Non-simple ow behavior in a polar van der Waals liquid structural relaxation under scope S. Arrese-Igor1A. Alegr a1 2and J. Colmenero1 2 3

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Non-simple ﬂow behavior in a polar van der Waals liquid: structural relaxation under

scope

S. Arrese-Igor,1A. Alegr´ıa,1, 2 and J. Colmenero1, 2, 3

1Centro de de F´ısica de Materiales (MPC), Centro Mixto CSIC-UPV/EHU,

Paseo Manuel Lardizabal 5, 20018 San Sebasti´an, Spain

2Departamento de Pol´ımeros y Materiales Avanzados UPV/EHU, Apartado 1072, 20080 San Sebasti´an, Spain

3Donostia International Physics Center, Paseo Manuel Lardizabal 4, 20018 San Sebasti´an, Spain

(Dated: October 6, 2022)

The non-exponential character of the structural relaxation is considered one of the hallmarks

of the glassy dynamics and in this context, the singular shape observed by dielectric techniques

has attracted the attention of the community for long time. Particularly, the exceptionally narrow

dielectric response of polar glass formers has been attributed so far to dipolar cross correlations.

Here we show that dipole interactions can couple to shear stress and modify the ﬂow behavior

preventing the occurrence of the simple liquid behavior. We discuss our ﬁndings in the general

framework of the glassy dynamics and the role of intermolecular interactions.

Liquids possess the ability to avoid crystallization upon

cooling -if the cooling rate is just high enough- and be-

come a solid glass in a phenomenon known as the glass

transition. When approaching the glass transition tem-

perature the dynamics of the supercooled liquid becomes

exponentially slower till eventually the system solidiﬁes

as a consequence of the arrest of the molecular motions

leading to the so called structural αrelaxation1,2. The

broad diversity in structural, chemical and physical prop-

erties of the materials capable of forming a glass compli-

cate a full understanding of the glass transition prob-

lem. Notwithstanding, substantial progress was made in

elucidating common generic features for the structural

αrelaxation3. In this quest for universal characteris-

tics however, it is important to properly identify those

molecular motions whose arrest ultimately lead to the

glass transition, since depending on the particular class of

materials these may coexist with other material speciﬁc

dynamics. As a consequence, in practice, unambiguous

determination of the characteristics of the αrelaxation is

not straightforward due to possible overlapped contribu-

tions from other processes which may apparently rule-out

some actual universal behavior4,5.

The nonexponential shape of the structural αre-

laxation is one of the hallmarks of glassy dynamics,

many works pointing to a common universal shape for

this process5–9. A singular behavior is found however

in this respect for polar systems as seen by dielectric

techniques10. The narrower lineshape observed in this

case has been ascribed to dipolar interaction eﬀects10–12,

though details on the microscopic origin and inﬂuence

on the structural relaxation though still remain unclear.

Under the assumption that depolarized dynamic light

scattering (DDLS) measurements render the αrelax-

ation, Pabst and co-workers exploited the diﬀerences ob-

served between the dielectric and DDLS data to identify

an additional slow contribution in the dielectric spec-

tra of a series of phenyl monoalcohols, glycerol polyal-

cohol and tributyl phospate (TBP) polar van der Waals

liquid11,13,14. The presence of a slow Debye-like relax-

ation in addition to the αone is a well-known feature

in many monoalcohols and it is commonly ascribed to

the relaxation of hydrogen bond mediated supramolecu-

lar structures15. However, although often addressed as

reminiscent of the Debye process in monoalcohols, for

other substances11,13,16–19 we still lack a full understand-

ing of the molecular origin of this slow Debye-like con-

tribution. Pabst et al. rationalized diﬀerences in DDLS

and dielectric data proposing the presence of an under-

lying and universal shape self part (which they denoted

αrelaxation) and a dominant slow cross contribution

in the dielectric response of glycerol and TBP. Support-

ing this view, recent molecular dynamics simulations on

model liquids show that cross-terms are slower than and

dominate over self-terms on the decay of the total dipole

moment correlation function for strongly polar liquids12.

According to the general believe, vitriﬁcation, relax-

ation of the structure in the glassy state (structural re-

covery) and the equillibrium dynamics above but close

to the glass transition are collective phenomena. As a

consequence, the idea that only the faster self or autocor-

relation contribution can render the structural dynamic

evolution was recently questioned19. Looking at the age-

ing behavior of TBP alkyl phosphate, Moch et al. stated

that the same collective dynamics governs the molecular

ﬂow, the structural recovery and the dielectric response,

claiming a crucial role in the structural dynamics for the

cross correlation eﬀects dominating the dielectric spectra

(Debye-like term), against the single particle contribution

identiﬁed by DDLS. Calorimetric studies of monoalcohols

on the other hand, indicate that their Debye relaxation

is not involved in the thermal glass transition20–22.

All the mentioned works put under the scope the ques-

tion of the nature and origin of the ’structural relaxation’.

Over several decades, many eﬀorts have been devoted to

the understanding of the vitriﬁcation phenomenon and,

for this, to the characterization of the dynamics of the

associated αrelaxation in glass-forming systems of di-

verse nature and by diﬀerent experimental techniques.

Probably inﬂuenced by the Mode Coupling Theory23,24,

arXiv:2210.01947v1 [cond-mat.soft] 4 Oct 2022

the term ’structural relaxation’ has been used since the

19900s to refer to the mechanism leading to the decay

of the coherent scattering function at the main struc-

ture factor peak, revealing thereby the time dependence

of inter-molecular correlations. The presence of diﬀer-

ent kind and degree of speciﬁc non-covalent interactions

though can potentially modify the dynamic response of

liquids. Moreover, ionic or hydrogen bonding for exam-

ple, are known to produce mesoscopic structures in some

cases25–27, so that additional dynamics could emerge re-

lated to the formation and relaxation of the mentioned

mesoscopic structures. Under such situations, the con-

cept behind ’structural relaxation’ is much broader and

could be applied to diverse mechanisms leading to the

decay of density ﬂuctuations at diﬀerent length scales,

including those involving speciﬁc interactions and meso-

scopic structures. The question is now, what dynamics

do we regard as αrelaxation? those contributing to the

vitriﬁcation? to structural recovery? to ﬂuctuations of

the enthalpy at equilibrium? to which extent do collec-

tive dynamics at intermediate timescales contribute to

the processes mentioned above? These are not trivial

questions at all. In the absence of additional complexity

introduced by non-covalent interactions or other pecu-

liarities, terms like αrelaxation, structural relaxation,

glass-transition dynamics and structural recovery have

often been indistinctly used. At the light of the last

ﬁndings,28, however , it seems that the scientiﬁc commu-

nity will need to clarify the universal or speciﬁc (inter-

action dependent) nature of the new emerging processes

and their role on the vitriﬁcation and the structural re-

covery phenomena.

In this regard, we present here for the ﬁrst time evi-

dence of the bimodal shear response of a polar van der

Waals liquid, TBP. The data presented herein demon-

strate that dipolar interactions are capable of modifying

the rheologic response of a liquid preventing the occur-

rence of the simple liquid behavior often assumed for

many low molecular weight glass forming systems. We

discuss and compare TBP results with the dynamic be-

havior observed for hydrogen bonded systems (mono and

polyalcohols) and other polar and non polar glass form-

ers, allowing us to introduce new perspective on the phe-

nomenology and role of speciﬁc non-covalent interactions

in the structural relaxation of glass forming systems.

The dielectric and shear response of glass forming liq-

uids in general is characterized by the presence of the

so called αrelaxation40. The simplest approach to de-

scribe the viscoelasticity of glass forming liquids is the

Maxwell model, G∗(ω) = Gp/(1 −i/ωτM). At high fre-

quencies, the crossing point of the real and imaginary

modulus G0(ωx) = G00 (ωx) marks a timescale for the α

relaxation, while at lower frequencies G0(ω) and G00 (ω)

show the so called terminal behavior, (G0(ω)∝ω2and

G00 (ω)∝ω) where the liquid presents pure viscous ﬂow.

Simple liquids closely satisfy this model, and in practice,

the non-exponential nature of the αrelaxation has little

impact in the low frequency ﬂank of the shear modulus,

-1 -0,5 0 0,5 1 1,5 2 2,5 3

ω1

J''

-1 -0.5 0 0.5 1 1.5 2 2.5 3

100

J' ,J'' (norm.)

ωJ''

-1

c) Compliance

log ω (s-1)

-dJ'/dlogω

ωJ'

Eta" Pa.s

G'Pa

G" Pa

0.001

0.01

0.1

G' ; G'' (norm.)

ωG'

ωG"

a) Modulus

ωx

eta'

Eta" Pa.s

0.1

η' ,η'' (norm.)

ωη''

1b) Viscosity

ωη'

FIG. 1: Shear relaxation of TBP at 146K: (a) modulus,

(b)viscosity and (c) compliance. Data in the y-axis was nor-

malized to the crossing value of the real and complex com-

ponents. Lines are guides for the eye representing diﬀerent

power law behaviors. The inset in (c) represents the deriva-

tive of J0.

so that pure viscous ﬂow is shortly established after the

crossing frequency ωx29. The separation between ωxand

the crossover frequency to terminal behavior ωtcan be

used then as a measure or indication of the 0simplicity0

of a certain rheologic response. Systematic comparison

of the separation between these two characteristic fea-

tures for diﬀerent glass forming liquids allowed to reveal

subtle eﬀects of hydrogen bonding on the shear response

of polyalcohols for example30.

Figure 1 shows the shear relaxation of TBP at 146K.

Although at ﬁrst sight the shear response of TBP seems

to be relatively simple, close inspection reveals that the

onset of the terminal behavior sets in more than a decade

below the crossing frequency ωx. This behavior is clearly

diﬀerent from that observed for other simple liquids29,30

either indicating non-universal shape for the structural

relaxation of TBP relative to other simple liquids, or the

presence of some additional slow contribution. Figure

2 compares the shear response of TBP with that of o-

tertphenyl (OTP), which is representative of the behav-

ior of simple liquids31. In order to compare the shape

of the relaxation, the frequency axis was normalized to

ωxfor the shear modulus, and the y-axis to the value of

the depicted magnitude at ωx. As it can be seen in panel

a), both samples show almost indistinguishable shape for

the viscosity losses at high frequencies but when decreas-

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Non-simpleowbehaviorinapolarvanderWaalsliquid:structuralrelaxationunderscopeS.Arrese-Igor,1A.Alegra,1,2andJ.Colmenero1,2,31CentrodedeFsicadeMateriales(MPC),CentroMixtoCSIC-UPV/EHU,PaseoManuelLardizabal5,20018SanSebastian,Spain2DepartamentodePolmerosyMaterialesAvanzadosUPV/EHU,Apartado1072,200...

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Non-simple ow behavior in a polar van der Waals liquid structural relaxation under scope S. Arrese-Igor1A. Alegr a1 2and J. Colmenero1 2 3

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