Ion Pair Formation in Water. Association Constants of Bolaform

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J. Phys. Chem. B 2005, 109, 23629-23637

23629

Ion Pair Formation in Water. Association Constants of Bolaform, Bisquaternary Ammonium, Electrolytes by Chemical Trapping Yan Geng Department of Chemical and Biomolecular Engineering, UniVersity of PennsylVania, Philadelphia, PennsylVania 19104

Laurence S. Romsted* Department of Chemistry and Chemical Biology, Rutgers, The State UniVersity of New Jersey, New Brunswick, New Jersey 08904 ReceiVed: August 16, 2005; In Final Form: October 22, 2005

The first and second association constants, K1 and K2, for ion pair formation in aqueous 0.02-3.5 M solutions of bis(trimethyl)-R,ω-alkanediammonium halides with variable spacer lengths, 1-n-1 2X (n ) 2-4, X ) Cl, Br) and bolaform salts and for tetramethylammonium halides (TMAX, X ) Cl, Br), KTMAX, were determined by the chemical trapping method. Values for KTMAX are small, KTMABr ) 0.83 M-1 and KTMACl ) 0.29 M-1, in agreement with literature values. For the bolaform salts, K1 depends on spacer length and counterion type, ranges from 0.4 to 17 M-1, is 2-10 times larger than K2, is larger for Br- than Cl-, and decreases by a factor of ∼3 for Cl- and ∼10 for Br- as n increases from 2 to 4. K2, for the formation of bolaform dihalide pair, is essentially the same as that for ion pair formation in TMAX solutions, i.e., K2 ≈ KTMAX. Values of K1 and KTMABr obtained from changes in 79Br line widths are in good agreement with those obtained by chemical trapping. The results are consistent with a thermodynamic model in which the ion association depends on the balance of the ion specific hydration free energies of cations and anions and their ion specific and hydration interactions in ion pairs. Spacer length dependent ion pairing by bolaform electrolytes, which are analogues of the headgroups and counterions of gemini amphiphiles, suggests a new model for the spacer length dependent sphere-to-rod transitions of gemini micelles. Neutral, but polar, headgroup-counterion pairs have a lower demand for hydration that free headgroups and counterions, and headgroup-counterion pair formation releases interfacial water into the bulk aqueous phase, permitting tighter amphiphile packing in rodlike micelles.

Introduction Ion specific effects in aqueous solutions are observed throughout chemistry and biology.1-10 Specific ion effects in aqueous solutions of simple inorganic electrolytes often follow the Hofmeister series,1,2,6 but not always.11,12 Solute dissolution and colligative properties depend on ion type, as do many properties of amphiphile association colloids such as the critical micelle concentration (cmc), counterion exchange, and association colloid effects on chemical reactivity.6,13,14 Biological examples include ion specific effects on protein solubility (Hofmeister’s original observations),15 cell permeability,16 and membrane surface charge densities.17 Nevertheless, the forces responsible for specific ion effects are still poorly understood.6,18 The order of effectiveness of a series of liked charged ions on a particular solution, membrane, or protein, property generally correlates with ion valence, size, and polarizability, e.g., the Hofmeister series.2,4 For example, of the halide ions, F- is the least polarizable and the most strongly hydrated and is considered a water structure maker (kosmotrope). Br- and Iare more polarizable, have weaker interactions with water, and are called water structure breakers (chaotropes). Cl- is in the middle. Alkali metal cation effects generally increase with cation size from Li+ to Cs+. However, ion specificity orders are not * Corresponding author: Ph 732-445-3639; Fax 732-445-5312; e-mail [email protected].

always the same. Eisenman11 measured and Wright and Diamond12 cataloged 11 different orders of the 125 permutations of the 5 alkali metal cations and 7 different orders of 4 halide ions out of 24 permutations for a wide variety of ion selective electrode surfaces and biological systems, respectively. Two factors contribute to ion specific effects: differences in hydration free energies or hydration numbers and ion pair formation. Zavitsas19 showed that the apparent deviations from ideality of the colligative properties of many different simple inorganic salts in water, at concentrations up to or approaching their solubility limits, disappear if the water molecules in the immediate vicinity of an anion and cation of a salt are assumed to be associated with the ions and are not counted as bulk water. The correlations were made without invoking ion pairing. However, substantial experimental and theoretical results support ion pair formation in water, although demonstrating ion association, even at high salt concentrations (e.g., >1 M), by simple monovalent ions is difficult,20,21 as is distinguishing between water separated and contact cation‚anion pairs (and cation‚cation and anion‚anion pairs).22,23 (Note: here and throughout the text a bullet indicates an ion‚molecule or ion‚ ion pair.) Ion pair association constants for simple inorganic salts, such as sodium halides, are generally small (ca. 1-10), but their presence is consistent with conductivity21 and neutron diffraction24 results and with Monte Carlo23,25 and molecular dynamics calculations.26-32 Estimates of ion pair association

10.1021/jp0546195 CCC: $30.25 © 2005 American Chemical Society Published on Web 11/19/2005

23630 J. Phys. Chem. B, Vol. 109, No. 49, 2005 SCHEME 1. Structures of Bolaform Salts and Gemini Amphiphile Analogues

constants and evidence for the formation of both water-separated and contact ion pairs has been reported for quaternary ammonium halides, R4NX (R ) Me, Et, 1-propyl, and 1-butyl, X ) Cl, Br, and I), by a variety of methods. 79Br line width changes were interpreted in terms of R4N+ induced disturbance of Br- ion hydration.33-35 Conductivity,36-38 capillary electrophoresis,39 neutron diffraction studies,40 and molecular dynamic simulations22,36,41 were interpreted in terms the formation of both contact and water-separated ion pairs. We decided to study the aqueous solution properties of the bolaform electrolytes bis(trimethyl)-R,ω-alkanediammonium halides as models for headgroup and counterion interactions in the interfacial regions of aqueous gemini amphiphile micelles (Scheme 1) for several reasons: because the solution properties of these dicationic salts have not been characterized previously, because electrolyte solutions are useful models for headgroup, counterion, and water interactions in the interfacial regions of ionic micelles,42-49 and because the results should provide new insight into the balance of forces controlling the solution properties of micelles of gemini amphiphiles. In general, the solution properties of ionic amphiphiles such as their cmcs, sphere-to-rod transitions, and Krafft temperatures are sensitive to the headgroup structure and counterion type and concentration as well as amphiphile tail length.6,50 The gemini amphiphiles, 12-n-12 2Br (n ) 2-4), Scheme 1, have dramatically different properties from those of their single-chain analogues51,52 despite having essentially the same hydrophilic-lipophilic balance (HLB), i.e., the same ratio of number of carbons to headgroup charges.50 For example, the cmcs of 12-n-12 2Br (n ) 2-4) amphiphiles are about an order of magnitude smaller than that of dodecyltrimethylammonium bromide (DTABr).51,53 Solutions of the gemini amphiphile 12-2-12 2Br are viscoelastic above 4.2 mM at 25 °C because they contain rodlike (or threadlike or wormlike) micelles.51 However, over 1 M NaBr is required to induce the formation of rodlike micelles DTABr solutions.53

Geng and Romsted In addition, the solution viscosities of gemini amphiphiles are “tunable” simply by changing the spacer length.51 12-3-12 2Br form threadlike micelles at higher concentrations than 12-2-12 2Br, but rod formation by 12-4-12 2Br amphiphiles has not been observed.51 These marked differences in the bulk properties of gemini amphiphiles and their single-chain analogues must depend on specific interactions between Br- and the headgroups and not just Coulombic screening of headgroup repulsions by Br- because the numbers of headgroup charges and Br- are the same for these gemini amphiphiles and their HLBs are the same as their single-chain analogues. Here, we use the chemical trapping method45,46 to determine the effect of the concentration of bolaform salts and spacer length (Scheme 2) on the concentration of “free”, i.e., unpaired, halide ion, [X-], in solution using tetramethylammonium halide, TMAX (X ) Cl, Br), solutions for comparison. (Note: [ ] here and throughout the text indicates molarity.) Detailed descriptions of the assumptions, protocols, and applications of the chemical trapping method are published.42-46,48,49,54,55 In brief, the watersoluble arenediazonium ion, 2,4,6-trimethylbenzenediazonium ion (1-ArN2+), Scheme 2, reacts competitively with H2O and the halide ions, Cl- and Br-, to give stable products 2,4,6trimethylphenol, 1-ArOH, 1-ArCl, and 1-ArBr, respectively. Product yields, measured by HPLC, are used to estimate [X-]. The arenediazonium ion is prepared as its tetrafluoroborate salt, 1-ArN2BF4,46,56 and its stoichiometric concentration in solution, 5 × 10-3 M, is generally one or more orders of magnitude lower than that of the salts and water. Thus, addition of 1-ArN2BF4 does not significantly perturb the equilibrium concentrations of other ions in solution. Ion-molecule exchange rates in solution are assumed to be near the diffusion-controlled rate limit, whereas the half-life of the dediazoniation reaction is about 0.5 h.46,56 Thus, all components in the solution are in dynamic equilibrium throughout the time course of the dediazoniation reaction. Two sets of dynamic equilibria are assumed to govern the product yields from the chemical trapping reaction (Scheme 2).45,46 One set is between arenediazonium ion ground states, the 1-ArN2+‚X- and 1-ArN2+‚H2O pairs. The concentrations of these pairs depend free halide ion concentration, [X-] (not in ion pairs), and concentrations of free water (not hydrating ions), respectively; i.e., the yield of 1-ArX depends on [X-] and not [XT], the stoichiometric concentration of halide ion in solution. The other set of equilibria are between X- and the free and paired forms of the bolaform salts, dicat2+, (dicat‚X)+ and (dicat‚X2). These equilibria determine [X-] at any bolaform

SCHEME 2. Equilibria Governing Chemical Trapping Product Yields (Left) and Ion Pair Equilibria of Bolaform Electrolytes (Right)

Bolaform Electrolyte Ion Pairs in Water

J. Phys. Chem. B, Vol. 109, No. 49, 2005 23631

TABLE 1: Bolaform Salt and Water Concentrations, HPLC Peak Areas, Observed and Normalized Yields for Dediazoniation of 5 × 10-3 M 1-ArN2+ in Aqueous 1-2-1 2Br Solutions at 40 °C and 0.01 M HBr, and Values for Selectivities, SWBr, and [H2O] M/[Br] M Molar Ratiosa 1-2-1 [BrT] (M)b

[H2O] (M)

0.00 0.02 0.04 0.06 0.08 0.11 0.21 0.31 0.51 1.01 1.51 2.01 2.51 3.01 3.51

55.5 55.3 55.2 55.0 54.9 54.7 54.1 53.4 52.2 49.1 45.9 37.0 28.1 22.8 21.4

peak areasc (106 µV‚s) 1-ArBr 1-ArOH

observed yields (%)d 1-ArBr 1-ArOH

0 0.02495 0.04457 0.06249 0.07997 0.09701 0.1704 0.2259 0.3715 0.5856 0.7735 0.9352 1.053 1.162 1.342

0 0.571 1.02 1.43 1.83 2.22 3.90 5.17 8.50 13.4 17.7 21.4 24.1 26.6 30.7

4.100 4.088 3.897 3.951 3.979 4.030 3.988 3.793 3.797 3.478 3.303 3.154 2.980 2.905 2.735

98.8 98.5 93.9 95.2 95.9 97.1 96.1 91.4 91.5 83.8 79.6 76.0 71.8 70.0 65.9

total yields (%) 98.8 99.1 94.9 96.7 97.8 99.3 100 96.6 100 97.0 97.0 97.6 95.8 97.0 95.2

normalized yields (%) 1-ArBr 1-ArOH

SWBr f

[H2OT] M/ [BrT] M

0 0.576 1.07 1.48 1.87 2.24 3.90 5.35 8.50 13.9 18.2 21.9 25.1 27.5 30.7

16.0 14.9 13.8 13.1 11.4 10.5 9.74 9.51 7.85 6.76 5.16 3.75 2.87 2.7

2770 1380 917 686 497 258 172 102 49.0 30.4 18.4 11.2 7.57 6.10

100 99.4 98.9 98.5 98.1 97.8 96.1 94.6 91.5 86.1 81.8 78.1 74.9 72.5 69.3

a Reaction time ca. 8 h. 1-ArN2BF4 added in 0.1 M stock solution in CH3CN. 100 µL of cyclohexane was layered on top of 1-2-1 2Br solutions in a 1 or 2 mL reaction flasks to prevent the evaporation of the volatile 1-ArBr. Prior to HPLC analysis, the product mixture was diluted 5-fold with MeOH to dissolve both the cyclohexane and the aqueous salt solution. b The total Br- concentration, [BrT] ) 2 × [1-n-1 2Br] + 0.01 M HBr. c 20 µL sample injected; peak areas are average values of three injections. d Observed yield: %1-ArX ) 100 [1-ArX]/% 1 × 10-3 M 1-ArN2BF4 (X ) OH, Br). The total dediazoniation product yield is 1 × 10-3 M because each reaction mixture was diluted 5-fold with MeOH prior to HPLC analysis. e Normalized yield (%): %1-ArOH ) 100 (%1-ArX)/(%1-ArOH + %1-ArBr). f SwBr ) [H2O](%1-ArBr)/[BrT](%1ArOH).

salt concentration and the product yields, %1-ArX and %1ArOH, which are used to estimate K1 and K2 and the concentrations of the free and paired ions (Scheme 2). The concentrations of free water and water of hydration around the free and paired ions was not estimated because water is in large excess except at the highest bolaform electrolyte concentrations and neither the chemical trapping or 79Br NMR line width measurements provide estimates of the concentrations of ions in waterseparated and tight ion pairs. The chemical trapping results described here and confirmed by 79Br line width measurements provide estimates of the association constants for TMAX (X ) Cl, Br), KTMAX, that are in agreement with literature values. They also provide new evidence for the formation of mono- and dihalo ion pairs in aqueous solution bolaform electrolytes in which K1 decreases with spacer length and is smaller for Cl- than Br-. K2 is independent of spacer length and equal to KTMAX. These chemical trapping results, in conjunction with chemical trapping experiments in 12-n-12 2Br (n ) 2-4) gemini micelles, support a novel explanation for the spacer length dependence of micellar sphere-to-rod transitions and for the shift in delicate balance of noncovalent forces controlling such transitions that is based on ion pairing and concomitant dehydration of the interfacial region of the micelles.57 Results Table 1 shows typical chemical trapping results in aqueous 1-2-1 2Br solutions from 0 to 3.51 M total Br- containing 0.01 M HBr. Similar tables for the other bolaform and TMAX salts are in the Supporting Information. The molarities of salt (dried to constant weight) and water in each solution were obtained by weight in volumetric flasks. HPLC peak areas (averages of triplicate injections and reproducible to ca. (5% or better) were used to obtain measured product yields from HPLC calibration curves (see Experimental Section) prepared with independently synthesized or purchased standards. Total yields, which varied between 94% and 100%, were converted to normalized product yields. The normalized yields were combined with the stoichiometric concentrations of H2O and X- to calculate the selectivity

Figure 1. Chemical trapping results for 1-n-1 2Br (n ) 2-4) bolaform electrolytes and TMABr plotted against total Br- concentration: (A) %1-ArBr yields, (B) %1-ArBr yield ratios in 1-n-1 2Br solutions to TMABr solutions, and (C) fractions of free and paired ions for 1-2-1 2Br calculated from the association constants for 1-2-1 2Br. Lines are drawn to aid the eye.

23632 J. Phys. Chem. B, Vol. 109, No. 49, 2005

Geng and Romsted 1A and 2A. Because the yield ratios are from two different measured numbers, their values are more sensitive to experimental error; e.g., the one point in Figure 2B is probably caused by the %1-ArCl yield in TMACl being too low (see Figure 2A). These yield ratios highlight several important features of the trapping results that are not obvious in Figures 1A and 2A: (a) the yield ratios decrease with decreasing methylene spacer length; (b) each curve is biphasic with an initial rapid decrease in the ratio followed by a plateau region in which the ratio is approximately independent of [XT]; (c) the intersection point at the beginning of the plateau occurs at lower [XT] as the spacer length decreases; (d) the change in the yield ratios is smaller for Cl- than Br-; and (e) the intersection points occur at higher [ClT] than [BrT] for the same number of methylene groups in the spacer. Below ca. 0.5 M [XT], these trends are consistent with the formation of (dicat‚X)+ pairs with association constants, K1 (eq 2, Scheme 2), by the bolaform electrolytes at lower [XT] K1

dicat2+ + X- y\z (dicat‚X)+ K1 )

Figure 2. Chemical trapping results for 1-n-1 2Cl (n ) 2-4) bolaform electrolytes and TMACl plotted against total Cl- concentration: (A) %1-ArCl yields, (B) %1-ArCl yield ratios in 1-n-1 2Cl solutions to TMACl solutions, and (C) fractions of free ions and ion pairs for 1-2-1 2Cl calculated from the association constants for 1-2-1 2Cl. Lines are drawn to aid the eye.

of the reaction toward X- relative to H2O, SWX (eq 1).

[(dicat‚X)+] [X-][dicat2+]

(2)

and with an increase in the extent of ion pairing with increasing [XT] and with decreasing spacer length. Above ca. 0.5 M [XT], the ratios plateau showing that the rate of decrease in %1-ArX is the same in 1-n-1 2Br and in TMAX solutions. Thus, formation of (dicat‚X2) pairs with association constants, K2 (eq 3, Scheme 2), has the same dependence on salt concentration as the formation of TMA‚X pairs from TMA+ and X- (eq 4); i.e., the free energy of association of X- to TMA+ is essentially the same as that for the association of a second X- to (dicat‚ X)+ and K2 ≈ KTMAX. K2

(dicat‚X)+ + X- y\z (dicat‚X2) K2 )

[(dicat‚X2)] [X-][(dicat‚X)+]

(3)

KTMAX

SWX )

[H2OT](%1-ArX) [XT](%1-ArOH)

TMA+ + X- y\z TMA‚X (1)

Both SWX and the [H2OT]/[XT] molar ratio decrease steadily with increasing [XT] for the bolaform electrolytes, e.g., Table 1. Trapping results in aqueous solutions of the other bolaform salts and in TMAX salts solutions from 0 to 0.31 M halide ion are in the Supporting Information. Trapping results for TMAX from 0.51 to 3.51 M were obtained earlier56 and are reproduced in Figures 1A and 2A. Figures 1A and 2A summarized the chemical trapping results. The %1-ArBr (Figure 1A) and %1-ArCl (Figure 2A) product yields increase continuously with added salt, the halo product yields are always greater for Br- than Cl-, and all plots are concave downward. The highest yields for Br- are in TMABr (Figure 1A) and for Cl- in TMACl (Figure 2A). For the bolaform electrolytes, the product yields decrease in the order 1-4-1 2X > 1-3-1 2X > 1-2-1 2X for both Br- and Cl- salts. Changes in %1-ArOH yields, e.g., Table 1 for 1-2-1 2Br and in the Supporting Information, are the inverse of changes in %1-ArX. Figures 1B and 2B are plots of the ratios of %1-ArX product yields from trapping in 1-n-1 2X solutions to %1-ArX yields from trapping in TMAX at each [XT] from the data in Figures

KTMAX )

[(TMA‚X)] [X-][TMA+]

(4)

To confirm these trends, 79Br line widths, w, were measured from 0 to 0.5 M [BrT] in aqueous solutions of TMABr and 1-n-1 2Br (n ) 2-4) (Figure 3). As with other 79Br NMR experiments in aqueous Br- solutions,58 we assume that the extreme narrowing condition for 79Br line widths holds, i.e., T1 ) T2, and that the rate of exchange of 79Br between water and ion pairs is fast on the NMR time scale. The literature value of w for 79Br in dilute solution is 485 Hz at 25 °C,58 close (within ca. 3%) to our initial value in 0.005 M TMABr of 499, Figure 3A (Table S9). Figure 3A shows that 79Br line widths increase with increasing [BrT] and follow the order TMABr < 1-4-1 2Br < 1-3-1 2Br < 1-2-1 Br. The value of wp, the line width for 79Br in ion pairs, should be different for different ion pairs and even at the lowest Br- concentration in 1-n-1 2Br solutions, i.e., w increases as n decreases. Thus, these 79Br line width changes are consistent with an increase in the fraction of ion pairs in solution with increasing [BrT] and with decreasing spacer length of the bolaforms, i.e., the larger the fraction of ion pairs in solution, the greater w. Figure 3B is a plot of 1-n-1 2Br/TMABr 79Br line width ratios. These plots show the same

Bolaform Electrolyte Ion Pairs in Water

J. Phys. Chem. B, Vol. 109, No. 49, 2005 23633 by combining eqs 2, 3, and 5, values for K1 and K2 () KTMAX), and the appropriate mass balance equations. The derivation of the cubic equation, its solution, and its use are described in the Supporting Information. The average percent deviations in calculated and measured %1-ArX yields for all chemical trapping reactions range between 1.7% and 4% for 14 points ([XT] ) 0 not included) for all the trapping experiments, and we assume that the uncertainties in K1 and KTMAX (and K2) are the same. Values of K1 for 1-n-1 2Br (n ) 2-4) and KTMABr for TMABr were also obtained from 79Br line width data (full details in the Supporting Information). As with earlier work,58 w for 79Br is assumed to be the weighted sum of the line widths of the free and paired ions

w ) pfwf + ppwp

Figure 3. 79Br line widths for 1-n-1 2Br (n ) 2-4) bolaform electrolytes and TMABr plotted against total Br- concentration: (A) %1-ArBr yields, (B) %1-ArBr yield ratios in 1-n-1 2Br solutions to TMABr solutions, and (C) fractions of free ions and ion pairs for 1-2-1 calculated from the association constants for 1-2-1. Lines are drawn to aid the eye.

basic dependence on [BrT] and spacer length as the chemical trapping results in Figure 2B, an initial rapid change that is spacer length dependent followed by plateau regions. As in Figure 3, 79Br line widths of TMABr solutions increase significantly with concentration in aqueous solution33-35 as well as in cationic micelles with quaternary ammonium headgroups.58 Table 2 summarizes the association constants for 1-n-1 2X bolaforms, K1 and K2, and for TMAX, KTMAX, salts. The process for estimating the constants is summarized here; full details are in the Supporting Information. The values of K1 were obtained by a nonlinear least-squares fits of the data in Figures 1A, 2A, and 3A. Expressions for the association constants, eqs 2-4, and the appropriate mass balance equations were fit using a computer program written in C. For the chemical trapping results, we assumed that the %1ArX yield is linear function of [X-]

%1-ArX ) A[X-]

(5)

where A is an empirical constant (see Table 2 footnote for values) determined by the least-squares fit. To solve for K1, we set K2 ) KTMAX because the yield ratios in Figures 1B, 2B, and 3B are essentially constant above ca. 0.5 M XT. Table 2 also includes an estimate of the uncertainty in the nonlinear leastsquares fits used to obtain values of K1 and KTMAX from the chemical trapping data (average percent deviations in %1-ArX are listed in parentheses). The error in the estimate of KTMAX was obtained by combining eqs 4 and 5, the value for KTMAX, and the appropriate mass balance equations for trapping in TMAX solutions and solving for %1-ArX at each [TMAX] concentration from a second-order equation. The average deviation was calculated from absolute difference between the measured and calculated value of %1-ArX (see footnote Table 2 and Supporting Information). The same process was used to estimate %1-ArX for the 1-n-1 2X salts from a cubic equation

(6)

where pf and pp are mole fractions, pf ) [Br-]/[BrT] and pp ) [(dicat‚Br)+]/BrT], and wf, and wp are the line widths of free and paired 79Br, respectively. To estimate KTMABr, eq 6 was combined with eq 4, and the appropriate mass balance equations and the data were fitted with a program written in C. Values of K1 were obtained from calculated values of pf and pp, using eq 6 combined with eq 2, and the appropriate mass balance equations. 79Br line width values up to the break point in the curves in Figure 3 were used to estimate K1. The concentration of (dicat‚X2) is negligible, e6% of the total bolaform salt at these concentrations (see Supporting Information). Figures 1C and 2C show the molar fractions of free and paired ions for 1-2-1 2X as a function of [XT], where

[X-] 2[dicat2+] 2[(dicat‚X)+] 2[(dicat‚X2)] + + + )1 [XT] [XT] [XT] [XT] (7) The mole fractions of each form in eq 7 were obtained by calculating the molarities of each form from K1 and K2, the values of A for Br- and A for Cl-, and the appropriate mass balance equations and then dividing by [XT] (see Supporting Information). The molarities of dicat2+, (dicat‚X)+, and (dicat‚ X2) were multiplied by 2 in eq 7 because each equivalent of added bolaform salt gives 2 equiv of Br-. Similar plots for 1-3-1 2Br, 1-4-1 2Br, 1-3-1 2Cl, and 1-4-1 2Cl are in the Supporting Information. Note that the concentration of dicat2+ goes through a maximum at low [XT] (Figures 1C and 2C). The calculated value of [dicat2+] is uncertain at low bolaform salt concentrations because it is obtained by difference, and small errors in measured %1-ArX have a large effect on its estimated value at low [XT]. The problem is not serious above ca. 0.5 M [XT] and does not significantly affect our estimates of interfacial concentrations of free and paired ions in the interfacial regions of gemini surfactants because the interfacial Br- concentration generally exceeds 1 M.42,43,45-49,57 Discussion The chemical trapping results in Figures 1 and 2, the 79Br line width data in Figure 3, and the association constants listed in Table 2 are completely consistent with the ion pair equilibria in Scheme 2 for the bolaform TMAX electrolytes. Neither the chemical trapping or 79Br line width results distinguish between water-separated and contact ion pairs (see below), and we apply Occam’s razor and assume that the properties of the bolaform and TMAX solutions are described by two states, i.e., hydrated free or paired states shown in Scheme 2. However, note that in concentrated solutions when [XT] ≈ 3 M (Table 1 and Tables

23634 J. Phys. Chem. B, Vol. 109, No. 49, 2005

Geng and Romsted

TABLE 2: Association Constants Obtained by Fitting Chemical Trapping Product Yields and 79Br Line Widths Measurements in Aqueous Solutions of TMAX and 1-n-1 2X Salts (X ) Br, Cl) Saltsa counterion

method

constant

1-2-1 2X

1-3-1 2X

1-4-1 2X

Br Br Br Br Cl Cl

trapping line width trapping line width trapping trapping

K1 K1 KTMABr KTMABr K1 KTMACl

16.7 (2.64%) 13.5

5.79 (1.68%%) 6.62

1.75 (3.96%) 1.84

TMAX

0.83 (2.12%) 0.74 1.20 (2.01%)

0.70 (2.54%)

0.44 (2.99%) 0.29 (1.71%)

The values of the fitting parameter A are A ) 30.5 for Br and A ) 14.3 for Cl (see text). Numbers in parentheses are average deviations for N ) 14 values of the association constants (values at 0 M salt not included) where average deviation ) ∑(1-ArX%(calc) - 1-ArX(exp))/N. The range in error for individual %1-ArX values is from 0.03% to 10.5%. See text for details. a

-

S1-S3) the [H2O]/[XT] molar ratio is 10 or less, and the formation of contact ion pairs is certainly reasonable. A number of aspects of the results in Figures 1-3 are consistent with the formation of ion pairs. First, the %1-ArX yields and 79Br line widths are not linear, but curve downward with increasing [XT], consistent with the formation of ion pairs and contrary to the dependence of solution properties on the concentrations of many simple salts.19 Second, both the %1ArX and 79Br plots have breaks in the curves at relatively low salt concentrations, showing a transition in the change in [X-] with [XT]. Third, the decrease in %1-ArX yields with decreasing spacer length of the bolaform salts at any one salt concentration follows the yield order TMAX > 1-4-1 2X > 1-3-1 2X > 1-2-1 2X. The increases in 79Br line widths are in the opposite order, and both trends are consistent with a decrease in [Br-] relative to [BrT] with increasing salt concentration. Fourth, the ratio plots, Figures 1B, 2B, and 3B, and changes in %1-ArX yields and 79Br line widths show initial rapid changes in the ratios followed by plateaus. In the plateau region, the rate of change in %1ArX for TMAX and each bolaform salt are the same and the rate of change of 79Br line widths are the same for 1-n-1 2Br (n ) 2-4) and TMABr. The presence of the plateau region strongly supports our assumption that K2 for the formation of the (dicat‚X2) pair is the same as KTMAX for the formation of the (cat‚X) pair. The similarities of the K1 values for the binding of the first Br- to dicat2+ (Scheme 2) obtained by the chemical trapping and 79Br line width methods also strongly support this interpretation. Note that the average error in the K1 and KTMAX values for the chemical trapping method is never greater than 4% (Table 2), showing that the values of K1 and K2 are reasonable. The assumptions that %1-ArX yields only depend on [X-] in solution, eq 5, i.e., that 1-ArN2+ does not react with X- in (dicat‚X)+ or (dicat‚X2) pairs and that 79Br line widths depend on the weighted sums of line widths for free and paired Br-, eq 6, provide a consistent and sufficient interpretation of the results. The association constants in Table 2 obtained from the chemical trapping data were used to estimate the fractions of free and ion pair forms of the bolaform salts at all [XT] (Figures 1C and 2C for 1-2-1 2X and Figures S2-S4 for the 1-3-1 2X and 1-4-1 2X salts (see Supporting Information)). For each bolaform electrolyte, the fraction of dicat2+ goes through a maximum and tends toward zero with increasing XT. The fraction of free X- decreases steadily, and the fractions of (dicat‚ X)+ and (dicat‚X2) go through shallow maxima and increase continuously with increasing [XT], respectively. The ion pair fractions are smaller when Cl- is the counterion than when Bris the counterion. The results for 1-3-1 2X and the 1-4-1 2X show the same trends, but the fractions of paired ions decrease with increasing spacer length. Finally, above about 1 M XT, a significant fraction of the halide ions are in ion pairs, unlike in TMAX solutions, because the dicat2+ binds the first X- more

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strongly than the second X-. The values of K1 and K2 and KTMAX in Table 2 are similar to literature values of association constants estimated for other quaternary ammonium halides with different alkyl groups and halide ions. The values of the association constants increase with both cation hydrophobicity and anion size but are on the order of 1-10 M-1. They were obtained by a variety of methods, including molecular dynamics,22 dielectric spectroscopy,40 capillary zone electrophoresis,39 and conductivity.36,38 Our values for TMACl and TMABr (Table 2) are similar to published results.22,40,41 Eisenman developed a thermodynamic model for changes in affinity orders for counterions by ion selective electrodes composed of different glasses in the 1960s.11 Diamond and Wright applied this approach to biological interfaces.12 In brief, free hydrated counterions and charged sites at glass and biological interfaces are in dynamic equilibrium with site‚ counterion pairs and selectivity depends on the balance between the ion specific free energies of hydration of the ions and ion specific free energy of interaction between the site and the counterion. In bolaform and TMAX salt solutions, hydrated TMA+ and dicat2+ and their hydrated counterions are in equilibrium with hydrated ion pairs, and the strength of these interactions depends on counterion type, Br- and Cl-, cation type, TMA+ and dicat2+, and bolaform spacer lengths. Molecular dynamics calculations suggested that the free energy difference between water-separated and contact ion pairs is small.22 The free energy of replacement of water of hydration by a counterion depends on the difference between the free energies of hydration of each ion and the free energy of the hydrated ion pair (water separated or contact), which depend on the nature of the cation and anion. Conductivity,38 neutron diffraction experiments,59 and molecular dynamics calculations41 are consistent with weak interactions between TMA+ and neighboring water molecules, more like apolar solute than a cation. However, Cl- and Br- interact with water in part via hydrogen bonds, and the interactions of water with Br- are weaker than those with Cl-.20,24,25,60 Thus, in moderate to concentrated solutions, ion pair formation by quaternary ammonium halides is not energetically prohibitive. In addition, paired ions are less strongly hydrated than free ions,21,31,61,62 consistent with ion pair formation being primarily an entropydriven process.21,61,62 The increase in the association constants of the bolaform salts with decreasing spacer length is consistent with stronger interactions between the dication quaternary ammonium groups and halide ions than with the monocation TMA+. Because Br- is more weakly hydrated and more polarizable than Cl-, Br- has larger association constants consistent with the Hofmeister series for anions.2,4 Specific ion pair formation and a reduced demand for hydration by ion pairs compared to free ions provides a straightforward explanation for the shift in the balance of noncovalent forces leading to sphere-to-rod transitions in

Bolaform Electrolyte Ion Pairs in Water micellar solutions.48,51,57,63 The hydrophobic effect, i.e., amphiphile hydrocarbon tails minimizing their contact with water, drives micelle formation. Balance is provided by stronger shortrange interactions between water and amphiphile headgroups and counterions. Because free energies of ion pair formation between quaternary ammonium and Cl- and Br- are small, the fraction of pairs ions becomes significant only in moderately concentrated solutions, e.g., greater than 0.2 M [BrT] (Figure 1) and 0.5 M [ClT] (Figure 2). However, the concentrations of headgroups and counterions in the interfacial regions of aqueous single tail cationic micelles are estimated to be the order of 1 M and greater in moles per liter of interfacial volume.42,44-47,64 At these high concentrations, the fraction of ion pairs within the interfacial region is significant, and because paired ions are less strongly hydrated than free ions, interfacial water is lost to the surround bulk phase, permitting tighter packing of the monomers in a cylindrical array. The amphiphile and counterion concentrations at which the sphere-to-rod transition occurs depend on headgroup and counterion type as noted in the Introduction and expressed here as association constants. Similar explanations should account for ion specific effects at biointerfaces and biomimetic interfaces,2-4,7,18 polyelectrolytes,65 and air/water interfaces.10 Conclusions Chemical trapping and 79Br line width results are consistent with ion pair formation by TMAX and 1-n-1 2X (n ) 2-4, X ) Cl, Br) bolaform electrolytes. The association constants estimated from the data for Br- determined by both methods are essentially the same. For TMAX, the association constants are small, KTMABr ≈ 0.8 and KTMACl ≈ 0.3, consistent with literature results. Two association constants were estimated for the bolaform electrolytes. The values K1 for the formation of the (dicat‚X)+ vary from 0.4 to 17 M-1. They decrease with increasing spacer length, n, and are larger for Br- than Cl- for the same spacer length. The values of the second constant, K2, for the formation of the neutral ion pair, (dicat‚X2), are demonstrated to be the same as those for TMAX salts with the equivalent counterion. Neither the chemical trapping nor 79Br line width methods distinguish between water-separated and contact ion pairs, but in solutions above 3 M bolaform electrolyte, the stoichiometric water concentration is very low and contact ion pair formation is sensible. The same short-range ion pair and hydration interactions that govern ion pairing in aqueous TMAX and bolaforms solutions should be present within the interfacial regions of single chain and gemini amphiphile micelles that are essentially concentrated solutions of headgroups and counterions. Ion pairing and interfacial dehydration driven by the hydrophobic effect provide a novel explanation for the shift in the balance of noncovalent forces that drive the sphere-to-rod transition. Experimental Section Materials. The arenediazonium salt, 2,4,6-trimethylbenzenediazonium tetrafluoroborate (1-ArN2BF4), was prepared by the method of Doyle and Bryker.56,66 Tetramethylammonium bromide (TMABr), tetramethylammonium chloride (TMACl), and the HPLC standards, 2,4,6-trimethylphenol (1-ArOH), 2,4,6trimethylbromobenzene (1-ArBr), 2,4,6-trimethylchlorobenzene (1-ArCl), and 1,3,5-trimethylbenzene (1-ArH), were purchased from Aldrich. Solvents were reagent grade and used as received. All dediazoniation experiments were carried out in carbonfiltered, deionized, distilled water.

J. Phys. Chem. B, Vol. 109, No. 49, 2005 23635 Bolaform Electrolytes, 1-n-1 2Br (n ) 2-4). Bis(trimethyl)-R,ω-alkanediammonium dibomide, 1-n-1 2Br, salts were prepared by reaction of excess methyl bromide (Aldrich) with the appropriate diamine, H2N(CH2)nNH2 (n ) 2-4) (Aldrich).67 1-n-1 2Cl salts were prepared by ion exchange from the dibromides. The synthetic procedures are given for 1-2-1 2Br and 1-2-1 2Cl. The other bolaform electrolytes were prepared by the same methods, and only the analytical data are shown. 1-2-1 2Br: N,N,N′,N′-Tetramethylethylenediamine (2.0 g, 17.2 mmol) dissolved in ca. 200 mL of MeOH and cooled to -10 °C (ice/MeOH bath). Bromomethane (5 mL, 173 mmol, 10 mol excess) was added rapidly to the stirred MeOH solution, removed from the ice bath and brought to room temperature (∼6 h), refluxed gently for ∼36 h, and returned to room temperature. The white precipitate was filtered under dry nitrogen, recrystallized three times from Et2O, and vacuumdried overnight, yielding 4.38 g of white solid (yield: 84%). 1H NMR (D O): δ 3.307 (s, 18H), δ 4.048 (s, 4H). Elemental 2 Analysis: Expected: C, 31.39; H, 7.24; Br, 52.27; N, 9.15. Found: C, 31.44; H, 7.28; Br, 52.50; N, 9.07. 1-2-1 2Cl. Dowex 1 × 4-30 Cl ion-exchange resin (45 g, ca. 10 mol excess Cl-) was packed in a 33 cm × 3.5 cm column. 2.5 g (8 mmol) of 1-2-1 2Br salt was dissolved in a small volume of water (ca. 8 mL), passed through the column with excess H2O, and collected in test tubes. Complete elution of the salt was confirmed by absence precipitate by a AgNO3 test. All aqueous solutions containing salt were combined and lyophilized, and the resulting white solid was recrystallized three times from CH3CN and vacuum-dried overnight. The ion-exchange procedure was repeated three times, giving 1.2 g of white solid (yield: 85%). 1H NMR (D O): δ 3.169 (s, 18H), δ 3.916 (s, 4H). Elemental 2 Analysis: Expected: C, 44.2; H, 10.2; Cl, 32.6; N, 12.9. Found: C, 42.63; H, 10.47; Cl, 30.56; N, 12.24; Br,