Dynamics of water-alcohol mixtures: Insights from nuclear magnetic resonance, broadband dielectric spectroscopy, and triplet solvation dynamics D. Sauer, B. Schuster, M. Rosenstihl, S. Schneider, V. Talluto, T. Walther, T. Blochowicz, B. Stühn, and M. Vogel Citation: The Journal of Chemical Physics 140, 114503 (2014); doi: 10.1063/1.4868003 View online: http://dx.doi.org/10.1063/1.4868003 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Comparative study of dynamics in glass forming mixtures of Debye-type N-ethylacetamide with water, alcohol, and amine J. Chem. Phys. 141, 104506 (2014); 10.1063/1.4895066 Solvation dynamics of tryptophan in water-dimethyl sulfoxide binary mixture: In search of molecular origin of composition dependent multiple anomalies J. Chem. Phys. 139, 034308 (2013); 10.1063/1.4813417 Dynamic properties of water/alcohol mixtures studied by computer simulation J. Chem. Phys. 119, 7308 (2003); 10.1063/1.1607918 Ion solvation dynamics in water–methanol and water– dimethylsulfoxide mixtures J. Chem. Phys. 110, 10937 (1999); 10.1063/1.479030 Molecular motion and solvation of benzene in water, carbon tetrachloride, carbon disulfide and benzene: A combined molecular dynamics simulation and nuclear magnetic resonance study J. Chem. Phys. 108, 455 (1998); 10.1063/1.475408

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THE JOURNAL OF CHEMICAL PHYSICS 140, 114503 (2014)

Dynamics of water-alcohol mixtures: Insights from nuclear magnetic resonance, broadband dielectric spectroscopy, and triplet solvation dynamics D. Sauer,1 B. Schuster,1 M. Rosenstihl,1 S. Schneider,1 V. Talluto,2 T. Walther,2 T. Blochowicz,1 B. Stühn,1 and M. Vogel1 1

Institut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstraße 6, 64289 Darmstadt, Germany 2 Institut für Angewandte Physik, Technische Universität Darmstadt, Schlossgartenstraße 7, 64289 Darmstadt, Germany

(Received 25 October 2013; accepted 26 February 2014; published online 19 March 2014) We combine 2 H nuclear magnetic resonance (NMR), broadband dielectric spectroscopy (BDS), and triplet solvation dynamics (TSD) to investigate molecular dynamics in glass-forming mixtures of water and propylene glycol in very broad time and temperature ranges. All methods yield consistent results for the α process of the studied mixtures, which hardly depends on the composition and shows Vogel-Fulcher temperature dependence as well as Cole-Davidson spectral shape. The good agreement between BDS and TDS data reveals that preferential solvation of dye molecules in microheterogeneous mixtures does not play an important role. Below the glass transition temperature Tg , NMR and BDS studies reveal that the β process of the mixtures shows correlation times, which depend on the water concentration, but exhibit a common temperature dependence, obeying an Arrhenius law with an activation energy of Ea = 0.54 eV, as previously reported for mixtures of water with various molecular species. Detailed comparison of NMR and BDS correlation functions for the β process unravels that the former decay faster and more stretched than the latter. Moreover, the present NMR data imply that propylene glycol participates in the β process and, hence, it is not a pure water process, and that the mechanism for molecular dynamics underlying the β process differs in mixtures of water with small and large molecules. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4868003] I. INTRODUCTION

Aqueous mixtures are of enormous relevance in biological and technological processes. For example, they play crucial roles in life and food sciences or in cryopreservation technologies. To gain fundamental insights, water-alcohol mixtures received considerable attention in the last decades. As alcohol molecules feature both polar and apolar groups, hydrophilic and hydrophobic interactions coexist in these mixtures, leading to complex structural and dynamical properties as well as complex phase behaviors. Such competition of hydrophilic and hydrophobic interactions can result in segregation phenomena at the microscopic scale1–3 and it can reduce the proneness towards ice formation at the macroscopic scale, constituting a useful effect for cryopreservation. Dynamical behaviors of glass-forming mixtures of water and alcohol molecules were investigated in broadband dielectric spectroscopy (BDS) studies.4–12 While a single relaxation process exists in the weakly supercooled temperature range, two relaxation processes were observed in the deeply supercooled temperature range. For aqueous mixtures containing small alcohol molecules, the slower low-temperature process is a continuation of the high-temperature one. Its time constant shows a Vogel-Fulcher-Tammann (VFT) tempera-

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ture dependence and the spectral shape can usually be described by a Cole-Davidson (CD) function, i.e., the loss peak is asymmetric on a logarithmic frequency axis. The faster low-temperature process exists also below the glass transition temperature Tg . In most works, its line shape is described by a Cole-Cole (CC) function, i.e., the loss peak is symmetric, and the time constant shows a kink in the temperature dependence at Tg , where an Arrhenius law with an activation energy of Ea ≈ 0.54 eV is often found below the glass transition. For aqueous mixtures containing large alcohol molecules, BDS work reported a different relaxation scenario.6 Here, the hightemperature process exhibits a CC shape and continues to the faster low-temperature process, whereas the slower lowtemperature process sets in as a new relaxation phenomenon upon cooling. In view of its VFT and CD behaviors, the slower lowtemperature process is usually identified with the α relaxation of the mixture, resulting from a cooperative motion of water and alcohol molecules. The molecular origin of the faster low-temperature process is still subject to controversial debate.4–12 Most authors agree that the faster lowtemperature process is related to water dynamics. For example, it was argued that bound and free water molecules, which do and do not form hydrogen bonds with alcohol

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molecules, can be distinguished based on different dynamical behaviors. While bound water molecules together with the alcohol molecules are involved in the slower process and, hence, the glass transition, free water molecules retain a higher mobility and cause the faster process.4–7 For aqueous mixtures comprising large alcohol molecules, it was proposed that the faster process reflects the motion of the more mobile water molecules in geometrical constraints formed by the less mobile alcohol molecules,6 resembling the situation for water in polymer and protein matrices.11, 13–15 For simplicity, we denote the faster low-temperature process as β process, notwithstanding possibly different molecular mechanisms associated with the faster process in aqueous mixtures and the secondary relaxation intrinsic to neat glass-forming liquids. In contrast to BDS, triplet solvation dynamics (TSD) is an invasive method, as molecular dynamics is probed by a dye molecule dissolved in the sample at low concentration. The dye is excited by a short UV laser pulse. By using the proper chromophore, reorientational dynamics of permanent electric dipoles can be probed similar to dielectric spectroscopy, but on a local scale, as the Stokes shift of the dye’s phosphorescence is influenced roughly by the first solvation shell.16 Such local probe is particularly useful when probing molecular dynamics in confinements17 or mixtures.18, 19 Here, we explore the possibility to apply TSD to water-alcohol mixtures, where microphase separation can occur.1–3 Then, TSD can possibly give indications for such segregation phenomena provided the solubility of the dye molecules is different in various microphases. In addition to BDS and TSD, nuclear magnetic resonance (NMR) techniques proved powerful tools to investigate molecular dynamics in aqueous mixtures. 17 O NMR spinlattice relaxation (SLR) analysis is useful to selectively ascertain the motion of water in mixtures with alcohols.20–22 We utilized 2 H NMR methods to study water dynamics in various mixtures and confinements.23–29 In addition to SLR, we analyzed solid-echo (SOE) and stimulated-echo (STE) measurements. Such combination of 2 H NMR techniques allowed us to determine rotational correlation times of water in a broad dynamic range of 10−10 –100 s. Furthermore, utilizing the fact that 2 H NMR provides detailed insights into not only the rates of the dynamics, but also the mechanisms for the motions, we provided evidence that the mechanism for water motion can be different in viscous and solid environments.23–29 Here, we exploit the capabilities resulting from a combination of BDS, TSD, and NMR to shed new light on the molecular origins of the relaxation processes in aqueous mixtures. In previous works,27, 28 we used BDS together with NMR to obtain valuable insights into molecular dynamics in mixtures of water with proteins or dimethyl sulfoxide. In this contribution, BDS and NMR are combined with TSD to study mixtures of water with propylene glycol. In BDS, we extend previous work12 on these water-alcohol mixtures to broader frequency and temperature ranges. In NMR, 2 H SLR, SOE, and STE methods are used to obtain information about rates and mechanisms for molecular motions in a wide dynamic range.

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II. THEORETICAL AND EXPERIMENTAL ASPECTS A. Theoretical background

Molecular rotational motion can be characterized on the basis of the autocorrelation functions Fl (t) =

Pl [cos θ (0)]Pl [cos θ (t)] . Pl [cos θ (0)]Pl [cos θ (0)]

(1)

Here, Pl denotes the Legendre polynomial of rank l, θ is an angle describing the molecular orientation, and the pointed brackets indicate an ensemble average. 1. Broadband dielectric spectroscopy

BDS enables measurement of the complex dielectric permittivity ε∗ (ω) = ε (ω) − iε (ω). Within the linear response regime, the imaginary part of the dielectric permittivity, the dielectric loss ε (ω), and the correlation function F1 (t) are related via a Fourier cosine transform,  ∞ ε (ω) = ε cos(ω t) F1 (t) dt, (2) ω 0 where ε is the dielectric relaxation strength. In previous works on aqueous mixtures,4–12 the dielectric permittivity was described by a superposition of relaxation processes, usually a Cole-Davidson (CD) function for the α relaxation and a symmetric Cole-Cole (CC) function for the β process. In our data, however, it is clearly apparent that a symmetric peak is not appropriate to describe the β process at low temperatures, but the peak is broader on the low frequency side, see below. Furthermore, in order to properly model the merging of the α and β relaxations, we use the Williams-Watts approach,30 which proved useful in studies on supercooled liquids31 and polymer melts.32 In time domain, it reads F1 (t) = Fα (t)[(1 − λ) + λ Fβ (t)].

(3)

Here, Fα (t) and Fβ (t) are the correlation functions of the α and β processes, respectively. The parameter λ describes the relative contribution of the β relaxation. We define Fα (t) and Fβ (t) by distributions of relaxation times. For the α relaxation, we use a generalized Gamma (GG) distribution   m  τ n − mn ττ 0 (4) GGG (ln τ ) = NGG (m, n) e τ0  n with the normalization factor NGG = mn m m/ ( mn ), where

(x) is the regular Gamma function. The properties of the GG distribution were discussed previously.33, 34 The line shape resulting for large values of the parameter m closely resembles that of a CD function, as employed in previous works on water-alcohol mixtures.4–12 For the β relaxation, we utilize the following distribution of relaxation times:33 Gβ (ln τ ) =

Nβ (a, b) , b (τ/τm )a + (τ/τm )−ab

(5)

with Nβ = a(1 + b)/π bb/(1 + b) sin [π b/(1 + b)] being the normalization factor. The resulting dielectric function bears certain resemblance to the HN expression, e.g., it leads to

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FIG. 1. Schematic picture of triplet solvation dynamics: dye molecule (red), solvation shell (dark blue), and molecular dipoles (green).

power laws ε ∝ ωa and ∝ ω−ab (0 < a, b ≤ 1) on the respective sides of the dielectric loss peak. Equation (5) has the convenient property that it reflects an underlying temperature independent distribution of activation energies when the temperature dependence of the shape parameters obeys a ∝ T and b = const.33 Both distributions are used to obtain data in frequency and time domains as weighted superpositions of Debye processes and exponential decays, respectively. For example, TSD correlation functions are calculated according to ∞ F1 (t) = −∞ G(ln τ ) e−t/τ d ln τ . 2. Triplet solvation dynamics

Like BDS, TSD measures the reorientation of molecular dipoles in a liquid as a response to an external electric field. However, in TSD, we do not apply a macroscopic field over the entire sample, but rather the field is generated locally in the sample itself.16 For this purpose, a dye is added to the sample in a very low concentration. When pumping with a pulsed UV Laser, the dye can be excited from the ground state S0 into a long-lived triplet state T1 , leading to a change in its permanent dipole moment, μ = μE − μG . The surrounding liquid molecules start to reorient in response to the changed electric field of the dye molecule, see Fig. 1. Due to the equilibration of the liquid with respect to the excited state, its polarization changes. As a consequence, the

energy of the ground state increases, while the energy of the excited state decreases,35 leading to a time-dependent mean emission energy ν(t). Together with the mean emission energies at t = 0 and t = ∞, see Fig. 2, one can define the Stokes-shift correlation function, CStokes (t) =

ν (t) − ν (∞) , ν (0) − ν (∞)

(6)

It describes the dynamics of the system detached from the absolute energy scale. Although it is not entirely settled whether CStokes (t) reflects the dielectric modulus (relaxation at constant charge) or the dielectric permittivity (retardation at constant field) or a scenario in between, it turned out that CStokes (t) often closely resembles the macroscopic permittivity in the time domain,36 i.e., we can assume CStokes (t) ≈ F1 (t).

(7)

A suitable phosphorescent probe molecule is quinoxaline (QX).16 It exhibits both a high quantum yield and a significant change in dipole moment μ = 1.31 D upon excitation. The spatial range of TSD is roughly limited to the first solvation shell around the dye,16 rendering TSD a very attractive technique to investigate local relaxation dynamics, in particular, in binary mixtures where not only microscale segregation phenomena,1–3 but also intrinsic confinement effects37 can be issues.

FIG. 2. Schematic energy diagram of the energy states S0 , S1 , and T1 . The metastable state T1 is populated by excitation from S0 to S1 , followed by inter-system crossing and internal conversion.

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3. 2 H NMR experiments

In 2 H NMR, we probe the quadrupolar contributions to the resonance frequencies of deuterons in water or alcohol O–D bonds. The quadrupolar frequency of a deuteron is approximately given by38 δ ωQ = ± (3 cos2 θ − 1) ∝ P2 (cos θ ). (8) 2 Here, the ± signs correspond to the two allowed transitions of the I = 1 nucleus, δ = 2π × 161 kHz denotes the anisotropy parameter of the interaction tensor, see below, and θ is the angle between the direction of the O–D bond and the external magnetic field B0 . Thus, for each deuteron, the quadrupolar frequency ωQ is determined by the molecular orientation, explicitly, by P2 (cos θ ). In the following, it is important that water and alcohol molecules exchange deuterons and, hence, both molecular species contribute to the 2 H NMR signals. Here, we use 2 H SLR to investigate the α process of aqueous mixtures. For isotropic rotational motion, the 2 H SLR time T1 depends on the spectral density J2 (ω), which is obtained from the correlation function F2 (t) via Fourier transformation. Specifically, T1 at a Larmor frequency ω0 is given by39 1 2 2 δ [J2 (ω0 ) + 4J2 (2ω0 )] . = T1 15

(9)

In the case of a Debye process, rotational motion is described by F2 (t) = exp (−t/τ ) and J2 (ω) = τ /(1 + ω2 τ 2 ), leading to a T1 minimum for τ ≈ 1/ω0 ≈ 1 ns. However, the α process of aqueous mixtures does not obey Debye form, but more a CD spectral shape. Therefore, we analyze our 2 H SLR data using the CD spectral density40   sin[βCD arctan ωτCD ] JCD (ω) = . (10)   βCD 2 2 ω 1+ω2 τCD 2

H STE experiments yield detailed information about rotational motion in the milliseconds regime.38, 39 Here, we generate a stimulated echo by applying the three-pulse sequence 90◦x – tp – 90◦−x – tm – 90◦x – tp . Then, the rotational correlation function F2cc (tm , tp ) ∝  cos[ωQ (0)tp ] cos[ωQ (tm )tp ]

(11)

can be measured when the height of this echo is observed for various mixing times tm and fixed evolution times tp , where we assume that molecular dynamics during the latter periods can be neglected, i.e., tp  τ ≈ tm . In general, F2cc deviates from F2 , see below. For an analysis of correlation functions of complex molecular dynamics, it is common practice to interpolate the decays with a Kohlrausch-Williams-Watts (KWW) function, FK (t) = exp[−(t/τK )βK ] where τ K and β K quantify the time scale and the nonexponential nature of the correlation loss. We note that the CD and the KWW spectral shapes can be obtained using Eq. (4) in certain limits of the parameter values.33 As the angular resolution of 2 H STE experiments is determined by the length of the evolution time, it is possible to obtain insights into the mechanism for rotational motion from a comparison of correlation functions F2cc (tm , tp ) for var-

ious values of tp .39, 41, 42 The angles of elementary molecular rotational jumps can be determined when analyzing the time scale of the decays for different evolution times. While the decay time is virtually independent of the value of tp for large-angle elementary jumps, it strongly decreases with increasing tp for small-angle elementary jumps. The overall geometry of molecular reorientation can be obtained from the evolution-time dependence of the residual correlation at long cc (tp ) = F2cc (tm τ, tp ). We use values of tp for which times, F∞ isotropic reorientation causes complete decays of the correcc (tp ) = 0. Thus, observation of finite lation function, i.e., F∞ long-time plateaus would indicate a substantial anisotropy, e.g., a small overall amplitude of the rotational motion under study. In principle, 2 H STE experiments also allow one to measure F2ss (tm , tp ), being the counterpart of F2cc (tm , tp ) with the cosine functions replaced by sine functions, see Eq. (11). On the one hand, it can be advantageous for a comparison of STE and BDS data to consider the former rather than the latter correlation function because, in the limit tp → 0, F2ss (tm ) yields F2 (tm ), while F2cc (tm ) does not decay.39 On the other hand, STE data are affected by SLR damping, see Sec. II B, which can be corrected for F2cc (tm , tp ), but not for F2ss (tm , tp ). Owing to the latter possibility, we focus on F2cc (tm , tp ). When comparing NMR results, in particular, F2cc data, with BDS or TDS findings, two aspects need to be considered. First, BDS and TSD provide F1 , while NMR yields F2 so that the respective time constants τ 1 and τ 2 can differ. For example, τ 1 is a factor of 3 longer than τ 2 in the case of isotropic rotational diffusion. Second, as discussed above, STE time constants can depend on the value of the used evolution time, e.g., they decrease with increasing tp when molecular reorientation results from consecutive small-angle elementary jumps. For example, in the case of isotropic rotational diffusion, correlation functions F2cc (tm , tp ) for finite values of tp yield correlation times shorter than τ 2 , which is obtained exploiting that F2 (t) is proportional to F2ss (tm , tp ) in the limit tp → 0, adding to possible differences between STE and BDS data in our study. To keep the latter deviations at a minimum, we set the evolution time to the shortest value allowing for a complete decay of F2cc (tm , tp ) in the case of isotropic reorientation, tp = 9 μs. 4. Mean logarithmic correlation times

As we utilize various methods to measure characteristic time constants of molecular dynamics that are governed by broad distributions of correlation times G(ln τ ), it is necessary to also appreciate that the respective characteristic time constants can correspond to different averages over G(ln τ ), which differ substantially for broad distributions.43 Striving for equal treatment, we use mean logarithmic correlation times τ c to characterize all dynamical processes. For the KWW and CD functions, this logarithmic average is given by44   1 Eu + ln τK ≡ ln τc , ln τ  = 1 − (12) βK ln τ  = ln τCD + ψ(βCD ) + Eu ≡ ln τc ,

(13)

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where Eu ≈ 0.58 is Euler’s constant and ψ(x) denotes the Digamma function. For the distributions GGG (ln τ ) and Gβ (ln τ ), τ c can be obtained according to  ∞ G(ln τ ) ln τ d ln τ ≡ ln τc . (14) ln τ  = −∞

We employ mean logarithmic correlation times rather than mean correlation times because the former are well defined for all present experimental results and interpolation functions, while the latter diverge for the distribution used for the β process, see Eq. (5), when a < 1, which is the case for the data under consideration.

B. Experimental details

BDS, TSD, and NMR samples were prepared by mixing appropriate amounts of deuterated water (Sigma Aldrich) and protonated propylene glycol (Acros Organics). The studied mixtures contain 30 wt. % (W30), 45 wt. % (W45), and 50 wt. % (W50) of deuterated water. As a consequence of deuteron exchange, the existing deuterons are distributed between water and alcohol molecules. Hence, the 2 H NMR signals comprise contributions from O–D bonds of both molecular species. In order to measure the dielectric permittivity from 10−4 Hz to 1011 Hz three dielectric spectrometers were used. The low frequency part from 10−4 Hz to 106 Hz was measured with a Novocontrol Alpha-N High Resolution Dielectric Analyzer, where temperature was controlled utilizing a Novocontrol Quatro cryosystem with reproducibility better than 0.5 K. The mid frequency range from 106 Hz to 1010 Hz was covered with a HP-4191A RF Impedance Analyzer, whereas the high frequency range (108 Hz to 1011 Hz) was measured with an Agilent N5230C PNA-L network analyzer equipped with the Agilent 85070E Dielectric Probe Kit using the slim form coaxial probe. The temperature for mid and high frequency ranges, was controlled with a home-built temperature controller with a reproducibility better than 1 K. In the TSD experiment, the dye is excited by the third harmonic of a pulsed Nd:YAG laser Innolas Spitlight 600 at 355 nm. To avoid bleaching of the dye the pulses are attenuated to a few mJ. The sample is filled into a rectangular quartz cell and mounted in a Cryovac Conti Spectro 4 contact gas optical cryostat, which can be temperature controlled in the range from 77 K to 320 K by a Lakeshore 336 temperature controller. To correct for a difference in absolute temperature between the Cryostat systems of BDS and TSD, we recorded data of propylene carbonate in each system and identified an absolute temperature difference of about 1.8 K in the relevant temperature range. When BDS and TSD data are compared below, the temperatures of the TSD data sets were corrected for this value. The TSD setup is shown in Fig. 3. The emitted light is collected under 90◦ to the incident laser beam by a liquid light guide fiber. The output of the fiber is collimated onto the entrance slit of an Andor Shamrock 500i grating spectrograph, which is equipped with a 150, 600, and 1800 lines/mm grating turret. An Andor iStar 340T iCCD camera with integrated

FIG. 3. Schematic view of the TSD setup: M: Mirror, HWP: Half wave plate, PBS: Polarizing beam splitter, BS: Beam stop, and L: Lens.

gate and delay generator is used to record the time-resolved emission spectra of the dye. For the 2 H NMR experiments, we utilize a home-built spectrometer, which operates at a Larmor frequency of ω0 = 2π × 46.1 MHz. Further details about the experimental setup can be found in previous works.24, 25, 45 SOE measurements use the solid-echo sequence, 90◦x –  – 90◦y , with an echo delay of  = 20 μs. SLR experiments are performed using the saturation-recovery sequence in combination with the solid-echo sequence for signal detection. Considering that heterogeneous dynamics can result in nonexponential SLR, a KWW function is employed to describe the time evolution of the magnetization M(t) after saturation:

   t βT 1 M(t) = exp − . (15) R (t) ≡ 1 − M(∞) T1 Then, a mean SLR time T1  can be calculated from the fit parameters according to T1  = (T1 /βT1 ) (1/βT1 ). STE experiments are performed utilizing the above threepulse sequence together with a phase cycle, which cancels out unwanted single-quantum and double-quantum coherences.46 We analyze the measured STE decays by fitting to F2cc (tm ) = FK (tm )R (tm ).

(16)

Hence, we assume that molecular reorientation leads to a complete loss of orientational correlation for the used values of tp so that it is not necessary to introduce a finite long-time cc as additional fit parameter, but it is sufficient to plateau F∞ utilize a KWW function FK (t). This assumption is motivated by our experimental findings, see below. Moreover, we take into account that, in experimental practice, relaxation effects of the spin ensemble lead to an additional damping of the STE decays. For the fits, we exploit that R (tm ) is obtained from independent SLR experiments and, hence, the corresponding parameters can be fixed. If not stated otherwise, the presented

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FIG. 4. Dielectric loss ε (ω) of the mixture W45 at the indicated temperatures. The solid lines are fits with Eqs. (4) and (5) utilizing the Williams-Watts approach, Eq. (3). Above 200 K, use of Eq. (4) is sufficient to describe the data (dotted lines).

STE data are scaled to obtain F2cc (0) = 1 when extrapolating the fitting functions.

III. RESULTS A. BDS results

Figure 4 shows the dielectric loss ε (ω) of mixture W45 at various temperatures. At temperatures T > 200 K, we see a single loss peak, which shifts to lower frequencies upon cooling. When the temperature is further decreased in the range 160–200 K, the loss peak broadens and splits into two processes until the slower process exits the accessible frequency range so that a single loss peak is again observed at temperatures T < 160 K. At variance with assumptions in previous work, the faster low-temperature relaxation of W45, i.e., the β process, has an asymmetric shape, as is clearly evident from the data at 150 K. Fits with Eq. (5) yield a temperature independent asymmetry parameter of b = 2.8 and a width parameter that follows the relation a = c · T with c = 0.0019 K−1 at T ≤ 170 K, see Fig. 5 (left). According to previous reasoning,33 the latter observation, along with the fact that the relaxation times follow Arrhenius behavior, see Fig. 6, indicates that the β process is characterized by a temperature independent distribution of activation energies in this temperature range.

0.65

a λ

0.6

2

1

1.8 0.8

0.55 0.5 a

The entire dielectric loss at temperatures above 200 K and the slower low-temperature relaxation, i.e., the α process, were analyzed in terms of Eq. (4), featuring the shape parameters m and n. It turns out that m = 20 can be kept constant for all temperatures while n increases with increasing temperature, starting from n ≈ 0.5 near the glass transition, see Fig. 5 (right). Such large temperature independent value of m implies that the spectral shape of this process is to good approximation characterized by a CD function,33 in accord with previous findings for the α process of water-alcohol mixtures.4–12 We note that the parameters m, n can be larger than one as they characterize a distribution of relaxation times where a delta distribution, i.e., a Debye-type relaxation, is approached for m, n → ∞.33 The temperature dependence of n at first glance implies deviations from the time-temperature superposition (TTS) principle. However, the temperature dependence of the line shape parameters of the α relaxation depends on the assumptions made for the β process, like a temperature independent asymmetry supposed to simplify the fit procedure. Thus, we cannot unambiguously demonstrate a violation of the TTS principle as both processes strongly overlap in the whole temperature range where the Williams-Watts ansatz is applied. In Fig. 6, we present the temperature dependence of the mean logarithmic correlation times τ c resulting from these interpolations. The α relaxation exhibits VFT behavior. The

1.6 1.4

0.6 λ

0.45 0.4

0.4 0.35

n

1.2 1 0.8

0.2 0.3

0.6

0.25

0 140

150

160 170 T/K

180

190

0.4 160 180 200 220 240 260 280 300 320 340 T/K

FIG. 5. Shape parameters of the (left) β process and (right) α process, see Eqs. (4) and (5). At low temperatures, the β relaxation is characterized by a temperature independent distribution of activation energies, as b = 2.8 for all temperatures and a ∝ T (dashed line). The weight λ of the β process in the Williams-Watts ansatz increases above Tg and reaches its maximum value at 180 K above which temperature it is kept constant at λ = 1. The shape parameter n of the α relaxation increases with temperature, while m = 20 for all temperatures. As m, n are parameters of a relaxation time distribution their values may be larger than 1.

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FIG. 6. Mean rotational correlation times of the studied mixtures W30, W45, and W50. In all cases, time constants τ c corresponding to mean logarithmic correlation times are shown. NMR data from SLR, SOE, and STE experiments are compared with BDS data for the α and β processes and with TSD data where both processes are not disentangled due to the limited dynamic range. The solid line is an interpolation of the BDS results for the α process of W45 with a VFT behavior, τ c (T) = τ 0 exp [BT0 /(T − T0 )], yielding B = 33 and T0 = 118 K. The dashed line is an Arrhenius law with an activation energy of Ea = 0.54 eV, which is meant to guide the eye.

correlation time of the α process amounts to about 100 s at the calorimetrically determined glass transition temperature Tg = 165 K, as expected. The temperature dependence of the β process is consistent with an Arrhenius law with an activation energy of Ea = 0.54 eV at T < Tg . Based on our observations for the temperature dependence and the spectral shape of both processes, we conclude that the high-temperature relaxation continues as the slower process at lower temperatures. This behavior is considered by the Williams-Watts approach, Eq. (3), where the β process is only relevant when it occurs on time scales shorter than or comparable to the α relaxation time. In addition, inspection of Fig. 6 reveals that the other studied water-alcohol mixtures show a very similar α process. Relating to the β process, the correlation times are somewhat longer for W45 than for W50. For W30, no clear splitting of the α and β processes was observed, hampering separate determination of time constants.

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FIG. 7. Comparison of the emission spectra of QX dissolved in the single components propylene glycol (PG) and deuterated water (D2 O) as well as in the mixture W45 at a fixed delay of 100 ms after the laser pulse.

the data yield no evidence for a preferential solvation. We note that the frequency shift caused by the dynamics of the solvation shell is significantly smaller than the shift depicted in Fig. 7. Figure 8 shows the Stokes-shift correlation functions of the mixture W45 in a time range 1 ms–1 s. While the shorttime limit is determined by the time required to populate the triplet state, see Fig. 2, the long-time limit is given by the phosphorescence life time of the dye. At first glance, the correlation functions decay in a single step, which can be described by a KWW function, while the dielectric loss shows two relaxation peaks in this temperature range. However, unlike neat glass forming liquids, which obey TTS principle to a good approximation, the present mixture exhibits a stretching parameter β K that strongly decreases from 0.4 to 0.2 when the temperature is lowered from 175 K to 165 K, implying that an actual separation of two distinct processes remains concealed due to the narrow time window of the TSD experiment and the pronounced spectral width of the relaxation processes. To further check the BDS and TSD data for consistency, we compare the Fourier transform of the dielectric loss with the Stokes-shift correlation function, as is exemplified for the case of 170 K in Fig. 8. It turns out that the BDS and TSD

B. TSD results

When adding a dye molecule to a binary mixture, the question arises whether the environment of the dye represents the average composition or whether the dye is preferentially dissolved by one of the components. To ascertain the solvation behavior of QX, we compare phosphorescence spectra for the neat components and for the mixture W45 at 170 K, using a delay after the laser pulse of t0 = 100 ms. Ideally, such comparison would involve a spectrum of liquid water at 170 K, which is not accessible, but valuable insights are already available from the data for crystalline water. As shown in Fig. 7, the spectrum of the mixture lies between the spectra of pure propylene glycol and of pure crystalline D2 O. Without being a proof, this finding implies that the emission is influenced by both components of the mixture and, hence,

FIG. 8. Stokes-shift correlation functions for the mixture W45. Solid lines are fits with a KWW function. The dotted black line is the Fourier transform of the dielectric loss at 170 K.

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correlation functions closely follow each other and that the α and β processes cannot be disentangled in the time domain at the relevant temperatures. As was mentioned in Sec. II B, we exploited for this comparison that a systematic temperature difference in the BDS and TSD cryostat systems can be corrected based on measurements for a neat glass former. Thus, within experimental accuracy, the macroscopic and the local dielectric probes yield the same results. Therefore, on average, the solvation shells of the dye molecules represent the composition of the overall mixture, rendering it unlikely that there is preferential solvation in mixtures with microphase separation. As α and β processes cannot be separated in time domain in the studied temperature range, the time constants obtained from the KWW interpolations of the TSD data represent average values. Nevertheless, we see in Fig. 6 that the mean logarithmic correlation times τ c resulting from the Stokes-shift correlation functions of W45 agree with that obtained for the α process of this mixture in our BDS studies.

C. NMR results

Next, we analyze 2 H SLR to study molecular dynamics in mixtures of water and propylene glycol. For none of the studied compositions and temperatures, the different molecular species exhibit distinguishable 2 H SLR behaviors, i.e., the magnetization is always built up in one rather than two steps. While 2 H SLR is exponential above 170 K, it becomes nonexponential at lower temperatures. To consider the latter effect, the data are fitted to Eq. (15) and the mean relaxation time T1  is determined. In Fig. 9, we see that T1  exhibits a clear minimum at T ≈ 235 K for W30, W45, and W50, indicating that molecular dynamics is comparable in this temperature range for the studied mixtures. A crossover from exponential to nonexponential relaxation upon cooling and a minimum of the relaxation time in the exponential regime are well known findings in 2 H SLR studies on the α process of glassforming liquids.39, 47 Therefore, our observations confirm that the high-temperature process of the water–alcohol mixtures can be identified with the α process and that it shows a correlation time of 1/ω0 ≈ 1 ns at T ≈ 235 K. The finding of a one-step build-up of magnetization even at T  Tg gives a first hint that there are no molecules, of any species, with a distinguishable dynamical behavior, implying that all molecules of the mixture participate in the β process. For a determination of temperature-dependent correlation times, we analyze the 2 H SLR in more detail. We restrict ourselves to the temperature range of exponential relaxation, i.e., T1  = T1 , to keep the analysis straightforward. In Fig. 9, it is evident that the minimum value of T1 deviates from the expectation for a Debye process for all studied samples. Hence, the correlation function F2 (t) is not a single exponential, as expected for the α process of supercooled liquids. To consider the nonexponentiality, we assume a CD spectral density, which is consistent with the above analysis of the BDS data and proved useful in previous SLR analyses on supercooled liquids.39, 47 Then, the width parameter βCD can be de-

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FIG. 9. Mean 2 H SLR times T1  of W30, W45, and W50. The dashed horizontal line marks the expectation for the minimum value in the case of a Debye process, as calculated for the experimental values δ = 2π × 161 kHz and ω0 = 2π × 46.1 MHz.

termined from the value of T1 at the minimum. We obtain βCD = 0.46 for W30, βCD = 0.47 for W45, and βCD = 0.49 for W50. Compared with this, the values of n observed in our BDS studies above 200 K, see Fig. 5 (right), correspond to width parameters βCD well above 0.8. Assuming for further analyses of the SLR data that, in first approximation, βCD does not depend on temperature in the vicinity of the minimum and inserting the resulting spectral densities JCD (ω) into Eq. (9), τCD can be extracted from T1 . The mean logarithmic correlation times, which are obtained from τCD and βCD according to Eq. (13), are included in Fig. 6. We see that the time scale of the α process does not depend on the composition of the studied mixtures. Contrasting the SLR and the BDS data, we find that both methods yield a comparable temperature dependence for the α process, supporting that a possible temperature dependence of the width parameter can be neglected for the SLR analysis in the studied range. Moreover, the comparison reveals that the time constants from NMR are about a factor of 3 shorter than those from BDS. In previous work on a water–dimethyl sulfoxide mixture,28 the same deviation was found based on a VFT extrapolation of BDS data. Considering that BDS and NMR probe the correlation functions F1 and F2 , respectively, a difference by a factor of 3 can be rationalized when assuming isotropic rotational diffusion and neglecting possible rate exchange.39 Further information about correlation times of molecular dynamics can be obtained from the temperature-dependent SOE intensity.48 This possibility is based on the fact that echo formation is hampered by rotational motion during the dephasing and rephasing periods of the echo sequence. Specifically, for various motional models, random-walk simulations showed that the SOE intensity is a minimum for τ ≈ 1/δ.49, 50 In Fig. 10, we observe that the minimum is located at ∼200 K for W30, W45, and W50. The correlation time τ ≈ 1 μs resulting from this analysis is in harmony with the BDS results for all studied samples, see Fig. 6. In addition, our finding that the SOE intensity vanishes nearly completely at the minimum is consistent with isotropic rotational motion, as assumed in our SLR analysis. 2 H NMR solid-echo spectra of W30 are presented in the insets of Fig. 10. Above ∼200 K, we observe a Lorentzian

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FIG. 10. Temperature dependence of the normalized 2 H NMR solid-echo intensity for W30, W45, and W50. The intensities were corrected for the trivial temperature dependence given by the Curie law. (Insets) 2 H NMR solid-echo spectra for W30. The spectrum for T = 206 K is fitted with a Lorentzian line, the typical liquid-state line shape. The spectrum for T = 183 K is interpolated with a Pake spectrum, the typical solid-state line shape, yielding an anisotropy parameter of δ = 2π × 161 kHz. In the latter case, line broadening due to nuclear dipolar interactions and excitation effects resulting from finite pulse lengths were considered.

line, confirming the existence of isotropic reorientation typical of the α process. Below ∼185 K, a Pake spectrum is found, indicating that the majority of molecules are static on the time scale of the experiment, τ ≈ 1 μs. Similar spectra result for the other concentrations. Finally, we exploit that 2 H NMR STE experiments enable measurement of rotational correlation functions. Figure 11(a) presents F2cc (tm ) of W50 for an evolution time of tp = 9 μs and various temperatures. We observe strongly nonexponential correlation functions that shift to longer times upon cooling. At none of the studied temperatures, the data yield evidence for the existence of a finite long-time plateau, cc , indicating that the observed motion has a large overall F∞ amplitude. Comparing STE data with and without correction for SLR damping reveals that relaxation effects become more prominent when the temperature is decreased. For quantitative analysis, the STE data are fitted to Eq. (16). In doing so, we exploit our knowledge about the SLR function R from independent measurements. From the resulting fit parameters, we calculate mean logarithmic correlation times according to Eq. (12). The results are included in Fig. 6. We see that the STE data deviate from the BDS data for the α process of the mixture. A comparison with findings for the β process reveals that the STE time constants are shorter than the BDS correlation times, but both exhibit a comparable temperature dependence, which, at T ≤ Tg , is consistent with an activation energy of Ea ≈ 0.54 eV, a value found for lowtemperature water dynamics in diverse environments.11 The observations are qualitatively similar when contrasting STE and BDS data for W45. Thus, the findings imply that the STE decays are dominated by the β process, although contributions from the α process cannot be completely neglected at the highest studied temperatures. Then, our finding of a complete loss of correlation means that, unlike the secondary relaxation of several neat systems,51–54 the β process of the studied mixtures does not result from a reorientation with substantial angular restriction near the glass transition. As discussed in Sec. II A 3, different values of BDS and NMR correlation

FIG. 11. Correlation functions F1 and F2 from BDS and NMR studies on W50. (a) 2 H NMR STE decays F2cc (tm ) for an evolution time of tp = 9 μs at the indicated temperatures. The open symbols are measured data, the solid symbols are divided by R (tm ) to correct for SLR damping. The solid lines are interpolations with Eq. (16). The dashed line is a correlation function obtained from the dielectric loss at 160 K. Specifically, the fit results were used to calculate the correlation function for the case that the β process causes a complete decay, i.e., for λ = 1.0 in the Williams-Watts ansatz, Eq. (3). The resulting data were further multiplied with R (tm ) to mimic SLR damping and their time axis was divided by a factor of 3 to consider possible differences between F1 and F2 . (b) The NMR data at 172 K are contrasted with correlation functions calculated from an interpolation of the dielectric loss at 170 K in different ways: (solid line) correlation function F1 (t) obtained directly from the dielectric loss, (dashed line) correlation function resulting from λ = 1.0 in the Williams-Watts ansatz, and (dotted line) correlation function resulting from λ = 0.8 in the Williams-Watts ansatz, corresponding to the fraction of deuterons belonging to water molecules, i.e., it is assumed that only water molecules contribute to the β process. All data calculated from BDS results were again multiplied with R (tm ) to mimic SLR damping. The NMR data are scaled (circles) to obtain F2cc (0) = 1 when extrapolating the fit with Eq. (16) and (crosses) to agree with the BDS data at tm = 10 μs.

times can result from the fact that F1 (t) and F2 (t) are probed, respectively. Moreover, it should be considered that the time constants of the correlation functions F2cc (tm , tp ) can depend on the length of the evolution time, as will be studied next. Further insights into the mechanisms for rotational motion can be obtained from comparison of STE decays for different evolution times and, hence, various angular resolutions. Figure 12 shows F2cc (tm , tp ) of W50, as obtained for several values of tp at 162 K. It is evident that the correlation functions decay faster for longer evolution times. To quantify this behavior, we interpolate the data with Eq. (16) and calculate mean correlation times using τ  = (τ K /β K ) (1/β K ). We switch to this type of average since it was studied in previous STE works and, hence, it enables straightforward comparison of results for different samples. In Fig. 13, we see that τ  becomes substantially smaller when the evolution time is extended, where the results are comparable for all temperatures in the studied range 153–167 K. Comparison with literature data reveals that the evolution-time dependence τ (tp ) of the β process of the present water mixture is different from

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FIG. 12. Evolution-time dependence of F2cc (tm ; tp ) for W50 at T = 162 K. The solid lines are interpolations with Eq. (16). The dashed line is the SLR function R (t) at this temperature.

that reported for water at protein surfaces,23, 25 which indicates jumps about large angles, e.g., the tetrahedral angle, while it resembles that observed for the α process of supercooled glycerol,42 which was successfully reproduced by assuming that 98% of the jumps involve an angle of 2◦ and 2% of the jumps an angle of 30◦ . Based on the evolutiontime dependence τ (tp ) for glycerol, we can estimate the difference between the time constants of F2cc (tm ; tp = 9 μs) and of F2ss (tm ; tp → 0) ∝ F2 (tm ). The analysis implies that time constants obtained from the measured STE decays are a factor of about 2 shorter than τ 2 associated with F2 . In addition to deviations between τ 2 and τ 1 in our case of small-step reorientation, this effect contributes to our observation that STE analysis yields shorter correlation times of the β process than BDS studies, see Fig. 6.

D. Comparison of BDS and NMR results

Finally, we quantitatively compare BDS and NMR results for W50 to study the molecular origins of the α and β processes. Specifically, we contrast F1 (t) calculated from BDS data with F2 (t) obtained from STE measurements. A priori, it is not clear to which extent the α and β processes observed in BDS contribute to the STE decay. Possible differences can result from the facts that diverse correlation functions are obtained, the reorientation of different vectors in

FIG. 13. Dependence of the mean correlation time τ  on the evolution time tp for W50 at the indicated temperatures. The results were obtained from fitting F2cc (tm ; tp ) to Eq. (16). The corresponding data for water at a protein surface23 and for pure glycerol42 are included for comparison. The present results were scaled to agree with the glycerol data at the shortest studied evolution time. To remove the dependence of the results on the value of the anisotropy parameter δ, the data are shown as a function of the reduced evolution time δtp .

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the molecular frames are probed, and the contributions of the molecular species are weighted differently. First, we assume that both processes contribute in the same way to the BDS and the STE data and calculate the correlation functions F1 (t) via Fourier transformation of the spectral density associated with the complete dielectric loss. In Fig. 11(b), we see for W50 at T = 172 K that F1 (t) (solid line) decays substantially slower than F2 (t). This mismatch is larger than that expected based on the differences between F1 and F2 correlation functions and the use of finite evolution times in the STE studies. Therefore, we next suppose that the faster β process dominates the STE decays. In detail, we compute the correlation function F1 (t) assuming that this contribution to the dielectric loss results in a complete decay of the STE signal, i.e., we use λ = 1 in Eq. (3). In Fig. 11(b), it is evident that F1 (t) (dashed line) resulting from this approach decays faster, as expected, but still slower than F2 (t), consistent with the above findings for the correlation times. Motivated by our observation that the BDS and NMR correlation times differ by about a factor of 3 in the hightemperature range, we also calculate a correlation function F1 (t), which is governed by the β process (λ = 1) and which is shifted by this factor to shorter times. We perform this analysis for T = 162 K < Tg so that the α process is too slow to be observed. The results are included in Fig. 11(a). We see that F1 (t) and F2 (t) decay on comparable time scales. This observation provides evidence that the STE results are dominated by the β process at sufficiently low temperatures, corroborating the above conclusion drawn on the basis of the temperature-dependent correlation times. However, the BDS and NMR correlation functions show substantial deviations with respect to the stretching of the decays, which is less pronounced for the former than for the latter. For the α process of neat glass formers, a different stretching of l = 1 and l = 2 correlation functions was attributed to a diverse relevance of the excess wing contribution.55 The origin of the different stretching observed for the β process of aqueous mixtures remains to be explained. One may speculate that a specific anisotropic molecular reorientation is involved so that O–D bonds and dipole vectors are affected differently. Such scenario could also rationalize the finding that the β process causes a stronger loss of correlation in NMR than in BDS. Finally, we address the question to which extent water and alcohol molecules contribute to the STE decay and, hence, to the β process. For this purpose, it is important to recall that O–D bonds of both water and alcohol molecules add to the 2 H NMR signals as a consequence of deuteron exchange. For W50, the ratio between water and alcohol molecules and, when assuming a statistical distribution, between water and alcohol O–D bonds amounts to 4:1. Thus, if the β process exclusively results from the water molecules, i.e., if the alcohol molecules do not participate, the correlation functions F2 (t) will not decay to zero but to 20% of the initial value before the α process sets in. To illustrate the effect, we calculate F1 (t) for the situation that the β process of the water molecules leads to a complete loss of correlation, while the alcohol molecules do not participate in this relaxation, leading to λ = 0.8 in Eq. (3). In Fig. 11(b), it can be seen (dotted line) for W50 at T = 172 K that there would be some bimodality of

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the decay if such scenario applied. Such bimodality is not observed for F2 (t), suggesting that propylene glycol takes part in the β process of the mixture, i.e., the latter phenomenon is not a plain water process, corroborating the above conclusions based on the one-step build-up of magnetization at T  Tg . Consistently, BDS work on water-xylitol systems reported that both molecular species contribute to the β process of the mixture.56 IV. SUMMARY

We investigated aqueous mixtures comprising propylene glycol in a composition range where glasses are formed upon cooling, specifically, for 30–50 wt. % of water. Employing BDS, TSD, and NMR, the slowdown of glassy dynamics was followed in a broad temperature range. We found that BDS, TSD, and NMR yield highly consistent, but partly complementary results, rendering combined application of all of the methods very useful. For all studied aqueous mixtures, we observed a comparable α process related to a glass transition at Tg ≈ 165 K. It exhibits the typical VFT and CD behaviors. In the weakly supercooled regime, the α correlation times resulting from the different methods differ by about a factor of three. This difference can be rationalized when assuming isotropic rotational diffusion and considering that BDS and NMR probe rank one and rank two rotational correlation functions, respectively. In the deeply supercooled regime, BDS reveals a separation of a β process from the α relaxation, while in TSD a bimodal correlation decay is not obvious due to the limited time window. However, in a direct comparison, BDS and TSD correlation functions turn out to be entirely consistent, providing evidence that preferential solvation of the dye molecules in a microheterogeneous mixture does not play a major role in the sample. While the dielectric loss exhibits two peaks for W45 and W50 close to Tg , NMR correlation functions, like TSD data, do not provide evidence for bimodal decays. Detailed comparison of BDS and NMR correlation functions indicated that the main contribution to the NMR STE decays comes from the β process rather than the α process. The finding that the β process causes a stronger loss of correlation in NMR than in BDS suggests that a specific anisotropic reorientation is involved. For water, an extreme example of such motion would be preferred rotation around the molecular symmetry axis, which results in ample reorientation of water bond vectors, but not in a variation of water dipole moments so that it produces strong effects in NMR, but none in BDS. At T < Tg , the α process is too slow to be observed and the β process is probed by both methods. Here, the NMR correlation times are shorter than the BDS time constants, but both methods yield a similar temperature dependence. For W45 and W50, the temperature dependence of the β process is described by an Arrhenius law with an activation energy of Ea ≈ 0.54 eV, but the absolute value of the correlation time is shorter for higher water concentration so that a separate β peak is not observed for W30. These findings are in harmony with results for low-temperature dynamics of water in mixtures with small molecules, polymers or proteins and of

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water in various types of nanoscopic confinements,4–15, 20–28 implying universal water dynamics at sufficiently low temperatures. For future work, it would be worth to ascertain to what extent the β process of aqueous systems is related to the β process of neat supercooled liquids, which usually involves more restricted molecular reorientation,51–54 and to the α  process observed for the more mobile component of non-aqueous dynamically asymmetric mixtures in the glassy matrix of the less mobile component.37 To ascertain the microscopic nature of the β process, we exploited that NMR STE experiments provide insights into not only the rate, but also the geometry of a motion. In a mixture with propylene glycol, we found that water dynamics related to the β process, at least near Tg , involves large-amplitude reorientation that comprises consecutive small-angle elementary jumps. These findings resemble recent results for water dynamics in a mixture with dimethyl sulfoxide,28 but they differ from previous observations for water motion near protein molecules or silica walls.23–27, 29 Specifically, near protein and silica surfaces, water reorientation is characterized by higher anisotropy and comprised of large-angle elementary steps. Thus, despite comparable temperature dependence and composition dependence of secondary water relaxations, the molecular mechanisms can differ in various environments. We propose that a common activation energy of low-temperature water dynamics is a consequence of the fact that breaking of hydrogen bonds is required for water reorientation, independent of the specific environment, while the mechanism for water reorientation depends on the relative mobility of the environment. While small-angle elementary jumps prevail in mixtures with small molecules, where both components have comparable mobility, large-angle elementary jumps dominate in mixtures with large molecules, where the second component shows much lower mobility than water and, hence, water dynamics occurs in an essentially rigid environment, resembling the situation in silica pores. Consistent with this argument, large-angle elementary jumps were also observed for mobile plasticizer molecules in rigid polymer matrices.39, 54, 57 In previous studies on aqueous mixtures, the β process was often regarded as water process. Therefore, we addressed the question to which extent water and alcohol molecules contribute to the β process in our case. If there are two fractions of molecules, which do and do not participate in the β process, two-step decays would be observed in relaxation functions and correlation functions obtained from SLR and STE experiments, respectively, since deuterons in both molecular species contribute to these 2 H NMR signals. However, we observed monomodal rather than bimodal time evolution in our measurements, providing evidence that both water and alcohol molecules contribute to the β process of the studied aqueous mixtures and justifying the use of the Williams-Watts approach, Eq. (3), in the analysis of the dielectric data. ACKNOWLEDGMENTS

The authors thank the Deutsche Forschungsgemeinschaft (DFG) for funding through Grant Nos. VO 905/8-1, BL 1192/1-1, and STU 191/6-1.

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Dixit, J. Crain, W. C. K. Poon, J. L. Finney, and A. K. Soper, Nature 416, 829 (2002). 2 A. Wakisaka and T. Ohki, Faraday Discuss. 129, 231 (2005). 3 Y. Hayashi, A. Pruzenko, and Y. Feldman, J. Non-Cryst. Solids 352, 4696 (2006). 4 S. S. N. Murthy, J. Phys. Chem. 104, 6955 (2000). 5 S. Sudo, M. Shimomura, N. Shinyashiki, and S. Yagihara, J. Non-Cryst. Solids 307–310, 356 (2002). 6 S. Sudo, S. Tsubotani, M. Shimomura, N. Shinyashiki, and S. Yagihara, J. Chem. Phys. 121, 7332 (2004). 7 N. Shinyashiki, S. Sudo, S. Yagihara, A. Spanoudaki, A. Kyritsis, and P. Pissis, J. Phys.: Condens. Matter 19, 205113 (2007). 8 S. Capaccioli, K. L. Ngai, and N. Shinyashiki, J. Phys. Chem. B 111, 8197 (2007). 9 S. Capaccioli, K. L. Ngai, S. Ancherbak, P. A. Rolla, and N. Shinyashiki, J. Non-Cryst. Solids 357, 641 (2011). 10 S. Cerveny, G. A. Schwartz, A. Alegria, R. Bergman, and J. Swenson, J. Chem. Phys. 124, 194501 (2006). 11 S. Cerveny, A. Alegria, and J. Colmenero, Phys. Rev. E 77, 031803 (2008). 12 J. Sjöström, J. Mattson, R. Bergman, E. Johansson, K. Josefsson, D. Svantesson, and J. Swenson, Phys. Chem. Chem. Phys. 12, 10452 (2010). 13 S. Cerveny, G. A. Schwartz, R. Bergman, and J. Swenson, Phys. Rev. Lett. 93, 245702 (2004). 14 S. Khodadadi, S. Pawlus, and A. P. Sokolov, J. Phys. Chem. B 112, 14273 (2008). 15 C. Gainaru, A. Fillmer, and R. Böhmer, J. Phys. Chem. B 113, 12628 (2009). 16 R. Richert, J. Chem. Phys. 113, 8404 (2000). 17 R. Richert and L. M. Wang, J. Phys.: Condens. Matter 15, S1041 (2003). 18 F. He and R. Richert, Phys. Rev. B 74, 014201 (2006). 19 M. Preuss, C. Gainaru, T. Hecksher, S. Bauer, J. C. Dyre, R. Richert, and R. Böhmer, J. Chem. Phys. 137, 144502 (2012). 20 Y. Ishihara, S. Okouchi, and H. Uedaira, J. Chem. Soc., Faraday Trans. 93, 3337 (1997). 21 K. Yoshida, A. Kitajo, and T. Yamaguchi, J. Mol. Liq. 125, 158 (2006). 22 T. Takamuku, Y. Tsutsumi, M. Matsugami, and T. Yamaguchi, J. Phys. Chem. B 112, 13300 (2008). 23 M. Vogel, Phys. Rev. Lett. 101, 225701 (2008). 24 S. A. Lusceac, M. R. Vogel, and C. R. Herbers, Biochim. Biophys. Acta, Proteins Proteomics 1804, 41 (2010). 25 S. A. Lusceac and M. Vogel, J. Phys. Chem. B 114, 10209 (2010). 26 M. Vogel, Eur. Phys. J.: Special Topics 189, 47 (2010). 27 S. A. Lusceac, M. Rosenstihl, M. Vogel, C. Gainaru, A. Fillmer, and R. Böhmer, J. Non-Cryst. Solids 357, 655 (2011). 28 S. A. Lusceac, C. Gainaru, D. A. Ratzke, M. F. Graf, and M. Vogel, J. Phys. Chem. B 115, 11588 (2011).

J. Chem. Phys. 140, 114503 (2014) 29 M.

Sattig and M. Vogel, J. Phys. Chem. Lett. 5, 174 (2014). Williams and D. C. Watts, Trans. Faraday Soc. 67, 1971 (1971). 31 A. Kudlik, C. Tschirwitz, T. Blochowicz, S. Benkhof, and E. Rössler, J. Non-Cryst. Solids 235–237, 406 (1998). 32 D. Gomez, A. Alegria, A. Arbe, and J. Colmenero, Macromolecules 34, 503 (2001). 33 T. Blochowicz, C. Tschirwitz, S. Benkhof, and E. A. Rössler, J. Chem. Phys. 118, 7544 (2003). 34 T. Blochowicz, A. Brodin, and E. A. Rössler, Adv. Chem. Phys. 133, 127 (2006). 35 C. Reichardt, Solvents and Solvent Effects in Organic Chemistry (WileyVCH, Weinheim, 2002), p. 534. 36 R. Richert, F. Stickel, R. S. Fee, and M. Maroncelli, Chem. Phys. Lett. 229, 302 (1994). 37 T. Blochowicz, S. Schramm, S. Lusceac, M. Vogel, B. Stühn, P. Gutfreund, and B. Frick, Phys. Rev. Lett. 109, 035702 (2012). 38 K. Schmidt-Rohr and H. W. Spiess, Multidimensional Solid-State NMR and Polymers (Academic Press, London, 1994). 39 R. Böhmer, G. Diezemann, G. Hinze, and E. Rössler, Prog. Nucl. Magn. Reson. Spectrosc. 39, 191 (2001). 40 P. A. Beckmann, Phys. Rep. 171, 85 (1988). 41 G. Fleischer and F. Fujara, NMR - Basic Principles and Progress (Springer, Berlin, 1994), Vol. 30, p. 159. 42 R. Böhmer and G. Hinze, J. Chem. Phys. 109, 241 (1998). 43 M. Vogel, C. Brinkmann, H. Eckert, and A. Heuer, Phys. Chem. Chem. Phys. 4, 3237 (2002). 44 R. Zorn, J. Chem. Phys. 116, 3204 (2002). 45 C. R. Herbers, D. Sauer, and M. Vogel, J. Chem. Phys. 136, 124511 (2012). 46 D. Schaefer, J. Leisen, and H. W. Spiess, J. Magn. Reson. 115, 60 (1995). 47 W. Schnauss, F. Fujara, and H. Sillescu, J. Chem. Phys. 97, 1378 (1992). 48 C. Schmidt, K. J. Kuhn, and H. W. Spiess, Prog. Colloid Polym. Sci. 71, 71 (1985). 49 M. Vogel and E. Rössler, J. Magn. Reson. 147, 43 (2000). 50 M. Vogel, C. Herbers, and B. Koch, J. Phys. Chem. B 112, 11217 (2008). 51 M. Vogel and E. Rössler, J. Chem. Phys. 114, 5802 (2001). 52 M. Vogel and E. Rössler, J. Chem. Phys. 115, 10883 (2001). 53 A. Döß, M. Paluch, H. Sillescu, and G. Hinze, Phys. Rev. Lett. 88, 095701 (2002). 54 M. Vogel, P. Medick, and E. Rössler, Ann. Rep. Nucl. Magn. Reson. Spectrosc. 56, 231 (2005). 55 N. Petzold, B. Schmidtke, R. Kahlau, D. Bock, R. Meier, B. Micko, D. Kruk, and E. A. Rössler, J. Chem. Phys. 138, 12A510 (2013). 56 K. Elamin, J. Sjöström, H. Jansson, and J. Swenson, J. Chem. Phys. 136, 104508 (2012). 57 P. Medick, M. Vogel, and E. Rössler, J. Magn. Reson. 159, 126 (2002). 30 G.

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