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Volumn 79, Issue 17, 2009, Pages

Effects of hydrogen bonding on supercooled liquid dynamics and the implications for supercooled water

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EID: 67049158417     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.174205     Document Type: Article
Times cited : (19)

References (40)
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    • The monomethyl dimer and trimer samples contain a mixture of isomers.
    • The monomethyl dimer and trimer samples contain a mixture of isomers.
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    • As discussed in the text, the data at low temperatures can be well described by a VFT expression and thus a straight line in the linearized representation of Fig. 2. To estimate a characteristic temperature, T, for the crossover we approximate the high-temperature regime with a straight line and determine the crossover temperature as the intersection of the two lines. We estimate that we can generally determine T within ±2-3 K, as shown from the error bars in Fig. 2 (Tg is determined within ±1 K). We emphasize that we do not assign any physical significance to this choice of fitting function for the high-temperature regime but only use it as a straightforward means to consistently extract the crossover temperature. For the glycol tetramer, we have data only near Tg. However, since the crossover temperature is T =282±3 K for the longer chain glycols, T =282 K is used.
    • As discussed in the text, the data at low temperatures can be well described by a VFT expression and thus a straight line in the linearized representation of Fig. 2. To estimate a characteristic temperature, T, for the crossover we approximate the high-temperature regime with a straight line and determine the crossover temperature as the intersection of the two lines. We estimate that we can generally determine T within ±2-3 K, as shown from the error bars in Fig. 2 (Tg is determined within ±1 K). We emphasize that we do not assign any physical significance to this choice of fitting function for the high-temperature regime but only use it as a straightforward means to consistently extract the crossover temperature. For the glycol tetramer, we have data only near Tg. However, since the crossover temperature is T =282±3 K for the longer chain glycols, T =282 K is used.
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    • note
    • The standard way of parameterizing the VFT behavior as τα = τ0 exp [D T0 / (T- T0)] is often problematic; τ0 is the timescale at infinite temperatures and is thus defined outside the range of validity of the VFT expression and at T0 the system is out of equilibrium. This parameterization thus yields parameters without a clear physical validity, which for hydrogen bonded systems often becomes evident, for instance reflected in τ0 values that are inconsistent with a molecular vibrational timescale. In order to circumvent this problem, we here choose an alternative parameterization of the VFT expression. Instead of the parameters [τ0, D, T0], given T we can alternatively use [τ, Z, S], where τ is the timescale at the crossover temperature, Z through its definition is directly related to the slope in an Arrhenius plot at T, and S is a direct measure of the deviation from an Arrhenius behavior. This parametrization also has the direct advantage that the parameters are defined within the region of validity of the VFT expression. Interestingly, τ is generally ∼ 10-8 - 10-7 s for supercooled liquids (Ref.).
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    • A lower limit for the crossover temperature, T, is determined from the power law divergence near 216 K, estimated from a fit to dielectric data at high temperatures, as shown in Fig. 4. An upper limit is set by the homogeneous nucleation temperature ∼235 K, which measured properties such as the thermodynamic response functions and the structural relaxation time, approach in a power law-like manner.
    • A lower limit for the crossover temperature, T, is determined from the power law divergence near 216 K, estimated from a fit to dielectric data at high temperatures, as shown in Fig. 4. An upper limit is set by the homogeneous nucleation temperature ∼235 K, which measured properties such as the thermodynamic response functions and the structural relaxation time, approach in a power law-like manner.
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    • This value is consistent both with the behavior of the T / Tg ratio in Fig. 2 and with the fact that the structural relaxation time at T varies only slightly between the glycol samples (compare with results in Ref.) and for water it extrapolates to ∼6× 10-9 s.
    • This value is consistent both with the behavior of the T / Tg ratio in Fig. 2 and with the fact that the structural relaxation time at T varies only slightly between the glycol samples (compare with results in Ref.) and for water it extrapolates to ∼6× 10-9 s.
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    • The data set and our scaling estimate provide consistent pictures, both with regards to Tg values and apparent activation energies (Refs.).
    • The data set and our scaling estimate provide consistent pictures, both with regards to Tg values and apparent activation energies (Refs.).
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    • A natural explanation for the observed behavior is that two competing effects influence the β relaxation: a speed up when N<4-5 and a slowing down due to an increased OH-group density for shorter chains. The DMEs can only show the first effect, and as discussed in the main text, the MMEs will be dominated by the same behavior. The lack of a speed up for short N glycols suggests the formation of end-linked chains with an effective length always >4-5 monomer units.
    • A natural explanation for the observed behavior is that two competing effects influence the β relaxation: a speed up when N<4-5 and a slowing down due to an increased OH-group density for shorter chains. The DMEs can only show the first effect, and as discussed in the main text, the MMEs will be dominated by the same behavior. The lack of a speed up for short N glycols suggests the formation of end-linked chains with an effective length always >4-5 monomer units.
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    • The dielectric loss is well described by a Cole-Cole expression, which is typical for secondary relaxations (Ref.) and gives further evidence for an assignment of the dielectric relaxation as a β relaxation.
    • The dielectric loss is well described by a Cole-Cole expression, which is typical for secondary relaxations (Ref.) and gives further evidence for an assignment of the dielectric relaxation as a β relaxation.
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    • The Tg of dimethyl ether was estimated from the empirical finding that the ratio of the boiling and glass-transition temperatures is Tb / Tg ∼3.3 for the samples where it could be determined. Given the known Tb (248 K) of dimethyl ether, Tg was estimated at 76 K.
    • The Tg of dimethyl ether was estimated from the empirical finding that the ratio of the boiling and glass-transition temperatures is Tb / Tg ∼3.3 for the samples where it could be determined. Given the known Tb (248 K) of dimethyl ether, Tg was estimated at 76 K.


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