Dynamics in Supercooled Secondary Amide Mixtures: Dielectric and

Article pubs.acs.org/JPCB

Dynamics in Supercooled Secondary Amide Mixtures: Dielectric and Hydrogen Bond Specific Spectroscopies C. Gainaru,†,# S. Bauer,† E. Vynokur,† H. Wittkamp,† W. Hiller,‡ R. Richert,§ and R. Böhmer*,† †

Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany Fakultät für Chemie und Chemische Biologie, Technische Universität Dortmund, 44221 Dortmund, Germany § School of Molecular Sciences, Arizona State University, Tempe, Arizona 85287-1604, United States ‡

S Supporting Information *

ABSTRACT: Alkylacetamide-based model peptides display an intense Debyetype dielectric relaxation. In order to explore the extent to which this feature has to be regarded analogous to that in other supramolecular liquids, notably the monohydroxy alcohols, we applied broadband dielectric, time-dependent solvation, and near-infrared spectroscopies as well as shear rheology and various nuclear magnetic resonance techniques to mixtures of Nmethylacetamide (NMA) or N-ethylacetamide (NEA) with N-methylformamide. Compared in the modulus format, dielectric relaxation, solvation dynamics, and mechanical response indicate a common global and local dynamics. The present spin-relaxation measurements reflect motional processes which are significantly faster than the dominant Debye dielectric response, and a similar conclusion is drawn from measurements of the shear viscosity. The NH overtone stretching vibrations reveal a temperaturedependent hydrogen-bond equilibrium that changes its characteristics near temperatures of 325 K. Finally, dielectric low-temperature data recorded for (NEA)0.4(NMF)0.6 mixed with 2-picoline indicate the existence of a critical concentration akin to the situation in various monohydroxy alcohol mixtures.

1. INTRODUCTION Currently, so-called Debye liquids attract substantial attention due to their particular properties. These materials, typically good glass formers, usually display an intense and singleexponential relaxation process in their dielectric response that is slower than their structural relaxation. This signature of supramolecular association effects is most prominent for monohydroxy alcohols1,2 but known for other complex fluids as well. Among them are hydrogen-bonded liquids such as water,3 pharmaceuticals,4−7 and secondary amides8 but also species devoid of hydrogen bonds.9 For a long time, dynamic aspects related to supramolecular association of these liquids were studied almost exclusively using standard dielectric spectroscopy.10,11 Yet, the overall focus on only a single technique has long impeded progress regarding a microscopic understanding of the properties of, e.g., the monohydroxy alcohols. However, the recent application of nuclear magnetic resonance (NMR),12 nonlinear dielectric experiments,13 high-resolution rheology,14 and other techniques has allowed one to gain new insights regarding the previously largely elusive nature of the Debye process in these substances.15 The present work deals with secondary amides featuring amino groups. These amides are attractive to study because, e.g., they are often considered as model systems for peptide fragments. The classical works on secondary amides all apply standard dielectric spectroscopy techniques.16−20 Since the pure © 2015 American Chemical Society

substances display an enhanced crystallization tendency, typically only the stable high-temperature liquid phase was in the focus of NMR21 and vibrational spectroscopy studies.22−27 Together with molecular dynamics28,29 and quantum chemical calculations24,30,31 as well as X-ray and neutron diffraction investigations32 evidence has been accumulated that neat secondary “amides develop transient hydrogen-bonded chains in the liquid state”,33 similar to the situation for monohydroxy alcohols displaying large dielectric Debye peaks.15 Therefore, the opinion may not appear surprising that it is “plausible that the mechanism of the dielectric relaxation in the monohydric alcohols and the amides is the same”.34 However, many of the techniques helpful in advancing our understanding of the monohydroxy alcohols still await application to the secondary amides. To take full advantage of several of these methods it is necessary to cover a large spectral range. This includes spectroscopies operating at GHz frequencies and all the way down to the sub-Hz range in which the glass transition takes place. In other words, the deeply supercooled state of the secondary amides needs to be entered. As several studies have shown, this becomes possible by suitable mixing with, e.g., carbon tetrachloride34 or with other amides.35 Received: October 14, 2015 Revised: November 24, 2015 Published: November 25, 2015 15769

DOI: 10.1021/acs.jpcb.5b10034 J. Phys. Chem. B 2015, 119, 15769−15779

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The Journal of Physical Chemistry B

To extend previous broadband shear measurements37 into the regime of low mechanical moduli, we measured the complex shear modulus of (NEA)0.4(NMF)0.6 at 160 K using a Modular Compact Rheometer MCR 502 from Anton-Paar. A plate−plate geometry with a disk diameter of 8 mm was used. The distance of the plates was about 0.5 mm, and the strain amplitude was adjusted at each temperature to maintain linearity of response. Temperature-dependent near-infrared spectra were recorded with a CARY 2300 UV/vis-NIR photospectrometer from Varian characterized by a wavelength resolution of ∼0.8 nm and an absorbance accuracy of about 0.005. About 10 min after a temperature change, the sample temperature was stabilized within 30 mK using a Lake Shore 340 Temperature Controller. All spectra are corrected for temperature-induced density variations. Further experimental details can be found in ref 43. Deuteron NMR experiments at a Larmor frequency of ωL = 2π × 46.5 MHz were conducted in a home-built spectrometer featuring a superconducting magnet and a cryostat from Oxford instruments. The latter allowed for a temperature stability of ±0.2 K. The duration of the π pulse was 6 μs. Spin−lattice relaxation times, T1, were measured by means of inversion or saturation recovery pulse sequences augmented by echo refocusing, and spin−spin relaxation times, T2, were recorded using standard echo techniques. To access temperaturedependent translational diffusion coefficients, experiments were carried out for fully protonated (NMA)0.4(NMF)0.6 with ωL = 2π × 53.4 MHz in a static field gradient g of ∼19.9 T/m, as described in ref 44. Additional details are provided as Supporting Information.

N-Methylformamide (H-CO-NH-CH3, NMF) is one such mixing partner that was successfully employed in dielectric experiments together with N-ethylacetamide (CH3-CO-NHC2H5, NEA).8 For the present work, the scope of the dielectric techniques is broadened to include the solvation method which represents a locally sensitive probe.36 Furthermore, since in monohydroxy alcohols a mechanical signature of the Debye process was recently discovered,14 we decided to extend our shear mechanical measurements37 on mixtures of NEA and NMF into the low-modulus range. Apart from techniques probing the overall motion of the amide molecules on a global or a local length scale, it is promising to apply methods that are selectively sensitive to the molecular moiety driving the supramolecular structure formation. For the amides this is the hydrogen bonding N− H group which can be made amenable for NMR studies, e.g., by suitable isotope labeling. Since our attempts to synthesize N−D labeled NEA were not successful, we decided to study commercially available N-methylacetamide (CH3-CO-NDCH3, NMA-d1) with selective deuteration at the nitrogen site. As another method which provides access specifically to the properties of the amide group we carried out near-infrared studies. The optical experiments were performed for an NMA− NMF mixture in order to ensure a better comparability of the results from the two hydrogen bond specific spectroscopies. To check whether the NEA−NMF mixtures (used for the globally sensitive spectroscopies) and the NMA−NMF mixtures (employed for the H bond specific ones) can be considered more or less interchangeably, we performed broadband dielectric measurements on both types of mixtures. To enhance the consistency of the results, samples composed of 40 mol % N-alkylacetamide and 60 mol % NMF are studied which, in the NEA variant, demonstrated excellent glassforming ability.8 To anticipate one of our results, we find that the behaviors of (NMA)0.4(NMF)0.6 and (NEA)0.4(NMF)0.6 are very similar except that due to a slightly more pronounced supramolecular alignment in the NMA-containing mixture its dynamics freezes at a temperature a few Kelvin above that of the NEA mixture. In monohydroxy alcohols the Debye-like relaxation can be separated from the structural relaxation by mixing them with polar liquids devoid of a Debye relaxation.38,39 This separation turned out to be particularly valuable in enhancing the microscopic understanding of the Debye process. Triggered by these advances we carried out dielectric experiments on secondary amides mixed with 2-picoline.

3. RESULTS FROM DIELECTRIC SPECTROSCOPY 3.1. Broadband Relaxation. In order to check whether and how much the dielectric spectra of (NMA)0.4(NMF)0.6 differ from those of the previously studied8 (NEA)0.4(NMF)0.6 mixture, we present the complex dielectric permittivity of (NMA)0.4(NMF)0.6 in Figure 1. We find that at low frequencies the static dielectric constant of (NMA)0.4(NMF)0.6 reaches values near 500, slightly larger than for the NEA-containing mixture. An explicit comparison of the two mixtures is provided as Supporting Information. In ref 8 it was shown that the dielectric relaxation strength, Δε, depends sensitively on the composition of the mixture and that Δε increases as the NMF content increases. Hence, one may argue that due to the smaller size of the NMA with respect to that of the NEA molecule for the same 2:3 molar ratio the volume fraction of NMF molecules in our mixtures is larger. From ref 8 it is also known that an increase of the NMF concentration speeds up the main dielectric relaxation: In (NEA)0.2(NMF)0.8 the relaxation times τ are about 1 to 1.5 decades shorter than they are in (NEA)0.4(NMF)0.6. From that perspective and from the fact that the molecular volume of NMA is smaller than that of the NEA one expects that the relaxation of (NMA)0.4(NMF)0.6 is faster than that of (NEA)0.4(NMF)0.6. The explicit comparison (see the Supporting Information) shows, however, that the reverse is true. Expressed in terms of Tg,D = T(τD = 100 s) the dynamic glass transition is at 157 K for (NMA)0.4(NMF)0.6 and at 151 K for (NEA)0.4(NMF)0.6. The observation of slower dynamics of (NMA)0.4(NMF)0.6 as compared to (NEA)0.4(NMF)0.6 can be rationalized if the mixtures with NMA are assumed to build more stable supramolecular structures than those with NEA. Direct studies of the hydrogen bond cooperativity of NMA are

2. METHODS AND MATERIALS Broadband dielectric measurements were performed using a modular system from Novocontrol Technologies based on an Alpha-A analyzer connected to a ZGS test interface. The liquid samples were placed in invar/sapphire cells40 which in turn were inserted into a cryostat with a temperature stability of 0.2 K as achieved using a Quatro controller. To perform triplet solvation dynamics experiments we utilized quinoxaline (QX) as a chromophore. About 10−4 mol of QX was added to an (NEA)0.4(NMF)0.6 mixture. Subsequent to laser excitation, triplet-to-singlet (T1 → S0) emission spectra of QX were recorded for several temperatures in the time range 1 ms < t < 1 s. The long time limit is set by the phosphorescence lifetime of QX of about 0.3 s. More details regarding equipment and data analysis can be found elsewhere.41,42 15770


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description of spectral shapes of neat NMA probed via ultrafast optical Kerr effect spectroscopy.27 Using the results obtained for the relaxation strength Δε = (ΔεCC + ΔεD) from the fits one can estimate the degree of static orientational correlation between the reorienting dipole moments, usually quantified by the Kirkwood factor gK =

available,30,31 but similar investigations of NEA are needed to check this conjecture. In harmony with previous investigations of neat and binary secondary amides,8,18 the main dielectric absorption peak of (NMA)0.4(NMF)0.6 is characterized by a single relaxation time. In addition to the large Debye peak, the loss spectra display a relaxational feature at higher frequencies. This is best recognized in Figure 1(a) and (b) for the spectrum recorded at T = 165 K which may indicate the presence of another process. Following the considerations in ref 8, this additive contribution was accounted for by a Cole−Cole function so that one has ΔεCC ΔεD + 1 + 2πiντD 1 + (2πiντCC)αCC

nμ2

εs(ε∞ + 2)2

(2)

Here ε0 denotes the vacuum permittivity, kB the Boltzmann constant, εs = ε∞ + Δε the static permittivity, n the number density of dipole moments, and μ the electrical dipole moment. For dipoles lacking orientational correlations the Kirkwood factor equals 1, but it can be smaller or larger than unity depending on the tendency of adjacent molecules to align in antiparallel or parallel fashions, respectively. To estimate gK for binary mixtures of the type AxB1−x one may approximate the effective number density by n* = xnA + (1 − x)nB and the effective dipole moment by μ* = [xμA2 + (1 − x)μB2]1/2.45,46 Using the dipole moments μNMA = 3.84 D47 and μNMF = 3.86 D48 one obtains n* = 9.2 × 1027 m−3 and μ* = 3.85 D for (NMA)0.4(NMF)0.6. Since ε∞ ≈ 3, the estimated gK factor is about 4.1 at T = 165 K for this mixture. In arriving at this value we assumed that density is temperature invariant and that each molecular dipole unit participates in both relaxation processes, i.e., that εs = ε∞ + Δε ≈ 498.4. To compare our results with those from a previous investigation37 we employed the above procedure for the dielectric results of (NEA)0.4(NMF)0.6 obtained at T = 160 K because at this temperature the Debye peak frequency is the same (∼3 Hz) as for (NMA)0.4(NMF)0.6 at 165 K. Using μNEA = 3.87 D,49 for (NEA)0.4(NMF)0.6 we obtain n* = 8.6 × 1027 1/m3, μ* = 3.87 D, ε∞ ≈ 3, and εs ≈ 443. These values indicate that gK ≈ 3.8 at 160 K. For both mixtures the large Kirkwood factors agree well with reports for neat secondary amides.8,50 Their magnitude suggests a prevalent parallel local arrangement of adjacent molecules, in harmony with the chain-like supramolecular formation proposed for these systems. The difference in the calculated gK values suggests that the supramolecular alignment in (NMA)0.4(NMF)0.6 is slightly more pronounced than in (NEA)0.4(NMF)0.6. Hence, except for a slight (∼5 K) difference in their Tg,D, the behaviors of (NMA)0.4(NMF)0.6 and (NEA)0.4(NMF)0.6 are very similar. 3.2. Triplet Solvation Compared with Other Modulus Responses. While conventional dielectric spectroscopy probes the macroscopic response function of a given material (typically under constant field condition), solvation dynamics is able to access local polarization responses in a small volume restricted to the close proximity of the probe molecule. To study the local electric field response of secondary amides one can switch the electrical charge distribution of an embedded chromophore molecule and monitor its subsequent triplet state solvation dynamics.51 This way, by recording the average emission energy ⟨ν̅e(t)⟩ of the T1 → S0 emission spectra of QX in (NEA)0.4(NMF)0.6 as a function of time, the electric modulus response of the solvent is probed on a microscopic level. Figure 2(a) shows the time evolution of QX’s emission energies which are of the order of 21 000 cm−1. After laser excitation, ⟨ν̅e(t)⟩ changes by 580 cm−1 from an initial value ⟨ν̅e⟩0 to a red-shifted final value ⟨ν̅e⟩∞. The accessible time window is barely sufficient to cover the entire decay at each single temperature. However, since the temperature range

Figure 1. (a) Real and (b) imaginary part of the complex dielectric permittivity, ε*(ν), of (NMA)0.4(NMF)0.6 as a function of frequency for several temperatures. The solid lines reflect a fit using eq 1 for the data recorded at 165 K. At this temperature the spectrum was decomposed in two relaxation contributions with dielectric relaxation strengths of ΔεD ≈ 470 and of ΔεCC ≈ 25. A conductivity contribution is visible for frequencies below the loss peak (shown for 165 K). The dotted lines are fits performed close to the loss peak maximum using the imaginary part of the second term in eq 1 that corresponds to the Debye process. The dashed lines highlight the spectral contributions of the structural relaxation.

ε*(ν) = ε∞ +

9ε0kBT (εs − ε∞)(2εs + ε∞)

(1)

As demonstrated by the solid line in Figure 1 for T = 165 K, this approach [including a conductivity contribution in (b)] describes the spectrum in the entire frequency range. In eq 1 ε∞ is the high-frequency permittivity, and ΔεCC and ΔεD denote the relaxation strength of the Cole−Cole- and of the Debye-like process, respectively. The associated relaxation times are called τD and τCC in eq 1. In Figure 1 the dotted and dashed lines show the contributions of the two relaxation processes entering eq 1. At T = 165 K the stretching parameter of the Cole−Cole peak, αCC, is 0.5 for (NMA)0.4(NMF)0.6, a value also reported to describe the fast process of neat NEA.8 It is worth noting that a similar fitting procedure involving Debye and Cole−Cole terms was successfully applied also for the 15771


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Figure 2. (a) Symbols represent the time-dependent average emission energy ⟨ν̅e(t)⟩ of 10−4 mol QX in (NEA)0.4(NMF)0.6 as recorded for several temperatures. (b) Master plot obtained by overlapping the data in panel (a) with the results at 150 K. The solid line is a fit using a stretched exponential function, eq 3. Figure 3. For (NEA)0.4(NMF)0.6 this figure compares the imaginary parts of the Stokes shift modulus, C″(ν) (solid line), the mechanical shear modulus, G″(ν) (stars and crosses), and the electric modulus M″(ν) (open circles). To extend the rheological data to lower moduli the spectrum measured at 160 K (crosses, this work) was shifted horizontally to match previous 153 K data (open stars, from ref 37). To facilitate a direct comparison of the characteristic frequencies for various loss functions, the composite shear loss spectrum was shifted vertically so that its maximum amplitude matches that of the electric modulus M″(ν). All these modulus functions peak at a frequency which is much larger than that at which the dielectric loss, ε″(ν) (filled circles), is maximum.

covered by the data in Figure 2(a) is relatively narrow, like for other solvation studies,51,52 the validity of time−temperature− superposition, i.e., a temperature-independent shape of the ⟨ν̅e(t)⟩ curves, can safely be assumed. Therefore, as illustrated in Figure 2(b) we shifted the data along the logarithmic time axis to achieve best overlap of all data sets with the results recorded at 150 K. Finally, we normalized the ⟨ν̅e(t)⟩ master curve so that it decays from 1 to 0 as time progresses. This procedure, with ⟨ν̅e⟩0 = 21 240 cm−1 and ⟨ν̅e⟩∞ = 20 820 cm−1, yields the Stokes shift correlation function C(t). The solid line in Figure 2(c) shows that a stretched exponential function53 of the form C(t ) =

β ⟨νe̅ ⟩(t ) − ⟨νe̅ ⟩∞ = e−(t / τ) ⟨νe̅ ⟩0 − ⟨νe̅ ⟩∞

like and the structural relaxation are spectrally very close so that so far only phenomenological fits allow one to try and disentangle their contributions. For monohydroxy alcohols the situation is different: Here, by mixing them with other polar liquids the time scales of the Debye-like relaxation can be separated from the structural one by more than 4 orders of magnitude.55 In an attempt to induce a similar separation for the amides we studied mixtures with various liquids, but for none of those56 and for none of those studied by Li et al.46 could a significant time scale separation be achieved. As an example of our attempts to gain insights into the nature of the amide’s relaxation processes we focus on 2picoline mixtures. Due to its high polarity liquid 2-picoline is a good solvent for secondary amides, and yet its relatively low dielectric relaxation strength57 ensures a good static contrast to (NEA)0.4(NMF)0.6. Furthermore, with a glass transition temperature of ≈130 K, 2-picoline exhibits also a useful dynamic contrast to the amides. In Figure 4(a) and (b) we show the real and imaginary part, respectively, of the complex dielectric constant of several amide−picoline mixtures covering the entire range of (NEA)0.4(NMF)0.6 mole fractions x. One recognizes a smooth evolution of the dominant relaxation step which implies that Δε(x) is roughly proportional to x. Analyzed in terms of eq 1 this behavior is confirmed quantitatively (see the inset of Figure 4(a)). A composition-dependent separation of two processes is not obvious from the data in Figure 4. However, as the inset of Figure 4(a) also reveals the peak time scales, νpeak(x), evolve nonlinearly with x, bearing interesting implications (see Section 5, below).

(3)

provides a very good quantitative description of the measured time-dependent emission energies for an exponent of β = 0.4. In Section 5, we will demonstrate that the average solvation time scales, τS, obtained from the shift factors used to generate the master curve shown in Figure 2(b) agree with those from other modulus quantities. Let us now compare the shape of C(t) or its frequency equivalent, the complex Stokes shift modulus, C*(ν), with the global mechanical shear modulus, G*(ν), and with the electric modulus M*(ν) = 1/ε*(ν), i.e., with the inverse of the dielectric permittivity, ε*(ν). In Figure 3 we show the imaginary part, C″(ν), of C*(ν) as obtained from the Laplace transform54 of eq 3 and the imaginary part, M″(ν), of the electric modulus recorded for a sample of (NEA)0.4(NMF)0.6 at 153 K. Figure 3 reveals that the peak frequencies, νpeak, of all three loss moduli agree with each other and that νpeak is close to the structural relaxation contributions to the dielectric loss, ε″. In other words, losses for all three quantities are deemphasized at frequencies corresponding to the Debye-like peak in the dielectric loss. Furthermore, the present shear mechanical measurements reveal that the low-frequency flank of G″(ν) shows no particular features down below 106 Pa, thereby extending the previously accessible modulus range37 by more than an order of magnitude. In particular, this implies that a supramolecular mechanical signature, similar to that observed for monohydroxy alcohols, is not (maybe still not) discernible on the extended low-G scale accessible in the present work. 3.3. Mixtures of Secondary Amides with Polar Liquids. One of the obstacles on the way to clarifying the detailed origin of the secondary amides’ relaxation behavior is that the Debye15772


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(or of molecular correlation times, τc).58 In accord with experiments on many small-molecule glass formers (see, e.g., ref 59) λ ≈ 0 is found for T > Tg or for the spin−lattice relaxation of the protonated samples. Figure 5 summarizes the spin−lattice relaxation times determined for the secondary amides in a wide temperature

Figure 5. Deuteron (filled squares) and proton (filled circles) spin− lattice relaxation times T1 of (NMA)0.4(NMF)0.6. Deuteron spin−spin relaxation times, T2, are also included (open squares). For the 2H NMR measurements NMA labeled at the nitrogen site was studied. For the 1H NMR measurements fully protonated liquids were used.

Figure 4. Frequency dependence of (a) real and (b) imaginary part of the complex dielectric constant of [(NEA)0.4(NMF)0.6]x[2-picoline]1−x mixtures is shown for several mole fractions x. The solid lines are fits using eq 1. The inset depicts the relaxation strength Δε(x) which displays ideal mixing behavior and τ(x) which strongly deviates from it. The lines are drawn to guide the eye.

range. For the 2H−T1 data a minimum is clearly resolved at T ≈ 210 K. At lower temperatures, in a range of about 25 K, T1 measurements could not be performed reliably. This is due to a loss of signal caused by short spin−spin relaxation times, T2 (T2 times are also included in Figure 5). The T1 times measured just below 170 K are seen to follow the trend inferred from higher temperatures, and for T < Tg one recognizes that T1 tends to saturate. At the temperature of the T1 minimum the molecular correlation time is about τc = 0.616/ωL ≈ 2 ns. This follows from the approach due to Bloembergen, Purcell, and Pound (BPP) according to which T1−1 = 2/15δ2Q[J(ωL) + 4J(2ωL)].60 This expression features a spectral density J(ωL) = τc/(1 + ω2Lτ2c ) and a quadrupolar anisotropy parameter δQ = 3e2qQ/ (4ℏ). As given, these equations imply exponential and isotropic relaxation. However, lifting these conditions changes the above expression for τc very little.61 More important is the finding, obvious from Figure 5, that for T > 200 K the 1H−T1 times follow the same trend as the 2 H−T1 times suggesting that the correlation times do not depend on the molecular site at which they are probed. Due to an enhanced crystallization tendency of our fully protonated (NMA)0.4(NMF)0.6 specimen, no measurements could be taken across the incipient T1 minimum. However, subsequent to quenching the sample with a rate of 10 K/min low-temperature data could be acquired, and they indicate that T1 shortens upon cooling. This behavior resembles that in monohydroxy alcohols where it indicates that the methyl groups rotate fast on the time scale of the inverse Larmor frequency.62 The 1H−T1 times are considerably longer than the 2H−T1 times. This reflects the fact that the quadrupolar anisotropy parameter, δQ (for a discussion of its value see ref 21), is considerably larger than the dipolar coupling parameter. The latter should be used (instead of δQ) when analyzing proton data in terms of the BPP approach.

4. RESULTS FROM SPECTROSCOPIES OF THE HYDROGEN BOND In monohydroxy alcohols, techniques such as magnetic resonance and infrared spectroscopy yielded important information regarding the formation of their supramolecular structure.15 This is because these methods allow one to specifically monitor phenomena occurring near the hydrogen bonds. In particular, for monohydroxy alcohols with strong Debye-like features, NMR spin−lattice relaxation measurements have shown that the hydrogen dynamics within that bond is significantly slower than that of the molecule’s overall motion. We performed corresponding NMR measurements also for fully protonated and for N−D labeled (NMA)0.4(NMF)0.6 and present them next. Then, in Section 4.2 we will discuss near-infrared absorbance experiments carried out in the spectral range of the first overtone of the N−H stretching vibration. 4.1. Nuclear Magnetic Resonance. Spin−lattice relaxation times, T1, were determined from proton and deuteron longitudinal magnetization recovery curves, M(t), at Larmor frequencies close to 50 MHz. The 2H data were obtained on a (NMA-d1)0.4(NMF)0.6 sample labeled at the N−D group. For the 1H experiments fully protonated samples were used so that the magnetization signal is dominated by the methyl groups. The measured M(t) was fitted using a Kohlrausch function, M(t) = M∞ + (M0 − M∞)exp[−(t/T1)1−λ]. In this expression, initial and final magnetization are denoted M0 and M∞, respectively, and λ is a measure for the deviation from exponential magnetization recovery. Such deviations are significant only for the deuteron data at temperatures T < Tg at which we find λ = 0.3 ± 0.1, a typical value that predominantly reflects the underlying distribution of T1 times 15773


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respectively, to the first overtones of stretching modes of the free N−H group of the monomer, terminal-free (free-end) N− H groups of the dimer and oligomers, and hydrogen-bonded N−H groups of the dimer and oligomers of NMA”.22 In harmony with the nomenclature used for O−H stretching vibrations of monohydroxy alcohols,66 we labeled the bands in Figure 6(a) as the α/β band at 6790 cm−1 for the free N−H group, as the γ band for the absorbance of terminal N−H oscillators appearing between 6630 and 6580 cm−1, as the ο band around 6370 cm−1 representing N−H groups within small oligomeric H-bonded structures, and as the δ band at ∼6290 cm−1 that reflects the absorbance of strongly hydrogen-bonded N−H oscillators in linear suprastructures. The absorbance of nonbonded free NH groups, labeled as the α/β band and found near 6800 cm−1, is not clearly resolved in the present temperature range. By substituting the N−H groups in (NMA)0.4(NMF)0.6 by N−CH3 groupswhich do not support supramolecular aggregation19,33,67the bands in the 6100 and 6900 cm−1 spectral regime should disappear. In other words, in the given spectral region the absorbance should be very low for a mixture of N,N-dimethylformamide (DMF) with N-dimethylacetamide (DMA) if no other vibrational bands interfere. This expectation is nicely confirmed; see the (DMA)0.4(DMF)0.6 spectra included in Figure 6(a). With the goal to monitor the equilibrium among broken and intact hydrogen bonds we performed measurements in a large temperature range. Figure 6(b) presents NIR spectra of (NMA)0.4(NMF)0.6 from 180 to 390 K which suggest that the bands undergo large thermally induced frequency shifts. From absorbance difference spectra, ΔA(ν̅, T) = A(ν̅, T) − A(ν,̅ Tref), with Tref = 180 K denoting an (arbitrarily chosen) reference temperature, these shifts appear much less pronounced (see Figure 6(c)). It is remarkable that the oligomeric and the polymeric bands can be observed as separate bands only near room temperature and only in the absorbance spectra but not in the difference spectra. In other words, usually the o and δ bands cannot be resolved. In Figure 7(a) we collect the absorbances of the various bands as determined from the maxima of A(ν̅, T) or from the maxima or minima of ΔA(ν̅, T)/A(ν̅, Tref). Upon heating, the absorbance A(λα/β) of the free N−H groups obviously increases at the expense of A(λδ), the band which reflects bonded N−H groups. From the ratio of the two bands one can determine the reaction enthalpy ΔH(T) = −R∂ ln[A(λα/β)/A(λδ,o)]/∂(T−1) that increases from about 2 kJ/mol at 190 K to ≈12 kJ/mol at 390 K (cf. Figure 7(b)). Similar trends are observed when evaluating the difference spectra based on the ratio ΔA(λα/β)/ ΔA(λδ). At first sight, the increase of ΔH with increasing temperature may appear surprising, but it resembles findings reported for other hydrogen-bonded liquids.68,69 For monohydroxy alcohols ΔH was found to evolve continuously from 1 to 2 kJ/mol below to 9−14 kJ/mol just above ≈250 K, in some cases reaching 20−25 kJ/mol at much higher temperatures. This behavior was interpreted to indicate that coming from high T a simple two-state (opened/closed) hydrogen bond equilibrium at low T is superseded by a more complex equilibrium among different supramolecular structures which differ only little in their enthalpy. In a range of monohydroxy alcohols the “transition” among these two regimes (coined the “250 K anomaly”) was assigned to a change in hydrogen-bond cooperativity that was scrutinized for a few of those liquids.70

In addition to the time scale inferred from the minimum deuteron spin−lattice relaxation time, the only roughly defined minimum in the deuteron spin−spin relaxation time allows one to estimate a time scale according to τc ≈ δQ−1, which is about 1 μs.63 Furthermore, we employed the deuteron stimulated-echo technique to determine molecular correlation times in the milliseconds to seconds range and present them in Section 5. 4.2. Near-Infrared Spectroscopy. Using this technique, one usually follows the hydrogen bond equilibrium population rather than the molecular dynamics of hydrogen-bonded moieties. Figure 6(a) shows room-temperature near-infrared

Figure 6. (a) Near-infrared absorbance of NMA, NMF, and (NMA)0.4(NMF)0.6 in the spectral region in which the first NH stretching vibration overtones occur. The labeling of the non- or proton-acceptor bonded (α/β), proton-donor bonded (γ), oligomeric (o), and polymeric (δ) bands is indicated. Comparison is made with the methylated mixture (DMA)0.4(DMF)0.6 for which hydrogen bonding is inhibited. (b) Temperature-dependent absorbance spectra recorded for 390, 370, 350, 330, 310, 285, 270, 250, 230, 210, 190, and 180 K. (c) Absorbance difference spectra calculated from the data shown in panel (b) for a reference temperature Tref = 180 K.

(NIR) spectra of NMA, NMF, and (NMA)0.4(NMF)0.6 in the spectral range from about 6100 to 6900 cm−1. This range corresponds to the first N−H overtone stretching vibration, and the spectra all look similar. Taking into account quantum chemical calculations carried out for NMF,64,65 for the band identification of the mixture we follow the assignment provided by Liu et al.22 for pure NMA. On the basis of a two-dimensional correlation analysis these authors state that the “five bands at 6790, 6650, 6510, 6440, and 6250 cm−1 are assigned, 15774


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Figure 7. (a) Temperature-dependent absorbance of various bands as determined from the data shown in Figure 6. The lines are drawn to guide the eye. (b) Temperature dependence of the reaction enthalpy ΔH which governs the hydrogen bond equilibrium in (NMA)0.4(NMF)0.6. In both panels the full symbols refer to the absorbance spectra and the open symbols to the absorbance difference spectra.

Figure 8. (a) Dielectric relaxation times for NMA (orange diamonds) from ref 78 and those for (NMA)0.4(NMF)0.6 (blue circles) from this work. Full symbols refer to Debye relaxation times, τD, and open symbols to structural relaxation times, τα. The high-temperature NMR results for pure NMA and for pure NMF are from ref 21. For NMA they refer to the N−H bond from 1H NMR (τH) and 15N NMR (τN), and for NMF they refer to the C−H bond from 1H NMR (τH) and 13 C NMR (τC). Time constants from deuteron NMR (stimulated echoes τSE, spin−lattice relaxation τT1, and spin−spin relaxation τT2), and from field gradient proton NMR (τDiff) for (NMA)0.4(NMF)0.6 (all from this work) are also shown. (b) Dielectric relaxation times τD and τα for NEA and (NEA)0.4(NMF)0.6 are from ref 8 or cited therein. For the mixture the electrical modulus loss peak time scale τM is also shown. The solvation dynamics data (τS) for (NEA)0.4(NMF)0.6 are from the present work. Shear loss peak data (τG) and shear viscosities (yellow filled triangles pointing to the right) are taken from ref 37. Only the viscosity data refer to the right axis. The solid lines reflect fits using eq 4.

Overall, the pattern in Figure 7(b) looks similar to the one just described; however, the amide data suggest that something like a “transition” occurs rather near 325 K. Furthermore, it is likely that in the present investigation the high-temperature regime which would display a simple two-state equilibrium and enthalpies ΔH ≫ 12 kJ/mol was not reached. Interestingly, a peculiar change of the temperature-dependent hydrogen bond length was reported from X-ray scattering experiments to show up for NMA near 350 K.32 While this finding appears to corroborate the present NIR observation, structural studies also on amide mixtures would be useful.71

5. DISCUSSION 5.1. Temperature-Dependent Time Scales. In Figure 8(a) and (b) we present the characteristic relaxation times as determined from various methods for (NMA)0.4(NMF)0.6 and for (NEA)0.4(NMF)0.6, respectively. Panel (a) summarizes dielectric and NMR results for (NMA)0.4(NMF)0.6 from the present work as well as NMR data on pure NMA and pure NMF from ref 21. The pure liquids tend to crystallize, and so only high-temperature spin relaxation times are available. From the dielectric data the relaxation times τD,α = (2πνD,α)−1 were assessed. To describe the relaxation times, we applied the phenomenological Vogel−Fulcher law B τ = τ0 exp T − T0 (4)

presence of rotational diffusion for the techniques that essentially probe the molecular dynamics via Legendre polynomials of rank 2 (NMR) or rank 1 (dielectric spectroscopy). Thus, for the amides spin-relaxation methods detect a time scale which is significantly shorter than corresponding to the dominant Debye-type relaxation, similar to the situation for the monohydroxy alcohols. For those the hydrogen-bonding moiety displays a relaxation time, τOH, slower than the structural one,12 and τOH could be assigned to the time scale of structural diffusion of the transient supramolecular chains. Since for the amides the analogous NMR time scales, τNH, appear to be the shortest ones, it is not straightforward to apply this argument to those liquids. However, any comparison with structural relaxation must keep in mind that the underlying distribution of relaxation times is relatively broad (with a full width at half-maximum of about three decades73 for the given parameter αCC = 0.5). The data in Figure 8(b) refer mostly to (NEA)0.4(NMF)0.6 and demonstrate that all modulus time scales (from dielectric

The line shown in Figure 8(a) reflects an attempt frequency τ−1 0 ≈ 1.2 × 1012 s−1, a parameter B = 800 K, and a divergence temperature T0 = 133 K. From Figure 8(a) one recognizes that the time constants τD and τα barely differ but that the reorientational correlation times determined from the deuteron spin-relaxation times T1 and T2 are almost 10 times shorter than τD,α.72 This is more than the factor of 3 expected in the 15775


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dynamic quantity does not. Its concentration dependence indicates strong deviations from ideal behavior which evolves similar to that of alcohol mixtures such as of butanol with bromobutane or of 2-ethyl-1-hexanol (2E1H) with 2-ethyl-1hexyl bromide.55,39 In these mixtures, the nonideal behavior was taken to indicate that at large alcohol concentrations the hydrogen-bond-induced supramolecular aggregates remain essentially intact down to a critical concentration xc below which they are more and more destabilized. While this suggests a large degree of similarity of the behavior of the mixed alcohol and the mixed amide systems, a remarkable difference persists. For the amides the supramolecular structures are likely to remain intact down to amide concentrations x < xc because a breakdown of the main relaxation’s amplitude that should otherwise be observed for the amide mixtures is not visible in Figure 4. This suggests that chain-like amide aggregates are present in practically all 2-picoline mixtures, but that their number decreases with decreasing x. Overall these observations corroborate the interpretation that the main peak in the amides is analogous to the Debye peak in monohydroxy alcohols. Similar conclusions were recently drawn from a combined dielectric and calorimetric study of NEA with water which finds that “the main relaxation dynamics in the NEA−water mixtures largely behave like that in the mixtures composed of two Debye liquids”.46 This study reports on an almost linear increase of the glass transition temperature when water is added to NEA. Regarding dynamic quantities, the existence of a critical concentration was also revealed by ultrafast optical Kerr experiments performed on binary mixtures of NMA with water and also with carbon tetrachloride.26 This observation implies that beyond a certain degree of dilution the solvent polarity plays a minor role in enhancing the destabilization of supramolecular aggregates. In turn this indicates that this destabilization is related to a reduction of cooperativity effects within the hydrogen-bonded network formed by the amide molecules themselves. These insights clarify why such a network destabilization occurs also if the temperature is increased beyond a certain threshold in neat secondary amides,26 compatible with related findings for monohydroxy alcohols.43

relaxation, solvation dynamics, and mechanical shear) agree over the range of accessible temperatures. For comparison we also determined the zero-shear viscosity η0 = η′ = G″(ν → 0)/ (2πν) from our shear data and included them in Figure 8(b). These data refer to the right axis which was shifted such that η0 = 1012 Pa s corresponds to a relaxation time (plotted on the left axis) of 100 s. Applying the usual viscosimetric criterion that η0 is 1012 Pa s at Tg, on the one hand, one determines a glass transition temperature Tg,η = 147.5 K. On the other hand, from an extrapolation of the Debye relaxation τD to lower temperature one infers an associated kinetic temperature TD of 155 K or higher. This large temperature difference, which does not rely on distinguishing susceptibilities from moduli, vindicates previous arguments8 that the main peak in the amides does not correspond to the structural relaxation. A decoupling of viscosity from structural relaxation, which would weaken the argument just put forward, is sometimes invoked.74,75 However, explicit scrutiny of this issue reveals that such a phenomenon is not relevant for (NEA)0.4(NMF)0.6.37 From the translational self-diffusion coefficients Dt presented in the Supporting Information we calculated the time constants τDiff = 2R2H/(3Dt) on the basis of the Stokes−Debye equation76 applied for rank-1 Legendre polynomials. Here RH denotes the hydrodynamic radius; its value was tuned so that τDiff agrees best with the dielectric results for τD in the temperature range where τD and τDiff overlap (see Figure 8(a)). This procedure yields RH ≈ 6.4 Å, a radius much larger than the one corresponding to the effective van der Waals molecular radius, RvdW ≈ 3.7 Å.77 Together with the results for the Kirkwood factor, the large hydrodynamic radius RH suggests that the moieties giving rise to the dielectric Debye process in secondary amides are supramolecular in nature, resembling the situation for monohydroxy alcohols.62 Interestingly, the inclusion of the high-temperature data for τDiff in Figure 8(a) suggests that the value of the prefactor τ0 in the Vogel−Fulcher function, eq 4, obtained by fitting the dielectric results for τD is underestimated. In particular, if such a fit includes τD and τDiff (not shown) we find τ0 ≈ 10−11 s, a value close to the one previously reported for neat NEA.8 As pointed out in ref 8 such a large τ0 is atypical for structural relaxation processes, but with the present result included, it seems to be a more general feature of slow Debye processes in hydrogen-bonding liquids. 5.2. Mixtures of Amides with Other Polar Liquids. Attempts to induce a separation of Debye process and structural relaxation by mixing amides and other liquids with the goal to study both contributions separately were not successful so far. Nevertheless, the measurements of the picoline−amide system (see Figure 4) allow for interesting observations. At first glance, the dielectric spectra suggest a smooth evolution of the dominant relaxations among two liquids with vastly differing relaxation strengths. Since 2picoline does not display processes on the low-frequency side of the structural relaxation, can this observation unambiguously be taken to indicate that the dominant relaxation in the amide is also structural? No, it just means that the two polar liquids are miscible even at low temperatures. This statement is supported by the near linearity of the dielectric relaxation strength, Δε(x) (see the inset in Figure 4), which furthermore confirms that dielectrically the 2-picoline component is practically “invisible”. Hence, while the static property, Δε(x), looks quite common, the dielectric relaxation time τ(x) as a

6. CONCLUDING REMARKS To summarize, we applied several globally sensitive and hydrogen-bond-selective experimental methods to study mostly the slow dynamics of secondary amides, thus complementing experimental work directed at studying their fast dynamics.24−26 Time scales corresponding to the dominant dielectric relaxation of formamide−alkylacetamide mixtures were monitored close to their glass transition temperatures and compared with results from viscosity measurements and spin-relaxation techniques. It was found that the dielectric time scales are considerably longer than those from shear mechanical and spin relaxation measurements which are obviously more sensitive to the structural relaxation. While our attempts to separate the Debye process from the structural relaxation by means of mixing the secondary amides with suitable liquidswe reported dielectric results on the amide−picoline system were not successful so far, a kind of separation seems to be possible by combining various experimental techniques which couple to different degrees of freedom in the secondary amides. Overall, the results that we obtained in the present work strengthen the view that the dominant dielectric relaxation in the amide system is analogous to that in other hydrogen15776


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(8) Wang, L. M.; Richert, R. Identification of Dielectric and Structural Relaxations in Glass-Forming Secondary Amides. J. Chem. Phys. 2005, 123, 054516. (9) Griffin, P. J.; Holt, A. P.; Wang, Y.; Novikov, V. N.; Sangoro, J. R.; Kremer, F.; Sokolov, A. P. Charge Transport and Structural Dynamics in Carboxylic-Acid-Based Deep Eutectic Mixture. J. Phys. Chem. B 2014, 118, 9378−9385. (10) Dannhauser, W.; Cole, R. H. Dielectric Properties of Liquid Butyl Alcohols. J. Chem. Phys. 1955, 23, 1762−1766. (11) Levin, V. V.; Feldman, Y. D. Dipole Relaxation in Normal Aliphatic-Alcohols. Chem. Phys. Lett. 1982, 87, 162−164. (12) Gainaru, C.; Meier, R.; Schildmann, S.; Lederle, C.; Hiller, W.; Rössler, E. A.; Böhmer, R. Nuclear-Magnetic-Resonance Measurements Reveal the Origin of the Debye Process in Monohydroxy Alcohols. Phys. Rev. Lett. 2010, 105, 258303. (13) Singh, L. P.; Richert, R. Watching Hydrogen Bonded Structures in an Alcohol Convert from Rings to Chains. Phys. Rev. Lett. 2012, 109, 167802. (14) Gainaru, C.; Figuli, R.; Hecksher, T.; Jakobsen, B.; Dyre, J. C.; Wilhelm, M.; Böhmer, R. Shear-Modulus Investigations of Monohydroxy Alcohols: Evidence for a Short-Chain-Polymer Rheological Response. Phys. Rev. Lett. 2014, 112, 098301. (15) Böhmer, R.; Gainaru, C.; Richert, R. Structure and Dynamics of Monohydroxy Alcohols − Milestones towards Their Microscopic Understanding, 100 Years after Debye. Phys. Rep. 2014, 545, 125−195. (16) Lin, R.-Y.; Dannhauser, W. Dielectric Constant of HydrogenBonded Liquids. II. N-Monosubstituted Acetamides. J. Phys. Chem. 1963, 67, 1805−1810. (17) Bass, S. J.; Nathan, W. I.; Meighan, R. M.; Cole, R. H. Dielectric Properties of Alkyl Amides. II. Liquid Dielectric Constant and Loss. J. Phys. Chem. 1964, 68, 509−515. (18) Dannhauser, W.; Johari, G. P. Intermolecular Association and Dielectric Relaxation in Some Liquid Amides. Can. J. Chem. 1968, 46, 3143−3149. (19) Barthel, J.; Buchner, R.; Wurm, B. The Dynamics of Liquid Formamide, N-Methylformamide, N,N-Dimethylformamide, and N,NDimethylacetamide. A Dielectric Relaxation Study. J. Mol. Liq. 2002, 98−99, 51−69. (20) Swiergiel, J.; Jadzyn, J. Fractional Stokes−Einstein−Debye Relation and Orientational Entropy Effects in Strongly HydrogenBonded Liquid Amides. Phys. Chem. Chem. Phys. 2011, 13, 3911− 3916. (21) Seipelt, C. G.; Zeidler, M. D. Correlation Times and Quadrupole Coupling Constants in Liquid N-Methylformamide and N-Methylacetamide. Ber. Bunsenges. Phys. Chem. 1997, 101, 1501− 1508. (22) Liu, Y.; Ozaki, Y.; Noda, I. Two-Dimensional Fourier-Transform Near-Infrared Correlation Spectroscopy Study of Dissociation of Hydrogen-Bonded N-Methylacetamide in the Pure Liquid State. J. Phys. Chem. 1996, 100, 7326−7332. (23) Whitfield, T. W.; Martyna, G. J.; Allison, S.; Bates, S. P.; Vass, H.; Crain, J. Structure and Hydrogen Bonding in Neat NMethylacetamide: Classical Molecular Dynamics and Raman Spectroscopy Studies of a Liquid of Peptidic Fragments. J. Phys. Chem. B 2006, 110, 3624−3637. (24) Herrebout, W. A.; Clou, K.; Desseyn, H. O. Vibrational Spectroscopy of N-Methylacetamide Revisited. J. Phys. Chem. A 2001, 105, 4865−4881. (25) Zanni, M. T.; Asplund, M. C.; Hochstrasser, R. M. TwoDimensional Heterodyned and Stimulated Infrared Photon Echoes of N-Methylacetamide-D. J. Chem. Phys. 2001, 114, 4579−4590. (26) Hunt, N. T.; Wynne, K. The Effect of Temperature and Solvation on the Ultrafast Dynamics of N-Methylacetamide. Chem. Phys. Lett. 2006, 431, 155−159. (27) Turton, D. A.; Wynne, K. Structural Relaxation in the Hydrogen-Bonding Liquids N-Methylacetamide and Water Studied by Optical Kerr Effect Spectroscopy. J. Chem. Phys. 2008, 128, 154516.

bonded liquids, notably the monohydroxy alcohols. It would be useful to obtain further insights into the amide’s structure and dynamics from simulation studies addressing the nature of the Debye process79 and from the application of experimental techniques that have been successful in clarifying related phenomena in monohydroxy alcohols. These latter efforts include high-pressure experiments which show peculiar behavior in the presence of a Debye process, 80 the simultaneous performance of modulated calorimetry and dielectric or other spectroscopies,81 as well as diffraction studies of the prepeak in suitable mixtures with molecules that dilute or disrupt the hydrogen-bond network.82

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b10034. Additional dielectric data on binary and ternary amide mixtures and details about several additional NMR experiments. The latter include results from field gradient diffusometry and from homonuclear and heteronuclear two-dimensional chemical shift correlation spectroscopy (PDF).

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +49 231 755 3514. Fax: +49 231 755 3516. E-mail: [email protected]. Present Address #

(C.G.) Department of Chemistry, Tennessee University, Knoxville, TN 37996-1600, USA. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This project was financially supported by the Deutsche Forschungsgemeinschaft under Grant No. Bo1301/8-2. REFERENCES

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Dynamics in Supercooled Secondary Amide Mixtures: Dielectric and

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