Dynamical and structural properties of monohydroxy alcohols exhibiting a DebyeprocessP. Wieth and M. Vogel Citation: The Journal of Chemical Physics 140, 144507 (2014); doi: 10.1063/1.4870654 View online: http://dx.doi.org/10.1063/1.4870654 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/14?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Born-Oppenheimer molecular dynamics and electronic properties of chlorophyll-c2 in liquid methanol J. Chem. Phys. 138, 225102 (2013); 10.1063/1.4808177 Communication: Thermodynamic scaling of the Debye process in primary alcohols J. Chem. Phys. 134, 041103 (2011); 10.1063/1.3540636 Hydrogen-bonding alcohol-water interactions in binary ethanol, 1-propanol, and 2 -propanol + methane structureII clathrate hydrates J. Chem. Phys. 133, 074505 (2010); 10.1063/1.3469776 Structure and dynamics of the hydration shells of the Zn 2 + ion from ab initio molecular dynamics and combinedab initio and classical molecular dynamics simulations J. Chem. Phys. 132, 194502 (2010); 10.1063/1.3421542 Structural and spectroscopic properties of an aliphatic boronic acid studied by combination of experimental andtheoretical methods J. Chem. Phys. 128, 124512 (2008); 10.1063/1.2885053

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.22.67.7

On: Wed, 03 Dec 2014 00:00:41

THE JOURNAL OF CHEMICAL PHYSICS 140, 144507 (2014)

Dynamical and structural properties of monohydroxy alcohols exhibiting aDebye process

P. Wieth and M. Vogela)

Institut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany

(Received 14 February 2014; accepted 26 March 2014; published online 14 April 2014)

We perform molecular dynamics simulations to study dynamical and structural properties of variousprimary monohydroxy alcohols. Comparing rotational correlation functions for the individual dipolemoment of the molecules and the total dipole moment of the system, it is shown that the studiedmodels exhibit a Debye process, which is slower than the α process, in harmony with experimentalresults. Performing cluster analysis, it is found that hydroxyl groups tend to form hydrogen-bondedaggregates, in particular, chain structures, which are transient in nature. To ascertain a possible re-lation between the Debye process and aggregate fluctuations, we devise an algorithm allowing usto follow the time evolution of transient chains. It is observed that the life times of transient chainsare substantially shorter than the correlation times of the Debye process, indicating that the latterrelaxation is not a direct consequence of the chain reorganization in the studied models. We assurethat this conclusion is not affected when hydrogen-bond cooperativity is mimicked in the simulationsor when the polarity of the molecules and the size of the systems are varied. On the other hand, wefind that orientational correlations of molecular dipole moments are not limited to hydrogen-bondedchains, but they also exist in more globular regions around these objects, implying that the neigh-boring molecules are polarized in the dipole field exerted by the hydrogen-bonded chains. Furtherevidence for a relevance of dipole fields comes from the observation that some correlation betweenthe initial orientation of the total dipole moment and the instantaneous orientations of the moleculardipole moments is retained up to the time scale of the Debye process. The simulation results arediscussed in terms of a La-Ola wave model with diffusive propagation. © 2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4870654]

I. INTRODUCTION

The Debye process is a very intriguing relaxation of anumber of liquids, which is time honored, but still awaitsfull explanation. About a century ago, this phenomenon wasfirst reported by Debye in studies on the dielectric responseof alcohols.1 Today, it is established that the dielectric lossspectrum of primary monohydroxy alcohols exhibits a De-bye peak with a high amplitude and a low frequency, whichis augmented by lower relaxation peaks at higher frequen-cies, including, especially, the α process, which is related tothe viscosity of the liquid.1–4 The Debye process is partic-ularly prominent for primary monohydroxy alcohols, but itwas also observed for other associating liquids, like water andamides.5, 6 In all cases, a Debye shape of the relaxation peakindicates exponential relaxation. The Debye process is moststriking in dielectric spectroscopy, but it was also probed byother techniques, e.g., nuclear magnetic resonance.7 Whilecalorimetric or mechanical signatures of the phenomenonwere not observed in early works,8–10 evidence for a Debyeprocess was reported in recent rheological experiments.11

Over the years, a number of models were put forwardto explain the microscopic origin of the Debye process.In consideration of the type of liquids showing this relax-ation phenomenon, it was often attributed to an existence of

a)Electronic mail: michael.vogel@physik.tu-darmstadt.de

hydrogen bonds and inhomogeneous structures. In particular,it was rationalized in terms of hydrogen bonded (HB) aggre-gates. The switch-and-wait-model assumes that groups of HBmolecules have to wait for favorable conditions for switchingto another arrangement.5 Then, the different frequencies andamplitudes of the relaxation processes come from a differentdegree of association of the molecules in the liquid. However,it seems that this conjecture is at variance with the experi-mental finding that the rate for HB network reorganizationis much higher than the frequency of the Debye process.12

Other workers proposed that the Debye process results frommolecular rotations around the axes of chain-like clusters ofHB hydroxyl groups8 or that it is caused by transitions amongstates that are energetically equivalent unless an external elec-tric field is applied.9, 10 Recently, it was advocated that thetransient chain model rationalizes all puzzling phenomena as-sociated with the Debye process.7 This model proposes thatchain-like aggregates of hydroxyl groups show a snake-likemotion resulting from a successive loss of members at its oneend and a gain of members at its other end. It is obvious thatthe relaxation of these structures results in larger changes ofthe macroscopic dipole moment than the relaxation of sin-gle molecules, explaining high intensities of the Debye peakin dielectric spectra. Moreover, low frequencies of this re-laxation result from the fact that a reorientation of transientchains involves many successive attachment and detachmentprocesses.

0021-9606/2014/140(14)/144507/8/$30.00 © 2014 AIP Publishing LLC140, 144507-1

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.22.67.7

On: Wed, 03 Dec 2014 00:00:41

144507-2 P. Wieth and M. Vogel J. Chem. Phys. 140, 144507 (2014)

Molecular dynamics (MD) simulations are an attrac-tive method for in-depth analysis of structural and dynam-ical properties of alcohols, including their Debye process.Previous computational studies revealed that the polar hy-droxyl groups of alcohol molecules form chain-like or ring-like structures, which are separated from the nonpolar alkylrests.13–15 This observation shows that HB aggregates exist,as assumed in several modelling approaches to the Debye pro-cess. To prove that these supramolecular structures are at theorigin of this relaxation, analysis of static snapshots of theHB network is, however, not adequate, but it is necessary tofollow the time evolution of HB clusters and to demonstratethat these entities are long lived and account for the low fre-quencies of the Debye process. In the case of ibuprofen, MDwork rationalized the Debye process in terms of internal cis-trans conversions,16 consistent with results from experimen-tal work.17 However, owing to the specific explanation anda weak amplitude of the Debye relaxation, it is questionablewhether the results for ibuprofen can be generalized to otherliquids.

Here, we perform MD simulations for various primarymonohydroxy alcohols, from methanol to octanol, with a par-ticular focus on 1-butanol. Analyzing appropriate rotationalcorrelation functions, we demonstrate that the studied modelsexhibit a Debye process. To ascertain the origin of this relax-ation, we investigate the properties of transient chains. We de-termine not only their static properties, e.g., the average chainlength, but also their time evolution to extract their life times.Furthermore, it is studied to which extent our conclusions de-pend on the used simulation and analysis methodologies. Inparticular, we investigate the roles of the molecular polarity,the system size, and hydrogen-bond cooperativity.

II. SIMULATION DETAILS

We use the GROMACS simulation software package18 toperform MD simulations for alcohol models described by theOptimized Potentials for Liquid Simulations - United Atom(OPLS-UA) force field.19–21 The complete series of primarymonohydroxy alcohols up to 1-octanol was studied. Sincethe analysis does not yield evidence for fundamental dif-ferences between the alcohol species, we mostly focus on1-butanol in the present work. For comparison, some resultsfor methanol and 1-hexanol are presented. For 1-butanol at240 K, GROMACS analysis tools find a density of 0.78 kg/l,a molecular dipole moment of 2.34 D, and a permittivityof 11.4 ε0.

The used simulation boxes are cubic and contain up toN = 20 000 alcohol molecules. Periodic boundary conditionsare applied. The Particle-Mesh Ewald sum is used to accountfor Coulombic interactions.22 The temperature T and pres-sure p are adjusted using the Nosé-Hoover thermostat23, 24

and the Parrinello-Rahman barostat,25 respectively. The non-bonded interactions are calculated within a cutoff range of1.2 nm. Trajectories with lengths up to 500 ns are computedwith a time step of 2 fs. Prior to data acquisition, all sys-tems are equilibrated in the NpT ensemble, with the pressureset to p = 1 bar. The production runs are carried out in the

NVT ensemble and the system configurations are written outevery 1 ps.

An algorithm is designed to determine transient chainsas follows: A hydrogen bond is identified whenever two oxy-gen atoms and a hydrogen atom enclose an angle in the rangeθ = 180◦ ± 20◦ and the intermolecular distance between oxy-gen and hydrogen amounts to d ≤ 2.3 Å. The molecules arethen marked as being connected. Afterwards, a cluster analy-sis is performed to identify all interconnected HB moleculesas a transient chain. This analysis is done for each step and thedevelopment of a chain is followed from step to step by high-est match. Specifically, when a chain forks, we consider as itssuccessor that part of the chain that comprises most moleculesof the predecessor. With this method, it is possible to trackthe physical properties of a transient chain, e.g., the timeevolution of the dipole moment.

While most of our studies employ the above criteria toidentify hydrogen bonds, some investigations are performedusing the less strict criteria θ = 180◦ ± 30◦ and d ≤ 2.4 Å.Comparing the results for the former “strong” criteria andthe latter “weak” criteria, we determine whether the choiceof these parameters is critical for our analysis. Furthermore,we study the dependence of our findings on the molecularpolarity and the system size for the example of 1-butanol.To address the former and latter aspects, the modulus ofall charges is increased by up to 10% and the edge lengthof the simulation boxes is varied in the range 2–15 nm,respectively.

Theoretical26–28 and experimental29, 30 results indicated astabilization of hydrogen bonds when the involved moleculesform several of these bonds due to a higher delocalizationof electrons in larger HB entities. MD simulations cannotfully account for this effect since a delocalization of elec-trons is not possible. As a consequence of this drawback,one may expect that hydrogen bonds in long chains are notas stable as in nature and, furthermore, that chains breakup more often in the middle than at the end, as comparedto the real system. Therefore, it is desirable to extend MDsimulations by a mechanism mimicking the hydrogen-bondcooperativity. To determine the relevance of this effect, weuse time-dependent charges of atoms in hydroxyl groups insome simulations. In detail, after each update interval tup, theatoms in hydroxyl groups anew receive a charge bonus or acharge malus depending on the molecular position in a tran-sient chain. While single molecules receive the highest malus,molecules bonded to three or more molecules in both direc-tions receive the highest bonus. These boni and mali are ad-justed to keep the average dipole moment of the moleculesclose to that in the simulations for the regular OPLS-UA forcefield. For 1-butanol, this approach results in a 10% malusfor unbonded hydroxyl groups, no change for single bondedgroups, a 3% bonus for groups of molecules with 2 hydro-gen bonds, 5% bonus when two bonded neighbors alreadyhave a 3% bonus, and a 6% bonus when two bonded neigh-bours have a 5% or 6% bonus. To study the relevance of theupdate interval, we compare results for values in the rangetup = 1–200 ps.

To characterize the time scale of relaxation processesin the studied systems, we determine correlation times τ

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.22.67.7

On: Wed, 03 Dec 2014 00:00:41

144507-3 P. Wieth and M. Vogel J. Chem. Phys. 140, 144507 (2014)

from appropriate correlation functions C(t) according toC(t = τ )/C(t = 0) = 1/e, if not stated otherwise.

III. RESULTS

A. Identification of Debye process and α process

To identify the Debye process and the α process of thestudied primary monohydroxy alcohols, we calculate orienta-tional correlation functions for the molecular dipole moment,the total dipole moment, and various bond vectors. The reori-entation of the individual dipole moments of the molecules,mi(t), can be studied using the correlation function:

d(t) =⟨

mi(0)

‖mi(0)‖ · mi(t)

‖mi(t)‖⟩. (1)

Throughout the paper, the pointed brackets indicate a timeaverage over various time origins and, if not stated otherwise,an ensemble average over all alcohol molecules. To probe thereorientation of O–H, C–O, and C–C bond vectors of the al-cohol molecules, we define rotational correlation functions inanalogy with Eq. (1). The relaxation of the total dipole mo-ment of the system, M(t) = ∑N

i=1 mi(t), can be characterizedcalculating the correlation function

D(t) =⟨

M(0)

‖M(0)‖ · M(t)

‖M(t)‖⟩. (2)

Here, the averaging is restricted to different time origins.In Fig. 1, various rotational correlation functions are

compared for 1-butanol at 240 K. We see that diverse molec-ular subunits differ with respect to their dynamical behavior.Specifically, C–C bonds exhibit faster rotational motion thanC–O and O–H bonds. In addition, the decay is more stretchedfor the alkyl rest than for the polar groups. These findingsare consistent with results from nuclear magnetic resonancespectroscopy.7 The reorientation of the molecular dipole mo-ment, as characterized by the correlation function d(t), resem-bles that of the polar groups, as expected. For a quantitativeanalysis, correlation times τα are extracted from the decaysd(t) for various systems and temperatures. In Fig. 2, we com-pile results for methanol, 1-butanol, and 1-hexanol. It can beseen that τα rises when increasing the molecular weight or de-

100

101

102

103

104

t in ps

0.0

0.2

0.4

0.6

0.8

1.0

corr

elat

ion

func

tion

DdOHCOCC

FIG. 1. Results for the molecular dynamics of 1-butanol at 240 K. Correla-tion functions describing the rotational motion of O–H, C–O, and C–C bondvectors are compared with D(t) and d(t) characterizing the time evolution ofthe total and molecular dipole moments, respectively. Only the C–C bondsnext to the hydroxyl group are considered for the analysis.

2.8 3.2 3.6 4.01000 K /T

101

102

103

104

τ in

ps

methanol1-butanol1-hexanol

FIG. 2. Temperature-dependent correlation times for the alcohols methanol(squares), 1-butanol (circles), and 1-hexanol (triangles). The solid and dashedlines connect the time constants of the α process, τα from d(t), and that ofthe Debye process, τD from D(t), respectively. The dotted lines mark τF,as extracted from the correlation function F(t), see Eq. (4). The simulationresults are compared with experimental data for the (∗) α process and (×)Debye process of 1-butanol.7, 31

creasing the temperature, reflecting the slowdown of molecu-lar reorientation. In the studied high-temperature regime, thetemperature dependence can be described by an Arrheniuslaw. For 1-butanol, our results are compared with experimen-tal data. The values of τα are somewhat shorter, but still com-parable with the correlation times for the α process obtainedfrom dielectric spectroscopy, implying that d(t) probes thestructural relaxation of the studied model systems, while itdoes not yield evidence for a Debye process. Hence, τα is ameasure for the time scale of the α process, rationalizing theuse of the subscript α.

When intending to investigate the Debye process in MDsimulations, it is important to consider that the dielectric lossspectrum is, by Fourier transformation, related to the timecorrelation function of the total dipole moment rather thanof the molecular dipole moment. Therefore, we expect thatthe strong Debye process observed in dielectric spectra ofmonohydroxy alcohols at low frequencies shows up as a dom-inant exponential decay at long times in D(t), while the weakα process at higher frequencies should translate into a smallstretched decay of D(t) at short times. In Fig. 1, we see thatthe expected behavior is indeed observed for the correlationfunction of the total dipole moment of the 1-butanol system at240 K. Specifically, the relaxation of the macroscopic dipolemoment is governed by a slow and exponential decay, match-ing the properties of the Debye process. At shorter times,when molecular reorientation occurs, there is only a mild de-cay of D(t). In Fig. 2, it is evident that, for all studied alcohols,the correlation time τD obtained from D(t) is almost an orderof magnitude longer than τα from d(t), but both time constantsshow a comparable, though not identical temperature depen-dence. Moreover, for 1-butanol, we see that τD well agreeswith experimental values for the Debye process. All these ob-servations indicate that the studied alcohol models exhibit atleast a Debye-like process.

B. Dynamical properties of transient chains

Next, we study whether the Debye process is causedby a reorganization of transient chains, as was proposed in

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.22.67.7

On: Wed, 03 Dec 2014 00:00:41

144507-4 P. Wieth and M. Vogel J. Chem. Phys. 140, 144507 (2014)

2 4 6 8 10 12 14chain length

10-4

10-3

10-2

10-1

100

prob

abli

ty

modi, weakorigi, weakmodi, strongorigi, strong

FIG. 3. Probability of finding a molecule in a HB chain of a given length.We compare data resulting for weak and strong criteria to identify hydrogenbonds. Moreover, we contrast findings obtained for the original force fieldand for a modified force field mimicking hydrogen-bond cooperativity. SeeSec. II for details.

the literature.7 For this purpose, we ascertain static and dy-namic properties of chains of HB alcohol molecules. Theprobability of finding a molecule in a chain of given lengthis displayed for 1-butanol at 240 K in Fig. 3. We observethat about 70% of the molecules are not organized in HBclusters and that most of the remaining molecules group to-gether in short chains with a roughly exponential chain-lengthdistribution. For all studied systems, the mean chain lengthamounts to 2–3. Thus, the transient chains are relatively shortat higher temperatures accessible to MD simulations, whilechain lengths of 5–10 molecules were estimated based onexperimental results at lower temperatures.7

To determine the effects of the analysis and simulationmethodologies, we vary the involved parameters, as outlinedin Sec. II. In Fig. 3, we see that, on average, the chains arelonger when the criteria to identify hydrogen bonds are re-laxed, i.e., when the weak rather than the strong criteria areused. Likewise, the mean chain length is higher when the sim-ulations mimic hydrogen-bond cooperativity, i.e., when we donot use the time-independent atomic charges of the regularforce field, but vary the charges according to the instantaneousmolecular position in a transient chain. However, these weakchanges do not affect the qualitative behavior, specifically, theexistence of essentially exponential chain-length distributionswith high fractions of short chains. Hence, the choice of theparameters is not critical for our conclusions.

Having developed an algorithm that enables tracking oftransient chains, it is possible to characterize not only theirstatic properties, but also their dynamic ones. It appearspromising to follow the dipole moment of transient chainsand to ascertain whether its relaxation compares to the De-bye relaxation or to the α relaxation. To characterize the timeevolution of the chain dipole moments, we use the correlationfunction

dc(t) =⟨ ∑L(0)

i mi(0)

‖∑L(0)i mi(0)‖

·∑L(t)

i mi(t)

‖∑L(t)i mi(t)‖

⟩. (3)

Here, L(t) denotes the instantaneous chain length and thepointed brackets include an average over all transient chains.Figure 4 shows dc(t) for the typical example of 1-butanol at

0 200 400 600 800t in ps

10-5

10-4

10-3

10-2

10-1

100

d c(t)

1-butanolsingle expstretched exp

FIG. 4. Correlation function of the dipole moment of transient chains, dc(t),see Eq. (3). Results for 1-butanol at 240 K are fitted with a stretched expo-nential decay and a single exponential decay.

240 K. We do not observe a stretched exponential decay, butrather bimodal behavior. Considering also results for othertemperatures, the following picture emerges: The fast decay,on the one hand, occurs on a time scale of a few picosec-onds and is essentially independent of temperature, imply-ing that it is related to fast vibrational motion, which is oflittle interest for the present studies. The slow decay, on theother hand strongly depends on temperature, suggesting a re-lation to some kind of structural reorganization. This scenariois shared by other alcohol species. Therefore, we disregard thefast loss of correlation and fit the slow loss to an exponentialdecay. The resulting time constant of the slow decay, whichwe refer to as τ c, is used to characterize the life time of chaindipole moments in the following.

The temperature dependence of the time constant τ c isshown for 1-butanol in Fig. 5. We see that the life time ofthe chain dipole moment is substantially shorter than the cor-relation time of the Debye process, where the discrepancy ishigher at lower temperatures. Analogous results are found forthe other studied monohydroxy alcohols. To some extent, thelife time depends on the criteria used to identify hydrogenbonds. Specifically, higher values of τ c are observed for the

3.0 3.2 3.4 3.6 3.8 4.0 4.21000 K /T

101

102

103

104

τ in

ps

τD

τατ

c weak

τc strong

FIG. 5. Temperature-dependent correlation times of 1-butanol: Results forthe Debye process and the α process are related to the life times of the dipolemoments of transient chains, τ c. The latter time constants were obtained fromexponential fits of the long-time decay of the correlation functions dc(t), seetext for details. We compare life times that result when the strong and weakcriteria are used for the identification of hydrogen bonds and, thus, the tran-sient chains, see Sec. II.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.22.67.7

On: Wed, 03 Dec 2014 00:00:41

144507-5 P. Wieth and M. Vogel J. Chem. Phys. 140, 144507 (2014)

weak criteria than for the strong criteria. By further relax-ing the criteria, the life times of the chain dipole momentscan be pushed towards the correlation time of the α process,but the whole system ultimately forms a single chain all thetime. When assuming that the HB chains break up at ran-dom positions, one may rationalize that the life time of thechain dipole moment is somewhat shorter than the correla-tion time of the α process and, hence, of the O–H bonds.Then, the reorientation of one of several O–H bonds, possi-bly a fast one from a distribution, can be sufficient to destroythe chain dipole moment and, hence, this process is fasterthan the reorientation of an average O–H bond, in particular,for long chains and broad distributions of reorientation rates,or, equivalently, correlation times. Thus, these findings showthat the dipole moment of the transient chains is short-livedand, hence, its relaxation does not provide a straightforwardexplanation for the Debye process, at least for the studiedmodels.

C. Effects of bond cooperativityand molecular polarity

As transient chains are short-lived when the originalforce field with constant atomic charges is used, we nextmimic hydrogen-bond cooperativity by using variable atomiccharges, which are repeatedly adjusted during the simulationaccording to the molecular position within a transient chain,see Sec. II. As a consequence of a higher polarity of moleculeswithin these entities, transient chains could, then, exhibit ahigher stability and, hence, persist up to the time scale of theDebye process. In Fig. 6, the life times of the chain dipolemoments resulting for the original and modified force fieldsof 1-butanol are compared. We observe an increase of τ c by afactor of 2–3 when hydrogen-bond cooperativity is switchedon. Despite this increase, the time constants are, however, stillmuch shorter than τD. Furthermore, we find that the life timeof the chain dipole moment hardly depends on the length ofthe update interval for the readjustment of the atomic charges.This result cannot be understood when hydrogen-bond coop-erativity plays a decisive role. In detail, the reorganization ofthe transient chains can be tracked when tup is shorter than

100

101

102

103

tup

in ps

101

102

103

τ c in p

s

240 K300 K

FIG. 6. Relaxation time of the chain dipole moment, τ c, as a function ofthe update interval for the readjustment of the atomic charges in simulationsmimicking hydrogen-bond cooperativity. Results for 1-butanol at 240 K and300 K are shown. The dotted lines mark the relaxation times obtained for theoriginal force field, which does not consider hydrogen-bond cooperativity.

the time scale of structural relaxation, while the moleculeschange their arrangement faster than charge boni and maliare redistributed when tup is longer. Hence, a stronger at-tractive interaction of higher dipole moments within transientchains can enhance the durability of these objects in the for-mer case, while molecular dynamics averages out the corre-lation between atomic charge and molecular environment inthe latter case. Altogether, τ c should decrease with tup whenhydrogen-bond cooperativity is a critical factor for the lifetime of chain dipole moments in the studied model systems.Since such dependence is not observed, one may expect thatother effects are more relevant for the durability of transientchains.

Striving for an explanation for our observations, it isimportant to consider that, even though we chose the boniand mali on the atomic charges such that the mean molecu-lar dipole moment is affected as little as possible, we foundthat, on average, a 2% increase of the modulus of the chargesresulted after equilibration. Therefore, it may be rewardingto investigate the influence of the polarity of the alcoholmolecules on the life time of transient chains. To tackle thisproblem, we increase all atomic charges by the same factor,while we deactivate hydrogen-bond cooperativity. Figure 7shows the dependence of the dynamic properties of 1-butanolon the atomic charges. We see that all time constants increasewhen the absolute value of the atomic charges rises. Thiseffect explains our observation that switching on hydrogen-bond cooperativity leads to an increase of τ c to a large extentsince this approach also results in an increase of the molecularpolarity, as aforementioned. The dependence on the polarity isstrongest for the Debye process, suggesting that this process isparticularly sensitive to the magnitude of the molecular dipolemoment.

D. Debye process in molecular correlations

In order to identify the origin of the Debye process, itis desirable to find a molecular correlation decaying on thetime scale of τD. Since there is no straightforward relationbetween the transient chains and the Debye process for our

0 2 4 6 8 10increase of charge in %

102

103

104

τ in

ps

τD

τατ

c

FIG. 7. Dependence of correlation times on the polarity of the molecules,more precisely, on the increase of the modulus of the atomic charges withrespect to the values in the original force field. Data for 1-butanol at 300 Kare presented.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.22.67.7

On: Wed, 03 Dec 2014 00:00:41

144507-6 P. Wieth and M. Vogel J. Chem. Phys. 140, 144507 (2014)

100

101

102

103

104

t in ps

0.00

0.01

0.02

0.03

F(t

)

270K300K330K240K

FIG. 8. Correlation functions F(t), see Eq. (4), of 1-butanol at various tem-peratures. The dashed black lines are interpolations with exponential decays.

model systems, we consider another correlation function:

F (t) =⟨

M(0)

‖M(0)‖ · mi(t)

‖mi(0)‖⟩. (4)

Thus, the total dipole moment of the system at the time ori-gin, M(0), serves as a reference orientation from which theindividual dipole moments of the molecules, mi(t), decor-relate in the course of time. In other words, F(t) measuresthe time scale on which the memory of an initially preferredmolecular orientation is lost. Figure 8 shows the correlationfunction F(t) for 1-butanol at various temperatures. We seethat the correlation is overall small, but relatively durable.Specifically, F(t) decays in an exponential manner and on thetime scale τD, implying that the observed molecular dynam-ics is related to the Debye process. The relation between themolecular dynamics probed by F(t) and the Debye process isfurther corroborated when inspecting the correlation times τF

extracted from F(t) in Fig. 2. Evidently, τF and τD well agreefor all studied alcohols and temperatures.

E. Spatial arrangement of hydrogen-bondedmolecules

Next, we ascertain the local arrangement of alcoholmolecules without supposing an existence of chain-like struc-tures in the first place. Specifically, we study the relativeorientation of a given molecular dipole moment mi and aneighboring molecular dipole moment mj as a function ofthe intermolecular distance:

P (rij ) =⟨

mi

‖mi‖ · mj

‖mj‖⟩. (5)

Here, rij denotes the distance vector between the hydroxylgroups of molecules i and j. Furthermore, the pointed brack-ets symbolize that we average over all pairs of molecules inmany configurations along the trajectory. To remove perturb-ing influences from the existence of preferred intermoleculardistances, P (rij ) is normalized by the regular pair distribu-tion function. The resulting distribution is plotted in a two-dimensional plane, see Fig. 9. In the chosen representation,the hydroxyl group of molecule i is aligned along the x axiswith the oxygen atom at the origin and the hydrogen atom atx = 0.1 nm. The y values specify the shortest distance of thehydroxyl group of molecule j to the axis defined by the ori-

FIG. 9. Characteristic environment of 1-butanol molecules at 240 K, as mea-sured by P (rij ), see Eq. (5). The hydroxyl group of a given molecule isaligned along the x axis with the oxygen atom at the origin and the hydro-gen atom at x = 0.1 nm. High and low intensity mean that the dipole momentof the given molecule and that of another molecule, separated by a distancevector rij , have preferred parallel and antiparallel orientations, respectively.See text for details.

entation of the hydroxyl group of molecule i, reflecting therotational symmetry about this axis.

This representation of P (rij ) is displayed for 1-butanolat 240 K in Fig. 9. For rij corresponding to next neighbors,two peaks indicate preferred parallel orientation for relativearrangements that allow for hydrogen bonds between the hy-droxyl groups of molecules i and j. The peak on the posi-tive x axis can be ascribed to a hydrogen bond between thehydrogen of molecule i and the oxygen of neighbor j, whilethe other peak can be attributed to a hydrogen bond betweenthe oxygen of molecule i and the hydrogen of neighbor j.In the latter case, a bend geometry results from the molec-ular structure in combination with sterical hindrance. Whenthe intermolecular distance increases, orientational correla-tions of the dipole moments diminish, but they are retainedup to ∼1 nm in all directions. Near the x and y axes, pos-itive and negative values of P (rij ) indicate preferred paral-lel and antiparallel orientations, respectively. Taken together,these findings mean that there are clusters of molecules withcorrelated orientations of their dipole moments. While hy-drogen bonding causes the predominance of parallel orien-tation along the direction of the hydroxyl group of moleculei, this effect does not explain the antiparallel orientation inthe perpendicular direction. Rather, the latter observation im-plies that the dipole moments of molecules in the shell ofthe clusters are aligned in the dipole field, which is im-posed by the strong overall dipole moment of the moleculesin the core, which are connected by hydrogen bonds andform chain structures. Performing the same analysis for othertemperatures, we find that the size of the orientationally or-dered clusters hardly depends on temperature and amountsto 1–2 nm.

F. Correlation times of sphere dipole moments

The existence of clusters with correlated molecular ori-entations and high dipole moments calls for an investigationof their reorganization. For this purpose, we define

δ(r, t) =⟨

ps(r, 0)

‖ps(r, 0)‖ · ps(r, t)

‖ps(r, t)‖⟩. (6)

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.22.67.7

On: Wed, 03 Dec 2014 00:00:41

144507-7 P. Wieth and M. Vogel J. Chem. Phys. 140, 144507 (2014)

0 2 4 6 8 10 12 14r in nm

2000

4000

6000

8000

τ δ in p

s

5 nm box15 nm box

τα

τD

FIG. 10. Correlation times characterizing the fluctuations of the overalldipole moment of spherical regions as a function of the sphere radius. Re-sults for 1-butanol at 240 K are shown. The horizontal solid lines indicatethe corresponding correlation times of the α process and the Debye process.The vertical dashed line marks the typical size of clusters with correlatedmolecular orientations.

Here, ps denotes the dipole moment resulting from allmolecules in a sphere with radius r centered at a givenmolecule. Then, δ(r, t) resembles d(t) for small radii andD(t) for large radii and, hence, it probes the α process andthe Debye process, respectively. Thus, the time constantsτ δ obtained from δ(r, t) should depend on the value of r.Specifically, based on the observed cluster size, one might ex-pect a crossover from τ δ = τα to τ δ = τD at r = 1–2 nm. InFig. 10, we show τ δ(r) for 1-butanol at 240 K. At variancewith this reasoning, we do not observe a crossover at suchradii, but a gradual increase until the limit τ δ = τD is reachedwhen the radius of the spheres is comparable to the size of thebox, which amounts to ∼5 nm in this case.

Such observation necessitates an investigation of finite-size effects. Therefore, we repeat our analyses for systemsof various sizes. Figure 11 shows the dependence of τα andτD on the edge length of the simulation box for 1-butanolat 330 K. Evidently, neither of these correlation times is in-fluenced by finite-size effects. Consistently, we find that thecorrelation times of the structural relaxation, τα ≈ 1 ns, andthe Debye process, τD ≈ 8 ns, are not altered for 1-butanol at240 K, when increasing the box size from 5 nm to 15 nm. InFig. 10, we see that the situation is different for τ δ(r), whichclearly depends on the size of the system. Two effects arestriking when replacing the smaller system by the larger sys-

2 4 6 8 10 12 14box size in nm

0

100

200

τ in

ps

τD

τα

FIG. 11. Correlation times of the α process (τα) and the Debye process (τD)as a function of the system size. Results for 1-butanol at 330 K are shown.

tem. First, τ δ significantly decreases for sphere radii amount-ing to a few nanometers and, second, it reaches the limit τ δ

= τD at a substantially larger value of r. Implications of theseobservations will be discussed in Sec. IV.

IV. DISCUSSION

Our studies revealed the existence of HB chains withshort life times. In view of the high instability, the relationbetween these transient chains and the Debye process is notstraightforward. More detailed analysis showed that corre-lations of molecular orientations exist not only along HBchains, but also around these objects. We conclude that themolecules in the core of these clusters, which form hydrogenbonds and carry a high overall dipole moment, polarize themolecules in the shell of the clusters, which are usually notlinked by hydrogen bonds. For the typical size of the clusters,we found values of 1–2 nm.

On the quest for the life time of the clusters, we stud-ied fluctuations of the overall dipole moment associated withspheres of various radii. For radii of a few nanometers, it wasobserved that the corresponding correlation times τ δ substan-tially depend on both the size of the considered spheres andthe size of the simulation box, see Fig. 10. Both findings canbe explained, when we assume that the clusters with a highdipole moment and a size of ∼1 nm do not remain bound toa given group of molecules, but roam around like an “exci-tation” carried by a “diffusive” La Ola wave. While moving,the clusters carry away the high dipole moment from the ini-tially “excited” group of molecules and from the initial loca-tion. Considering that the clusters escape from larger spheresat later times than from smaller spheres, such scenario canaccount for the observed rise of τ δ with increasing sphereradius r. Also, such moving clusters allow us to rationalizethe influence of the box size. When increasing the size of thesimulation box, it becomes less likely that a cluster with ahigh dipole moment, which has escaped from a given sphereat some time, returns to that sphere at a later time via periodicboundary conditions and, thus, restores the initial dipole mo-ment. While the clusters roam around, the orientation of theirdipole moment changes. Also, in the course of time, thermalfluctuations can annihilate the excitation. We propose that theDebye process is associated with these effects, leading to theobserved saturation τ δ = τD for sufficiently large spheres.

The proposed scenario of a “diffusive” La Ola wave hassimilarities and differences with the transient chain model.Like in the latter model, the Debye process results from therelaxation of the high dipole moment of a HB entity, whichwanders around by exchanging its members. Unlike in thismodel, the diffusion of the HB entity does not necessarily re-sult from attachment and detachment processes at the endsof transient chains, which are driven by hydrogen-bond reor-ganization. In view of short life times of transient chains inour study, we rather suggest that the high dipole moment ofa HB chain polarizes molecules in the neighborhood, leadingto a propagation of the excitation. In both models, the HB en-tity exchanges molecules on the time scale of the α process.However, breaking and forming of hydrogen bonds should re-sult in an exchange of single molecules at the ends of transient

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.22.67.7

On: Wed, 03 Dec 2014 00:00:41

144507-8 P. Wieth and M. Vogel J. Chem. Phys. 140, 144507 (2014)

chains during each diffusion step, while several molecules canbe polarized at the same time, depending on the range of thedipole field. Thus, the step size of the diffusion process canbe larger in our model than in the transient chain model and,thus, the propagation of the excitation can be faster than thediffusion of transient chains or single molecules. Also, thesuggested scenario has similarities and differences with a reg-ular La Ola wave. While an excitation is transported in bothcases, there is a defined direction of propagation for a regularwave, while a diffusive motion results in our case from a com-bination of polarization effects with the statistical process ofhydrogen-bond formation in newly polarized regions.

V. CONCLUSION

Performing MD simulations for various primary mono-hydroxy alcohols in broad temperature ranges, we identi-fied transient chains composed of hydrogen-bonded hydroxylgroups. While their high dipole moments are consistent withthe high amplitude of the Debye process, their life timesare much shorter than the correlation times associated withthis relaxation phenomenon. For the studied model systems,the breakup and reformation of the transient chains happensso fast that it is not appropriate to speak of chains windingthrough the system collecting molecules in its path and losingmolecules on the other end. Increasing the polarity of the al-cohol molecules and introducing hydrogen-bond cooperativ-ity into the simulations resulted in a slowdown of moleculardynamics, but did not alter the qualitative picture. Likewise,our conclusions are not affected by finite-size effects. On theother hand, our simulations revealed a possible relation be-tween the Debye process and transient clusters comprisingmolecules with orientational correlations. Within these clus-ter, molecules forming hydrogen bonds, e.g., transient chains,polarize molecules in the neighborhood. We propose that theDebye process is associated with the diffusion of these tran-sient clusters, which is driven by the polarization of neighbor-ing molecules, involves a reorganization of hydrogen bonds,and results in a reorientation of the high cluster dipole mo-ment, possibly in combination with an annihilation of these“excitations” due to thermal fluctuations. Thus, a “diffusiveLa Ola wave” may illustrate the proposed scenario.

ACKNOWLEDGMENTS

The authors thank the Deutsche Forschungsgemeinschaft(DFG) for funding through Grant No. VO 905/9-1.

1P. Debye, Polar Molecules (Hirzel, Leipzig, 1929).2D. W. Davidson and R. H. Cole, J. Chem. Phys. 19, 1484 (1951).3G. P. Johari and M. Goldstein, J. Chem. Phys. 53, 2372 (1970).4C. Hansen, F. Stickel, T. Berger, R. Richert, and E. W. Fischer, J. Chem.Phys. 107, 1086 (1997).

5U. Kaatze, R. Behrends, and R. Pottel, J. Non-Cryst. Solids 305, 19(2002).

6S. J. Bass, W. I. Nathan, R. M. Meighan, and R. H. Cole, J. Phys. Chem.68, 509 (1964).

7C. Gainaru, R. Meier, S. Schildmann, C. Lederle, W. Hiller, E. A. Rössler,and R. Böhmer, Phys. Rev. Lett. 105, 258303 (2010).

8D. Fragiadakis, C. M. Roland, and R. Casalini, J. Chem. Phys. 132, 144505(2010).

9L.-M. Wang and R. Richert, J. Phys. Chem. B 109, 11091 (2005).10L.-M. Wang and R. Richert, J. Phys. Chem. B 109, 8767 (2005).11C. Gainaru, R. Figuli, T. Hecksher, B. Jakobsen, J. C. Dyre, M. Wilhelm,

and R. Böhmer, Phys. Rev. Lett. 112, 098301 (2014).12C. Gainaru, S. Kastner, F. Mayr, P. Lunkenheimer, S. Schildmann, H. J.

Weber, W. Hiller, A. Loidl, and R. Böhmer, Phys. Rev. Lett. 107, 118304(2011).

13J. L. MacCallum and D. P. Tieleman, J. Am. Chem. Soc. 124, 15085 (2002).14L. Zoranic, F. Sokolic, and A. Perera, J. Chem. Phys. 127, 024502

(2007).15J. Lehtola, M. Hakala, and K. Hämäläinen, J. Phys. Chem. B 114, 6426

(2010).16F. Affouard and N. T. Correia, J. Phys. Chem. B 114, 11397 (2010).17K. Adrjanowicz, K. Kaminski, M. Dulski, P. Wlodarczyk, G. Bartowiak, L.

Popenda, S. Jurga, J. Kujawski, J. Kruk, M. K. Bernard, and M. Paluch, J.Chem. Phys. 139, 111103 (2013).

18E. Lindahl, B. Hess, and D. van der Spoel, J. Mol. Model. 7, 306 (2001),available at http://link.springer.com/article/10.1007%2Fs008940100045.

19W. L. Jorgensen, J. Phys. Chem. 90, 1276 (1986).20G. Widmalm and R. W. Pastor, J. Chem. Soc., Faraday Trans. 88, 1747

(1992).21J. K. Shah, J. F. Brennecke, and E. J. Maginn, Green Chem. 4, 112 (2002).22U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G.

Pedersen, J. Chem. Phys. 103, 8577 (1995).23S. Nosé, Mol. Phys. 52, 255 (1984).24W. G. Hoover, Phys. Rev. A 31, 1695 (1985).25M. Parrinello and A. Rahman, J. Appl. Phys. 52, 7182 (1981).26R. P. Sear and G. Jackson, J. Chem. Phys. 105, 1113 (1996).27B. A. Veytsman, J. Phys. Chem. 97, 7144 (1993).28X.-N. Jiang, C.-L. Sun, and C.-S. Wang, J. Comput. Chem. 31, 1410 (2010).29H. Kleeberg, D. Klein, and W. A. P. Luck, J. Phys. Chem. 91, 3200 (1987).30R. B. Gupta and R. L. Brinkley, AIChE J. 44, 207 (1998).31S. K. Garg and C. P. Smyth, J. Phys. Chem. 69, 1294 (1965).

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.22.67.7

On: Wed, 03 Dec 2014 00:00:41