littlewood, Ed., Elsevier, Amsterdam, 1967, p 3. (2) D. E. Martire and P. Riedl, J. Phys. Chem., 72, 3478 (1968). (3) D. F. Cadogan and J. H. Purnell, J. Chem. SOC.A, 2133 (1968). (4) D. F. Cadogan and J. H. Purnell, J. fhys. Chem., 73, 3489 (1969). (5) C. Eon, C. Pommier, and G. Guiochon, C. R. Acad. Sci., 168, 1553 (1969). (6) C. Eon, C. Pomrnier. and G. Guiochon, J. Phys. Chem., 75, 2632 (1971).
(7) D. L. Meen. F. Morris, and J. H. Purnell, J. Chromatogr. Scb, 9, 281 (1971). (8) R. Vivilecchia and E. L. Karger. J. Am. Chem. SOC., 93, 6598 (1971). (9) C. Eon and B. L. Karger. J. Chromatogr. Sci.. 10, 140 (1972). (10) J. P. Sheridan. D. E. Martire, and Y . B. Tewari, J. Am. Chem. SOC.,94, 3294 (1972). (11) J. P. Sheridan, M. A. Capeless, and D. E. Martire, J. Am. Chem. SOC., 94, 3298 (1972). (12) J. P. Sheridan, D. E. Martire. and F. P. Banda, J. Am. Chem. SOC., 95, 4788 (1973). (13) H. L. Liao, D. E. Martire, and J. P. Sheridan. Anal. Chem., 45, 2087 (1973). (14) J. H. Purnell and 0. P. Srivastava, Anal. Chem., 45, 1111 (1973). (15) C. A. Wellington. Adv. Anal. Chem. Instrum., 11, 237 (1973). (16) H. L. Liao and D. E. Martire, J. Am. Chem. SOC., 96, 2058 (1974). (17) G. M. Janini, J. W. King, and D. E. Martire, J, Am. Chem. SOC., 96, 5368 (1974). (18) D. E. Martire, Anal. Chem., 46, 1712 (1974). (19) C. Eon and G. Guiochon, Anal. Chem., 46, 1393 (1974). (20) R . J. Laub and R. L. Pecsok, Anal. Chem., 46, 1214 (1974). (21) R . J. Laub, V. Ramamurthy, and R. L. Pecsok. Anal. Chem., 46, 1659 (1974). (22) R. J. Laub and R. L. Pecsok, J. Chromatogr., 113, 47 (1975). (23) J. H. Purnell and J. M. Vargas de Andrade, J. Am. Chem. Soc.. 97, 3585 (1975). (24) J. H. Purnell and J. M. Vargas de Andrade. J. Am. Chem. SOC.,97, 3590 (1975). (25) D. E. Martire. J. P. Sheridan, J. W. King, and S. E. O'Donnell, J. Am. Chem. SOC.,in press. (26) S. D. Christian, J. D. Childs. and E. H. Lane, J. Am. Chem. Soc., 94, 6861 (1972). (27) E. H. Lane, S. D. Christian, and J. D. Childs, J. Am. Chem. Soc., 96, 38 (1974). (28) E. A. Guggenheim. Trans. faraday SOC.,56, 1159 (1960). (29) J. E. Prue, J. Chem. SOC.,7534 (1965). (30) R. L. Scott, J. Phys. Chem., 75, 3843 (1971). (31) G. M. Janini and D. E. Martire, J. Phys. Chem., 78, 1644 (1974). (32) L. C. Chow and D. E. Martire. Mol. Cryst. Liq. Cryst., 14, 293 (1971).
RECEIVEDfor review August 25, 1975. Accepted October 23, 1975. This research was supported by a grant from the National Science Foundation.
Gas Chromatographic and Nuclear Magnetic Resonance Determination of Linear Formaldehyde Oligomers in Formalin Wim Dankelman" and Jacq.
M. H. Daemen
Akzo R e s e a r c h Laboratories, Corporate Research Department, Arnhem, The Netherlands
Up to now, no method has been published for determining the oligomer distribution of polyoxymethylene glycols, present in formalin solutions. We found that this distribution can be determined up to the heptamer (HO(CH20),H, n = 7 ) by direct silylation with BSTFA (N,O-bis(trimethylsily1)trifluoroacetamide), followed by GLC analysis on a column filled with 10% OV-1 on Chromosorb W. The results were corroborated with a 220-MHr NMR analysis. Only at 220 MHz is the water signal sufficiently separated from the methylene hydrogen absorptions. The exact amounts of the oligomers with n = 1 and n = 2 and the sum of n 3 3 can be determined by NMR. The results are in accordance with the GLC analysis. Methanol, added as a stabilizer to avoid precipitation of paraformaldehyde breaks down high molecular oligomers of polymethylene glycols, thereby forming more soluble compounds.
According to Walker ( I ), formalin consists of free formaldehyde (
