Fractional Debye-Stokes-Einstein behaviour in an ultraviscous nanocolloid: glycerol and silver nanoparticles

One of hallmark features of glass forming ultraviscous liquids is the decoupling between translational and orientational dynamics. This report presents studies of this phenomenon in glycerol, a canonical molecular glass former, heading for the impact of two exogenic factors: high pressures up to extreme 1.5 GPa and silver (Ag) nanoparticles (NP). The analysis is focused on the fractional Debye-Stokes-Einstein (FDSE) relation $\sigma(T,P)*(\tau(T,P))^S = const$, linking DC electric conductivity $(\sigma)$ and primary $(\alpha)$ relaxation time $(\tau_\alpha)$. In glycerol and its nanocolloid (glycerol with Ag-NP) under atmospheric pressure only the negligible decoupling $(S = 1)$ was detected. However, in the compressed nanocolloid a well-defined transformation (at P = 1.2 GPa) from $S \thickapprox 1$ to the very strongly decoupled dynamics $(S \thickapprox 0.5)$ occurred. For comparison, in pressurized 'pure' glycerol the stretched shift from $S \thickapprox 1$ to $S \thickapprox 0.7$ took place. This report presents also the general discussion of FDSE behavior in ultraviscous liquids, including the new link between FDSE exponent, fragility and the apparent activation enthalpy and volume.


I. Conceptual background
Glass transition physics has remained a challenge for condensed and soft matter physics since decades. 1-3 The most intriguing feature is the set of strong previtreous effects for dynamic properties, with similar patterns for qualitatively different glass forming systems. 2 The key representative of such behavior is the super-Arrhenius (SA) evolution of various dynamic properties on approaching the glass temperature Tg: 2,3 where   denotes the apparent activation energy, Tg is for the glass temperature and R is the gas constant.
The basic Arrhenius equation can be restored for The 'universal' metric of the SA behavior is called 'fragility' and defined as follows:   5 All these suggests the significance of FDSE studies in ultraviscous liquids atemporal "research status quo". This is the target of the given report.
First, the resume of FDSE reference results, particularly focusing on eq. (4), is presented. This topic is concluded by the novel link between the FDSE exponent and basic characteristics of the SA behavior, namely: the fragility, the activation enthalpy and the activation volume.
Second, results related to the impact of exogenic factors on dynamics of glycerol, one of canonical glass forming liquids, are presented. They are: (i) high pressures up to challenging P=1.5 GPa and (ii) the addition of silver nanoparticles (Ag NP), forming a nanonocolloid/nanocomposite/nanofluid to the ultraviscous glycerol. The impact of nanoparticles lead to the crossover to the strongly decoupled region in the immediate vicinity of the glass transition (i.e. within the ultraviscous domain), a phenomenon which has been not reported before.

II. The translational-orientational decoupling
For coupling between translational and orientational processes in 'classical' liquids one can expect the validity of Debye, Stokes and Einstein relations: 2,14,41 , 14 where n is the number of electric charges/carriers,  denotes the DC electric conductivity and q is the electric charge, one obtains: const    (9) where eq. (8) recalls DS eq. (5) and eq. (9) is based on the Maxwell equation, as discussed above.
In low molecular weight liquids the DC conductivity arises from residual ionic dopants: salts or other ionic species that inevitably can get into samples during the synthesis. 12 For broad band dielectric (BDS) spectra such behavior always dominates at lower frequencies, often beginning just below the kHz domain. In ionic or highly conductive liquids this can be the governing factor also for the multi MHz region. It is notable that taking into account the Fluctuating local density excesses results in a distribution of barrier heights, which gives rise to the decoupling of primary relaxation time and diffusion related processes as well as to the stretched exponential (non-Debye) relaxation. For polymers this 'heterogeneous" model yields: The compilation of experimental data for polymeric glass formers confirmed the smooth dependence of  vs. fragility m predicted by the above relation. The important result of ref. 43 8 was that the chain relaxation and fragility should weakly depend on the material as well as be insensitive to local heterogeneities due to the large-scale averaged nature of C  . This behavior is in strong contrast to 'segmental' related dynamics (   Generally the pressure counterpart of SA eq.(1) is given by: 2,13,42 is the apparent activation volume ('free volume').
It can be called super-Barus (SB), since the basic equation proposed by Barus 44 can be rewritten as .
The SA eq. (1) enables determining of the apparent activation enthalpy via Following refs. 2,45-47 the SB eq. (15) yields the apparent activation volume via . Then, basing on the FDSE eq. (13) one obtains:  (16) Consequently, for the given point in the (P, T) plane: Direct implementations of the SA eq. (1) or SB eq. (15) for portraying experimental data are not possible, due to unknown forms of the apparent activation energy and volume.
Consequently, ersatz dependences are used. The dominant is the Vogel-Fulcher-Tammann (VFT) relation 2,12 or its pressure related quasi-counterpart introduced in ref. 48 : Their substitution into eq. (13) one obtains the link between fragility and the FDSE exponent: Dynamics of the pressurized glycerol and Ag-glycerol nanocolloid were tested via the piston-based high pressure set-up, described in ref. 52 The gap of the flat parallel measurement capacitor was equal to 0.2 mm. The macro-size of the gap made it possible to reduce parasitic artifacts associated with gas bubbles, finite dimensions or very large intensities of the measurement electric field, which appears for micrometric gaps.
The BDS spectrum, was monitored using the BDS Alpha Novocontrol spectrometer giving permanent 6 numbers resolution for imaginary and real part of dielectric permittivity.
This report focuses on the pressure evolution of DC conductivity  and the primary relaxation time   . The latter was estimated directly from peak frequency of dielectric loss curves via

Results and Discussion
This report focuses on the FDSE behavior in the nanocolloid composed of glycerol and Ag nanoparticles (NP). The 'background" behavior in ultraviscous glycerol, which has been lacked so far, is also discussed.   Results of the analysis of the translational-orientational decoupling on compressing up to P = 1.5 GPa is presented in Fig. 5 for glycerol and in Fig. 6     evolution in Fig.2 and Fig.7 enables a qualitative explanation of FDSE coupling/decoupling manifesting via eqs. (4) and (13). In Fig. 1

Conclusions
Glycerol is a versatile material due to its enormous significance in a variety of applications ranging from biotechnology to pharmacy, cosmetics, "green and biodegradable" plastics, textiles and foodstuffs industries. 66-69 Glycerol and Ag nanoparticles based nanocolloids/nanocomposites may appear important in these applications due to well known great antimicrobial activity of Ag nanoparticles. 70,71 From the fundamental point of view glycerol has a simple molecular structure, large permanent dipole moment and the relatively small electric conductivity, what coincides with preferred features for the broad band dielectric spectroscopy (BDS) monitoring. 12 It can be also very easily supercooled. All these caused that glycerol has gained the position of a model "classical" system in glass transition studies.