J. Phys. Chem. C 2007, 111, 15613-15619
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Proton Chemical Exchange in Aqueous Solutions of Dodecylammonium Chloride: Effects of Micellar Aggregation† Kosma Szutkowski,‡,§ Peter Stilbs,‡ and Stefan Jurga*,§ DiVision of Physical Chemistry and Industrial NMR Centre Department of Chemistry, Royal Institute of Technology, SE-10044 Stockholm, Sweden, and Department of Macromolecular Physics, Faculty of Physics, Adam Mickiewicz UniVersity, ul. Umultowska 85, PL61614 Poznan´ , Poland ReceiVed: May 14, 2007; In Final Form: August 20, 2007
Proton chemical exchange was studied in aqueous solutions of dodecylammonium chloride (DDACl) for two selected concentrations, 18 and 33 wt %. The Fourier transform Carr-Purcell-Meiboom-Gill (CPMG) NMR method combined with the Carver and Richards model for T2 dispersion curve analysis were employed to evaluate the temperature dependence of the proton exchange rates kex. An increase of the energy barrier height ∆Gq for the proton chemical exchange between water and ammonium cation (-NH3+) was observed as the DDACl concentration was increased. Results are complementary to previous studies of aggregation phenomena for various n-alkylammonium chlorides.
1. Introduction Nowadays, the process of obtaining new enhanced ceramic materials or composites containing carbon nanotubes is carried out via colloidal processing, which is founded on the efficient dispersion of the ceramic powders and subsequent selfassembly.1,2 Dispersing effectiveness and formation of the stable colloidal suspensions depend on the molecular structure of the amphiphile, charge size, and its location in the molecule. Controlled aggregation of colloidal suspensions and effective charge stabilization are thus central. Although many aspects of charge stabilization are already explained, there is still a need to develop a microscopic understanding of its origins.3 Quantitative determination of physicochemical interactions between water and lyotropic liquid crystal interfaces, likewise, are of interest. Surfactant-based systems are important in the food and chemical industry, in the role of stabilizers for numerous types of colloidal suspensions or emulsions. Our paper relates to the problem of the aggregation of dodecylammonium chloride (DDACl) in aqueous solutions. The DDACl/H2O system was chosen because the binary phase diagram is complex, yet interesting. For example, the existence of the hexagonal phase island surrounded by the isotropic phase and lack of the cubic phase still remain unexplained.4 We believe that our nuclear magnetic resonance (NMR) studies may also give an insight into the nature of the phase transition from the isotropic micellar to the hexagonal phase. Our studies are partly inspired by results obtained by Matulis and Bloomfield, who showed that hydrophobic aggregation of various alkylamines is related to pKa shifts of the hydrophilic -NH3+ group.5 This aggregation process is both temperature and concentration dependent and can be related to acid-base equilibriainwater.6,7 Dodecylammoniumchloride(C12H25(NH3)+Cl-) is a well-known crystalline material that transforms into a lyotropic liquid crystal with added water, and it belongs to the †
Part of the “Keith E. Gubbins Festschrift”. * To whom correspondence should be addressed. E-mail: stjurga@ amu.edu.pl, tel: +48 61 8295216, fax: +48 61 8295245. ‡ Royal Institute of Technology. § Adam Mickiewicz University.
group of a long-chain cationic surfactants often considered as model systems of biological membranes. With water, DDACl exhibits a number of different lyotropic liquid crystalline phases. Above the critical micelle concentration CMC ) 14 mmol/l, the following states occur: isotropic micellar, nematic, hexagonal, and lamellar.8-10 The lamellar phase is often of particular interest because it resembles biological systems, and thus is frequently considered as a model system for biological membranes.4,8,9 In aqueous solutions, n-alkylammonium chlorides dissociate to an ammonium hydrophilic cation R-NH3+ and further, through the deprotonation mechanism in the acid-base reaction, to an amine group R-NH2.5 Coupled to surfactant aggregation, hydrophilic -NH3+ groups tend to deprotonate, shift their pKa values, and decrease the magnitude of the standard Gibbs energy |∆G| for ammonium deprotonation. As shown by Matulis, pKa values decrease with increasing alkyl chain length and surfactant concentration.5 If this effect originates from a reduction in the double layer charge, then pH values in the solutions ought to decrease as well. pKa related equilibrium will also be manifested in changes of the proton exchange rates, which are easily measured by NMR methods (see also the theoretical section).11 To study this chemical exchange we have adopted the fact that one of the main sources of the enhanced water transverse relaxation is proton chemical exchange.12 It is known that mutual proton chemical exchange takes place between -OH, -COOH, -NH3+, or other groups. As pointed out by Hills,13 such a chemical exchange process between water and -NH3+ groups is an important pathway for transverse spin relaxation of the protons involved. Quantified data allow us to obtain first-order proton exchange rates (kex) between water and ammonium cations -NH3+.14 2. Theoretical 2.1. Absolute Rate Theory. Chemical exchange is described through the absolute rate theory of the kinetic processes.15-17 In the following we refer to the reaction R-NH2 + H+ h R-NH3+, where R denotes an alkyl chain. The enthalpy and entropy of activation for the protonation/deprotonation reaction
10.1021/jp073696s CCC: $37.00 © 2007 American Chemical Society Published on Web 10/04/2007
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for the activated complex can be calculated according to the Eyring absolute rate theory (eq 1),
( ) ( ) ( )
η)
τcp 2x2
κkBT -∆Gq kex(T) ) exp h RT )
κkBT ∆Sq -∆Hq exp exp h R RT
Ψ ) R-2 - ∆ω2 +
(2)
where ∆Hq is the enthalpy of activation, and ∆Sq is the entropy of activation. Determination of the exchange rates (kex) as a function of temperature allows an experimental determination of ∆Hq and ∆Sq. The free energy of activation (∆Gq) may be related to the Gibbs free energy (∆G) of chemical reaction. Such dependencies are named “linear” free energy relations. For a related series of spontaneous reactions, as the magnitude of the standard reaction Gibbs energy (∆G) increases, the activation barrier (∆Gq) decreases.11,18 2.2. Chemical Exchange Studied by Carr-Purcell-Meiboom-Gill NMR. Let us consider an interrelation between chemical exchange rate and NMR parameters. Basically, the influence of the chemical exchange onto the line width could be characterized by the Swift-Connick relations,19 relating chemical exchange rates to resonance line widths. More accurate methods for obtaining chemical exchange rates are based on studies of NMR transverse relaxation times (T2) by the CarrPurcell-Meiboom-Gill (CPMG) experiment.20,21 In the most preferred model, the T2 dispersion with RF pulse spacing is analyzed.22,23 To calculate exchange rates (kex) one may apply the Carver-Richards model relating chemical exchange phenomena with T2 dispersion curves for arbitrary cases of twosite exchange.24 A general two-site exchange model between sites A and B, coupled by the exchange rate kex, is given by eq 3,
A(Pa) h B(Pb)
(3)
where Pa and Pb are the respective exchangeable proton populations. The T2 dispersion curve for general two-site exchange process is described by the equation given by Hills,13,24
T2-1 ) -
1 ln λ τcp
(4)
where
ln λ ) - τcp
R+ + ln{(D+ cosh2 ξ - D- cos2 η)1/2 + 2 (D+ sinh2 ξ + D- sin2 η)1/2} 2D( ) ( 1 +
ξ)
τcp
(Ψ + 2∆ω2) (Ψ2 + ζ2)1/2
{([+ Ψ + (Ψ2 + ζ2)1/2]1/2}
2x2
4 τaτb
ζ ) 2∆ωR(1)
where κ is the transmission coefficient usually equal to 1, kB is the Boltzmann constant, and h is the Planck constant. The free energy of activation ∆Gq is given by eq 2,
∆Gq ) ∆Hq - T∆Sq
{([- Ψ + (Ψ2 + ζ2)1/2]1/2}
R- )
1 1 1 1 + T2a T2b τa τb
R+ )
1 1 1 1 + + + T2a T2b τa τb
∆ω ) ωa - ωb ω(a,b) ) 2πδ(a,b)ν0 Lifetimes in site A (τa) and site B (τb), populations Pa and Pb, and kex obey eqs 5 and 6.
Pa + Pb ) 1
(5)
P a Pb 1 ) ) ) kex τa τb τ
(6)
For exchange rates . 1/∆ω, the effective relaxation time (T2) could also be estimated from the 1H line-width at half-height ∆ν1/2, provided the instrumental resolution is high enough. There, one evaluates transverse relaxation time by using equation 7.
T2b )
1 π∆ν1/2
(7)
We will use this equation later to interpret some results obtained from dispersion curves and 1H NMR spectra. Despite its model nature, the system in our study is still quite complex. As a result of dissociation and hydration there are several types of water: bulk water, interfacial water, and bound water.25 Bound water molecules are strongly associated through hydrogen bonds with the hydrophilic groups (here, the ammonium ions -NH3+). Interfacial and bulk water molecules are not affected by the hydrophilic matrix,26 therefore they do not directly undergo chemical exchange with a hydrophilic group. A direct chemical exchange with hydrophilic ammonium ions takes place only with bound water molecules because only those can create hydrogen bonds with hydrophilic group. We may assume that, because of the fast self-diffusion of water and the fast structural diffusion of protons27,28 counteracting long lifetimes of water molecules at the surface, all types of water molecules can undergo exchange of some type, and populations could be averaged to a single population Pa. 3. Experimental Dodecylammonium chloride was synthesized from dodecylamine obtained from SIGMA according to the procedure given by Kertes.29 Samples were prepared by adding doubly distilled water to dry, solid DDACl to achieve the desired compositions. All samples were sealed in 8 mm NMR glass tubes. To achieve homogenization, our samples were heated to the isotropic phase (around 90 °C) and were kept in the bath for a couple of hours. The samples at this temperature were liquid, transparent, and without any color. We present two samples in this paper:
Proton Chemical Exchange in Dodecylammonium Chloride DDACl/H2O 18 wt % (C1218) and DDACl/H2O 33 wt % (C1233). The C1218 sample is characterized by the isotropic (micellar) phase only. The C1233 sample is characterized by following phases: lamellar at 20-25 °C, nematic at 25-30 °C, isotropic (micellar) at 30-50 °C, hexagonal (micellar) at 5070 °C, and high-temperature isotropic above ∼70 °C.9 Those temperatures are not strict, and they may vary. The existence of lyotropic phases was verified by polarized optical microscopy using a Leica DMLP microscope equipped with heating setup. NMR experiments were performed on a Bruker Avance DMX spectrometer operating at 400 MHz using XWin-NMR 2.6 PL6 software. The Micro2.5 microimaging probe with a bird-cage 10 mm resonator and 150 W 1H power amplifier. This probe was also used for conducting anisotropic diffusion measurements (data are not presented in this work). The disadvantage of this probe is that ideal shimming is almost impossible, and as a result, bottom parts of the resonance lines are slightly distorted. In our shimming procedure, we used Z, X, Y and Z2 shim values so that the pure water resonance line-width was about 8 Hz. 1H NMR spectra were taken from a Fourier transform inversion-recovery pulse sequence (180-τ-90°), where the τ delay was 100 us. This pulse sequence was used for the simultaneous T1 and spectra measurements (relaxation data will be published elsewhere). The CH3 protons were used as an internal standard and were set to 0.87 ppm. Transverse proton relaxation times were determined using the Fourier transform CPMG pulse sequence: 90°x-[τcp/2 - 180°y - τcp/2 - spin echo](n times). A sufficient number of acquisition cycles with a repetition delay of 10 s were applied where the 90-180° pulse spacing varied between 50 us and 3 ms. After the acquisition of 128 echoes for each τcp time, a discrete Fourier transform with a phase correction was made before the 2-dimensional (2D) display, then the 128 spectra (from 128 experiments) were wrapped up into semi-2D spectral form. Experimental intensities for T2 dispersion curves were taken from the amplitude of the water resonance line at around δ(H2O) ) 4.7 ppm. Chemical exchange rates (kex) were taken from simulations of the dispersion curves based on eq 4. Final simulations and fits were performed by means of MathCAD 13 software. The simulation procedure was required to represent eq 4 in a symbolic form. As a first step, all subequations were substituted using the mathcad symbolic engine. The resulting equation was then used for fitting to the experimental T2-1 data. As the convergence criteria, the least mean square error (LMS) was defined and minimized by the “Minerr” function using the conjugate gradient algorithm. There are seven parameters in eq 4: Pa, Pb, τa, τb, ∆ω, T2a, and T2b. The number of independent parameters is less than seven because Pa ) 1 - Pb, τb ) τa(1 - Pa)/Pa, and Pa/τa ) Pb/τb. Finally, after few substitutions we have five independent parameters: Pa, T2a, T2b, τa, and ∆ω. According to Hills, one can fit all of those parameters independently. We believe that it is possible; however, for the purpose of our fitting procedure, only the transverse relaxation time T2a was kept constant. The frequency difference ∆ω and population Pa values were allowed to change in the limited range of values (close to theoretical values) to search for a minimum value of LMS error. Finally, only three parameters were fitted freely: T2b, Pa, and τa. The exchange rate kex is obtained directly from the Pa/τa ratio given by eq 6. The relaxation time T2b of site B was set to that of the -NH3+ protons, and the transverse relaxation time T2a was set to that of the bulk water protons. Initial proton populations were taken
J. Phys. Chem. C, Vol. 111, No. 43, 2007 15615
Figure 1. Temperature dependence of the 1H NMR spectra for isotropic phase of DDACl + H2O 18 wt %.
from sample concentrations; all water protons were included into the Pa population, and all -NH+ 3 protons were included into the Pb population. 4. Results and Discussion 4.1. Proton NMR Spectra. 1H NMR spectra are very useful. They could be used to detect unique spectral features of each lyotropic phase and consequently used to resolve a phase diagram. The temperature change of the water resonance peak position provides information about the hydrogen bond state and the temperature/concentration dependent acid-base equilibria. Finally, 1H NMR resonance line-widths also gives us information about molecular dynamics and chemical exchange phenomena. The temperature dependence of 1H NMR spectra recorded for the isotropic phase of C1218 and C1233 are presented in Figures 1 and 2, respectively. The corresponding temperature dependence for hexagonal phase C1233 is presented in Figure 3. A high-resolution 1H NMR experiment reveals following proton signals coming from the alkyl chain of the alkylammonium salt: CH3(ω)-(CH2)8-CH2(γ)-CH2(β)-CH2(R)-NH3+.30 The resonance from the -CH3(ω) group is assigned to a triplet at ≈0.87 ppm; the long-chain methylene protons -(CH2)8- give a signal at ≈1.28 ppm. Resonance lines assigned to -CH2(R) protons are also visible at ≈3 ppm. If we consider an aqueous solution of alkylammonium salts, then the signal from ammonium protons should be visible at around 7-9 ppm; however, the intensity of this signal is strongly dependent upon the salt concentration and pH in the solution.14 The water 1H NMR resonance is usually observed at around 4.7 ppm. The presented spectra are significantly different from those obtained by the high-resolution NMR experiment.30 Lines are broadened so that the scalar couplings are not resolved, but resonances coming from -CH2(R), -(CH2)8-, and -CH3(ω) protons are visible in the spectra, so they could be used as an internal standard. For isotropic phase C1218 we have observed a low-intensity signal at around 8.7∼9 ppm that could be assigned to ammonium protons. We did not further consider those data more than using the value of 8.7 ppm for further reference. Contrary to the C1218 sample the ammonium protons resonance for isotropic phase C1233 was well-visible at around 7.8-8.5 ppm (Figure 2b). This pronounced ammonium proton visibility in DDACl 33% could be explained by lower pH values in the solution because of the higher DDACl concentration.
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Figure 2. 1H NMR spectra for isotropic phase of DDACl + H2O 33 wt %; (a) temperature dependence of the 1H NMR spectra, and (b) magnified 1H NMR spectra; chemical shifts in a range of R-NH3+, (c-d) selected spectra comparison at T ) 29 and 51 °C.
4.1.1. Lyotropic Phase Characterization. The characteristic spectrum of the isotropic phase consists of well-resolved signals from -CH2(R), -(CH2)8-, and -CH3(ω) protons (Figure 1). Contrary to the isotropic phase, the hexagonal phase spectrum is different in a significant way. A hexagonal phase could be characterized by broad, solid-like Gaussian contribution in the resonance line. This Gaussian part of the hexagonal spectra is best seen in Figure 3c, which shows a 10 kHz wide spectral component. This solid contribution to the 1H NMR spectra primarily arises from those protons that experience a decrease in mobility caused by an increase in intermicellar interactions.31 It is interesting that even in the hexagonal phase we are able to observe signals originating from -(CH2)8- and -CH3(ω) protons (Figure 3d). We attribute this to the lateral diffusion of molecules within the micelles. Dipole-dipole interactions are partially averaged then, so that signals from alkyl chains become more liquid-like and visible in the spectra. 4.1.2. Temperature Dependence of Chemical Shifts. Observed chemical shifts of water δ(H2O) are not constant with regard to the temperature (Figures 1, 2 and 3a). When raising the temperature, an upfield change (toward smaller ppm values) of δ(H2O) is observed. This result is usually referred to as a broken-down ice structure effect and could be explained by the breaking of hydrogen bonds and configurational alterations.32 Literature data indicate that δ(H2O) decreases with increasing temperature for 0.469 ppm at 20-65 °C and 0.209 ppm at 3050 °C.32 Our results shown in Figure 1 indicate that the δ(H2O) shift is bigger than that corresponding to bulk water. The chemical shift difference for C1218 in the temperature range 20-65 °C equals ≈ 0.64 ppm. This value is bigger by about 0.17 ppm with respect to bulk water. Although there are no experimental data for DDACl in aqueous solutions, our extra
Szutkowski et al.
Figure 3. 1H NMR spectra for the hexagonal phase of DDACl + H2O 33 wt %; (a) temperature dependence of the 1H NMR spectra, (b) selected spectra comparison at T ) 52 and 56 °C, (c) temperature dependence of the 1H NMR spectra shown in a broader chemical shifts range, and (d) magnified 1H NMR spectra; chemical shifts in a range of -(CH2)8- and -CH3(ω) groups.
change in water chemical shifts is well-explained by the additional structure-breaking influence of alkylammonium salts such as tetraalkylammonium chlorides in water solutions, where an increase of the temperature and the alkyl chain length promote an additional upfield water resonance shift.33 The upfield shift of the water chemical shift is also observed for isotropic phase C1233 (Figure 2a). For the temperature range 29-51 °C, the shift is equal to ≈0.24 ppm. This chemical shift change is nearly equal to that observed for pure water. As we see, the influence of the surfactant on the water resonance position is smaller for the C1233 sample in the isotropic phase then that corresponding for the C1218 sample. The temperature dependence of 1H NMR spectra for the C1233 hexagonal phase is shown in Figure 3a. The water chemical shifts are calibrated versus -(CH2)8- and -CH3(ω) shown in Figure 3d. The smallest water chemical shift of ≈2.43 ppm was recorded at 56 °C. This temperature is close to the middle of the hexagonal phase “island” of the phase diagram. The transition from the isotropic phase to hexagonal at 51-52 °C is governed by the enhanced water structure-breaking process and decrease in the number hydrogen bonds. A hexagonal phase is a more aggregated phase than the lowtemperature isotropic phase. We may hypothesize that the transition from isotropic to hexagonal phase might be governed by a decrease in pKa values because of the micellar aggregation process.5 Any change in the surface charge density could be ascribed to changes of the pKa of the cationic hydrophilic group in water solutions. The pKa shifts reflect information about neighboring charges and dipoles, dielectric permittivity, hydration, and counterion concentration on the surface of micellar systems.6,7,34,35 We can see in Figure 3a that the transition from hexagonal to isotropic phase starts above 57 °C. We observe
Proton Chemical Exchange in Dodecylammonium Chloride that the water chemical shift returns to higher values, characteristic for isotropic phase. If enhanced δ(H2O) shifts in the hexagonal phase are induced by pKa shifts enforced by aggregation, then the transition from the isotropic phase to hexagonal at 51-52 °C is governed by enhanced deprotonation of the micellar surface and a subsequent decrease in repelling electrostatic forces between micelles. This conclusion is based on the argument that elevated temperatures will destroy the charge stabilization of the micellar solution so that hexagonal packaging of the elongated micelles results. The hypothesis is the following; a phase transition from isotropic to hexagonal phase is related to a change of electrostatic repulsive interactions between positively charged micelles of DDACl. The “strength” of repulsions between micelles is related to the charge density on the micellar surface and the number of counter-ions at the micelle vicinity.36,37 If we consider the isotropic phase DDACl 33%, we clearly see that the ammonium resonances shown in Figure 2b and the water resonance shown in Figure 2a both shift upfield (lower δ values), and at the same time, the resonance difference decreases with temperature. For 29 °C we have 7.8 - 4.65 ) 3.15 ppm, and for 51 °C we have 7.16 - 4.41 ) 2.7 ppm. On the basis of the chemical shift changes shown in Figure 2, panels a and b, we observe that the difference of the chemical shifts between water and ammonium protons decreases with increasing temperature. The chemical shift difference at T ) 29 °C equals 7.8 - 4.65 ) 3.15 ppm and 7.16 - 4.41 ) 2.75 ppm at T ) 51 °C (Figure 2, panels a and b). The decrease of the difference between δ(H2O) and δ(NH3) with increasing temperature is a clear indication that a chemical exchange takes place. Furthermore, both water and ammonium line-widths are increased with increasing temperature. 4.1.3. Line-shape Analysis. Comparison of water resonance signals demonstrate that (beside considerable chemical shift change) 1H NMR spectra of water protons are remarkably broadened at elevated temperatures. Approximate values of water proton resonance line widths at half-height (∆ν1/2) were 48 and 130 Hz at T ) 20 and 65 °C, respectively. Furthermore the resonance of water protons broadens with increasing temperature (from 23 Hz at T ) 29 °C to 55 Hz at T ) 51 °C, Figure 2, panels c and d). Next, we consider the bulk water line-width. It is known that the dipole-dipole relaxation time is dependent upon the correlation time τc, which decreases as viscosity decreases with increasing temperature. The bulk water line-width is governed by the transverse relaxation time T2, dominated by the dipole-dipole relaxation mechanism. Thus, for pure water we would observe that the water 1H NMR linewidth simply decreases with increasing temperature as the T2 time becomes longer. The observed dependence of the water line broadening is the pure effect of the DDACl salt added, this will be discussed later. 4.2. FT-CPMG NMR. 4.2.1. T2 Dispersion CurVes. The temperature dependencies of water proton transverse relaxation times T2(τcp) for C1218 and C1233 are shown in Figures 4 and 5, respectively. Solid lines in Figures 4-5 indicate simulations of the Carver-Richards (CR) model. All necessary parameters used in simulations of the CR model are given in Table 1 for C1218 and Table 2 for C1233. The resulting exchange rates (kex) are presented in Figure 6, which represents proton exchange rates kex and their temperature dependence. The solid lines are fits to the Eyring equation (eq 1). The free energy of activation (∆Gq) at a given temperature is calculated using eq 2. Using calculated values of enthalpy of activation (∆Hq) and entropy of activation (∆Sq) given in Figure 6 for DDACl + H2O 18 wt
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Figure 4. The transverse relaxation times of water protons T2(τcp) measured as a function of τcp/2 in the CPMG experiment obtained for DDACl + H2O 18 wt %; solid lines indicate simulations based on the Carver-Richards model. ISO: isotropic phase.
Figure 5. The transverse relaxation times of water protons T2(τcp) measured as a function of τcp/2 in the CPMG experiment obtained for DDACl + H2O 33 wt %; solid lines indicate simulations based on the Carver-Richards model. The experimental points for the lamellar phase were obtained after cooling down the sample. LAM: lamellar phase; ISO: isotropic phase; HEX: hexagonal phase.
TABLE 1: Parameters Used in the Simulations of the Curves in the Figure 4a T [°C]
Pa
δω [ppm]
T2b [ms]
τa [ms]
kex [1/s]
20 25 30 35 40 45 50 60
0.97 ( 0.005 0.966 ( 0.01 0.955 ( 0.02 0.92 ( 0.05 0.975 ( 0.001 0.976 ( 0.002 0.976 ( 0.001 0.976 ( 0.001
4.03 ( 0.1 3.53 ( 0.1 3.68 ( 0.1 4.03 ( 0.1 3.78 ( 0.1 4.23 ( 0.1 4.23 ( 0.1 4.33 ( 0.1
0.90 ( 0.4 2.80 ( 0.6 5.00 ( 1.5 7.30 ( 3.0 2.40 ( 1.5 2.10 ( 0.3 2.30 ( 1.5 1.70 ( 0.2
64.0 ( 1.0 31.8 ( 0.5 19.8 ( 0.5 13.8 ( 0.5 7.7 ( 0.3 6.3 ( 0.6 3.5 ( 1.2 2.3 ( 0.2
15 ( 1 30 ( 1 48 ( 2 65 ( 5 126 ( 5 156 ( 15 301 ( 80 429 ( 20
a The theoretical value of Pa for DDACl 18 wt %, based on the sample composition, is 0.973, T2a ) 2 s, and δω) δ(NH3+) - δ(H2O).
%, we obtain ∆Gq18% ) 64.5 ( 1.7 kJ mol-1 as the value of the free energy of activation at 35 °C (308 K), and for DDACl + H2O 33 wt %, we obtain ∆Gq33% ) 66.6 ( 0.6 kJ mol-1. The observed value of ∆Gq increased with increasing DDACl concentration by 2 kJ mol-1. It is not possible to directly obtain proton signals of ammonium ions for some aqueous solutions.14 Therefore, we cannot measure the transverse relaxation time (T2b) in a direct way. We can only assume that this relaxation time (T2b) is
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TABLE 2: Parameters Used in the Simulations of the Curves in the Figure 5a T [°C]
Pa
28 30 35 50 60 70 80 85
0.943 ( 0.01 0.943 ( 0.02 0.943 ( 0.01 0.92 ( 0.01 0.943 ( 0.02 0.935 ( 0.01 0.933 ( 0.002 0.93 ( 0.002
δω [ppm]
T2b [ms]
3.35 ( 0.1 0.008 ( 0.003 3.35 ( 0.1 0.007 ( 0.002 3.15 ( 0.1 4.64 ( 0.6 3.55 ( 0.1 8.22 ( 1.5 3.55 ( 0.1 0.008 ( 0.004 3.45 ( 0.1 7.82 ( 4.0 3.55 ( 0.1 5.50 ( 2.0 3.55 ( 0.1 23.0 ( 30.0
τa [ms]
kex [1/s]
50.0 ( 1.0 44.0 ( 1.0 33.0 ( 1.0 12.2 ( 0.5 7.3 ( 0.1 3.6 ( 0.4 2.0 ( 0.3 1.7 ( 0.1
19 ( 1 22 ( 1 29 ( 1 75 ( 2 130 ( 2 262 ( 30 470 ( 50 558 ( 5
a The theoretical value of Pa for DDACl 33 wt %, based on the sample composition, is equal to 0.943, T2a ) 2 s, and δω ) δ(NH3+) - δ(H2O).
Figure 6. Eyring plot for proton exchange rates kex obtained for DDACl + H2O 18 and 33 wt %. Solid lines indicate fits to the Eyring equation; the obtained thermodynamical parameters are as follows: (O) ∆Hq ) 63.0 ( 1.0 kJ mol-1, ∆Sq ) -5.7 ( 3.5 J mol-1 K-1, (0) ∆Hq ) 51.8 ( 0.2 kJ mol-1, and ∆Sq ) -49 ( 1.5 J mol-1 K-1.
comparable to the overall transverse relaxation time of protons in the alkyl chain. The transverse relaxation time of those protons could be estimated from 1H NMR spectra using eq 7. The signals from -CH2 groups were not analyzed, because they originate from nonexchangeable protons, and a dispersion with τcp in the CMPG was not observed either. Normally, the observed relaxation time of water/ammonium protons was much shorter than the relaxation time for -CH2 and -CH3 protons. Characteristic dispersion curves were observed for isotropic micellar phases as shown in Figures 4 and 5.13,24,38 These effects result from many parameters and are basically described by the CR model given by eq 4. See Tables 1 and 2 for actual parameters used in our simulations. The most important governing parameter is the relation between the difference of the resonance frequencies ∆ν ) 1/2π∆ω, where ∆ω is given by eq. 4, and the relaxation time T2b , T2a. According to our assumptions, the relaxation time T2b is the transverse relaxation time of the ammonium cation protons -NH3+. However, within our simplified model we may assume that T2b is the transverse relaxation time of protons at the micellar surface. The resonance frequency difference (∆ν) depends on the chemical shift difference δω ) δb - δa, in ppm, and on the specific 1H NMR resonance frequency (ν0), which depends on the magnetic field strength used. All experiments were carried in a magnetic field with B0 ) 9.4 T, and the corresponding proton resonance frequency was ν0 ) 400 MHz. The resonance frequency difference will be expressed as ∆ν ) 400δω Hz. According to our simulations, the dispersion curve is evident if the line width measured at half-height (∆ν1/2) is much smaller than the resonance frequency difference (∆ν), then
∆ν1/2 , ∆ν. The relation between line width measured at halfheight (∆ν1/2) and transverse relaxation time T2b is straightforward and is given by eq 7. For ν0 ) 400 MHz and a chemical shift difference of δω ) 3.93 ppm, the Larmor frequency difference ∆ν is 1572 Hz. If we take the value of the transverse relaxation time T2b ) 3.6 × 10-3 s, then the related line width at half-height is ∆ν1/2 ) 88 Hz. Because the condition ∆ν1/2 , ∆ν is fulfilled for all isotropic micellar phases, interpretation of the observed dispersion curves becomes straightforward. The above condition is not fulfilled for the hexagonal phase, where we observe large decreases of the transverse relaxation time T2b up to 8 × 10-6 s, which results in ∆ν1/2 values of 10 kHz, and the dispersion curve becomes “flat”. As we can see in Figure 3c, there is indeed a detectable broad line component in the 1H NMR spectra with an estimated line width of 10 kHz. Accordingly, we conclude that the “flat” dispersion curve is in agreement with the existence of the broad Gaussian component in the hexagonal phase 1H NMR spectra. According to the linear free energy relations, there is a linear relation between standard Gibbs energy ∆G and free activation energy ∆Gq, where, for small changes of ∆G, we obtain δ∆Gq ) Rδ∆G.18 If we discuss the chemical exchange rate processes in the context of collision-related reactivity, then we may drive a conclusion that reactivity is decreased versus DDACl concentration and also that the fraction of collisions that lead to reaction decrease as well. From the previous discussion about chemical shift changes versus pKa changes, we find that the standard Gibbs free energy is thus lowered with concentration as a result of aggregation.5-7 This result is in agreement with linear free energy relations, where a decreasing value of |∆G| is paralleled with an increase of ∆Gq for the process. A decrease in the free Gibbs energy with an increasing DDACl concentration in the solution thus suggests that the charge on the micellar surface decreases with increasing concentration of DDACl in the solution. To justify this conclusion we use the following reasoning. A charge decrease on the surface layer will result in an increase of the degree of dissociation for the ammonium cations via the reaction R-NH3+ f R-NH2 + H+. This will induce a decrease in pKa and pH values in the solution. Indeed, we observe that pH values do change from pH ) 4.2 for a DDACl concentration of 20 wt % to below pH ) 3 for DDACL at 35 wt % (results not shown). This should suggest that the pKa values and free Gibbs energy ∆G decrease further with increasing DDACl concentration. The lowering of ∆G will evoke an increase in the free energies of activation ∆Gq, which will further govern a decrease of the chemical exchange rates kex. A decrease in the entropy of activation ∆Sq could be related to changes in the micellar shape from nearly spherical to the rod-like elongated ones or to an increase of the aggregation number.39,40 5. Conclusions The reverse temperature dependence of the effective transverse relaxation times T2 (i.e., T2 for long τcp) was observed for all samples, in that the transverse relaxation time of water signal decreased with rising temperature. This result is linked to the proton chemical exchange process observed.41 The experimental NMR sensitivity to the parameters in question decays rapidly with increasing temperature, especially in the spin-echo experiments, so that the diffusion of water molecules in the hexagonal phase becomes difficult to study by PGSE NMR. The T2 dispersion curves were not observable for the “solid” phases because of the short T2b. Our simulations give reliable
Proton Chemical Exchange in Dodecylammonium Chloride values of the transverse relaxation time T2b because they rest on an independent observation in the 1H NMR spectra: the existence of an additional broad Gaussian line. For increasing DDACl concentration in the aqueous solution, an increase of the energy barrier height ∆Gq for the proton chemical exchange between water and ammonium cation -NH3+ was observed. This result is explained by a decrease in the magnitude of the standard Gibbs free energy |∆G| for ammonium cation dissociation caused by hydrophobic aggregation. This general trend is in the agreement with linear free energy relations. We suspect that the isotropic-hexagonal temperature phase transition for the 33% aqueous solution of DDACl is driven by weakening of the charge stabilization in the micellar solution. The hexagonal packaging of the elongated micelles results from lower repelling forces governed by an enhanced deprotonation of the micellar surface. Acknowledgment. This work was supported under by The Polish State Committee for Scientific Research under grant No. 3 T09A 050 27. We wish to thank Prof. Istva´n Furo´ for valuable discussions and the Swedish Research Council (VR) and the Knut and Alice Wallenberg foundation for financial support. References and Notes (1) Guedes, M.; Ferro, A.; Ferreira, J. AdV. Mat. Forum III, Parts 1 and 2 2006, 514-516, 1369. (2) Vigolo, B.; Pe´nicaud, A.; Coulon, C.; Sauder, C.; Pailler, R.; Journet, C.; Bernier, P.; P., P. Science 2000, 290, 1331. (3) Patel, N.; Egorov, S. A. J. Am. Chem. Soc. 2005, 127, 14125. (4) Laughlin, R. G. The Aqueous Phase BehaVior of Surfactants; Academic Press: London, 1996. (5) Matulis, D.; Bloomfield, V. A. Biophys. Chem. 2001, 93, 37. (6) Matulis, D.; Bloomfield, V. A. Biophys. Chem. 2001, 93, 53. (7) Matulis, D. Biophys. Chem. 2001, 93, 67. (8) Rizzatti, M. R.; Gault, J. D. J. Colloid Interf. Sci. 1986, 110, 258. (9) Gault, J. D.; Leite, M. A.; Rizzatti, M. R.; Gallardo, H. J. Colloid Interf. Sci. 1988, 122, 587. (10) Szutkowski, K.; Klinowski, J.; Jurga, S. Solid State Nucl. Mag. 2002, 22, 394.
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