Unique dynamic crossover in supercooled x,3-dihydroxypropyl acrylate (x = 1, 2) isomers mixture

The previtreous dynamics in glass forming monomer, glycerol monoacrylate (GMA), using broadband dielectric spectroscopy (BDS) was tested. Measurements revealed the clear dynamic crossover at temperature $T_B = 254$ K and the time scale $\tau(T_B) = 5.4$ ns for the primary (structural) relaxation time and no hallmarks for the crossover for the DC electric conductivity $\sigma_{DC}$. This result was revealed via the derivative-based and distortions-sensitive analysis $dln{H_{a}}/d(1/T)$ vs. $1/T$, where $H_a$ is for the apparent activation energy. Subsequent tests of the fractional Debye-Stokes-Einsten relation $\sigma_{DC}(\tau_{\alpha})^S = const$ showed that the crossover is associated with $S = 1$ (for $T>T_B$)->$S = 0.84$ (for $T<T_B$). The crossover is associated with the emergence of the secondary beta relaxation which smoothly develops deeply into the solid amorphous phase below the glass temperature $T_g$.


Introduction
One of the most mysterious forms of the solidification is the vitrification at the glass temperature when passing from the metastable ultraviscous liquid/fluid to the metastable amorphous solid glass state [1]. Although the glass temperature cannot be directly considered as the phase transition, due to its stretched and depending on the cooling rate nature, it is associated with far previtreous effects signaling the vitrification even 100 K above . This inherent feature allows for the 'remote' estimation of value. Regarding the previtreous 'dynamic effects' one can recall such 'universal' behavior as (i) the non-Arrhenius evolution on the primary relaxation time (τ), viscosity (η) or electric conductivity (σ), (ii) the non-Debye distribution of relaxation time, (iii) the dynamic crossover between the ergodic and non-ergodic dynamical regimes, most often associated with the time scale = 10 −7±1 s, (iv) the emergence of the secondary relaxation in the ultraslowing domain for < = ( = ). The glass temperature is by convention associated with the time scale of the primary relaxation process, ( ) = 100 s which corresponds to empirically observed value in the heat capacity scan for the most standard cooling rate 10 K·min -1 [2,3]. The fascinating previtreous 'universal' behavior of dynamic properties on approaching the glass temperature is undoubtedly one of key reason that the problem of in-deep fundamental understanding of the glass transition is indicated as one of the greatest challenges for 21 st condensed matter physics, with enormous importance for the material engineering implementations [1][2][3][4]. One of lacking issues in this domain, which may appear essential for the ultimate insight, are studies covering domains on both sides of the glass transition, i.e. the metastable ultraviscous liquid and the metastable amorphous solid. In fact conclusive research on the latter is particularly difficult due to the fact that when passing the time scale ( ) the system time scale by decades exceeds the experimental one, making ultimate conclusions puzzling [2,3].
In this report it is shown that the secondary relaxation process [1][2][3], several decades faster than the primary relaxation time, seems to continue smoothly deeply within the solid glass state. Its evolution in this solid state clearly correlates with such basic feature of the liquid state as the dynamic crossover. Studies were carried out in glycerol monoacrylate monomeric system, important for application in ceramics formation.

I. Experimental
The tested glass former was glycerol monoacrylate which is a low-toxic monomer used for manufacturing ceramic materials through the gelcasting process, what makes results of this paper additionally important for developing in situ monitoring of this process.
The monomer, present in the ceramic slurry, polymerizes during the forming process inside the mold. As a result, the obtained green body models the shape of the mold. Glycerol monoacrylate is a mixture of two isomers: 2,3-dihydroxypropyl acrylate and 1,3dihydroxypropyl acrylate. It has a number of advantages when compared to different commercial monomers. It is water soluble, which allows conducting the process in water. Due to the presence of two -OH groups, the use of a crosslinking agent is not necessary.
The obtained green bodies have high rigidity when compared to those obtained from commercial monomers with additions of crosslinking agents [5][6][7]. The glycerol monoacrylate (GMA) mixture synthesized at the Warsaw University of Technology was used. The tested sample was composed from: 2,3-dihydroxypropyl acrylate (70 %wt.) and 1,3dihydroxypropyl acrylate (30 %wt.). Their molecular structures are shown in Fig. 1.
During measurements the sample was maintained under the nitrogen gas flow at a temperature range between 273 K and 143 K. The temperature was controlled using Quatro Cryosystem

II. The evolution of relaxation times and the dynamic crossover
One of key features of the glass previtreous dynamics is the super-Arrhenius behavior of the primary (α, alpha) relaxation time [1][2][3][4]: where ( ) stands for the apparent activation energy. This relation converts into the classical Arrhenius dependence when in the given temperature domain ( ) = = .
The generally unknown form of the evolution of the apparent activation energy causes in the portrayal of experimental data one have to use ersatz dependences. For decades the most popular was the Vogel-Fulcher-Tammann (VFT) dependence [1][2][3][4]8]: where DT denotes the fragility strength coefficient, T0 is for the ideal glass 'transition' temperature hidden in the solid glassy state and R stands for the gas constant. By comparing Eqs. (1) and (2) for the apparent activation energy following equation has been obtained In recent years, novel equations yielding more optimal ( ) or ( ) parameterizations and questioning the general validity of the VFT relation appeared [9][10][11][12][13][14][15][16].
Particularly, successful appears the relation empirically introduced by Waterton [17] in 1932 and recently validated as the output of the constraint theory applied to the Adam-Gibbs model by Mauro et al. [11], namely: It is notable that it has no final temperature divergence, which is the characteristic feature appears. Most liquids are characterized by 0.7 < S <1 [22]. However, in some liquid crystal's phases the exponent can be even lesser than 0.5 [23,24]. In Ref. [22] the link of the exponent S activation enthalpy of the process was shown.
One of 'universal' features of the previtreous dynamic is the emergence of the secondary, 'beta' (β), relaxation process for T < TB. Both 'alpha' and 'beta' relaxation processes splits at T = TB and when reaching Tg the difference between related time scale reaches several decades. It is notable that the secondary relaxation most often follows the Arrhenius pattern. In the case of polymeric glass formers the beta relaxation is linked to internal molecular relaxation processes [2,3]. at log 10 plot is related to electrode polarization appearing in highly conductive systems, to which GMA belongs. This low frequency part of spectra also serves for determining the DC-conductivity. Regarding the basic structural α-process dielectric loss curves exhibit a typical for complex glassy dynamics non-Debye shape. The obtained evolution of relaxation times is presented in Fig. 3a, covering both the ultraviscous liquid and solid states. Fig. 3b shows results of the supplementary distortions-sensitive and derivative based analysis of data, following the method recalled in the previous section.

IV. Conclusions
This report present the analysis of the dynamics in glycerol monoacrylate (GMA) mixture, being the glass former important in gelcasting technology in ceramics. The tested system shows relatively high electric conductivity, but despite this difficulty the broadband dielectric scanning enabled tests of the temperature evolution of orientational and translational relaxation processes. The structural relaxation time ( ) shows a clear dynamic crossover from the Arrhenius to Super-Arrhenius behavior at the temperature ≈ 254 K. The crossover is absent for the DC electric conductivity, related to translational processes. The crossover is clearly visible also in tests focused on the occurrence of the fractional Debye-Stokes-Einstein law. In the solid amorphous state the primary relaxation time ( ) ceases to be directly detectable due to the enormous increasing of the system time scale.
Notwithstanding, there is a clear manifestation of the qualitatively faster relaxation process, which after the extrapolation to the ultraviscous liquid state merges with the structural relaxation time at T = TB, what allows to claim that for the given system the secondary relaxation processes smoothly develops from the metastable ultraviscous liquid state to the metastable solid glass state without a hallmark when passing the solidification point at the glass temperature. V.