In their comment, Bogdan and Loerting1 (hereafter called BoLo) question the validity of the experimental data of Lienhard et al.2 (hereafter called LZZKP) concerning the glass transition temperatures (Tg) of binary aqueous citric acid and aqueous malonic acid solutions. BoLo present own measurements and find disagreements between their results and the results published by LZZKP. In this reply, we show calorimetric thermograms from which the results published by LZZKP are derived and discuss why BoLo's criticisms are unjustified. Below, we address each of the four claims.1
(i) Mineral-oil/lanolin vs. halocarbon-oil/lanolin as emulsion matrix: BoLo question the validity of the emulsion data reported in LZZKP because the mineral-oil/lanolin (mineral-oil CAS number 8042-47-5) mixture which is used forms itself a glass around 177 K, here referred to as
The emulsion experiment with a citric acid weight fraction of 0.550 in Fig. 1(c) shows only one glass transition upon cooling, although both the mineral-oil/lanolin matrix and the aqueous droplets vitrify. The reverse transition (glass to supercooled liquid) occurs in the heating cycle followed by cold crystallization and was interpreted as Tg of the aqueous droplets, which in this experiment coincides with
BoLo's emulsion measurements with a halocarbon-oil/lanolin matrix and their bulk measurements yield a Tg which is 3 K lower than ours, which is not surprising as Tg depends on the cooling rate of the experiment, with larger cooling rates leading to higher Tg.6 They used a cooling rate of 3 K/min, whereas we applied the widely used cooling rate of 10 K/min.7 One order of magnitude reduction in the cooling rate typically lowers Tg by 3–5 K.8 In fact, when this difference is taken into account, the bulk measurements of BoLo agree with those from LZZKP within the experimental uncertainty. This interpretation of BoLo's results reduces the inconsistencies to a single experiment, namely, the one with aqueous droplets containing a citric acid weight fraction of 0.6 embedded in a mineral-oil/lanolin. However, we believe that the Tg-curve in Fig. 1 of LZZKP, which is based on a series of unambiguous bulk measurements, is much more convincing than this single experiment of BoLo. For comparison, we included BoLo's measurements in the phase diagram of the citric acid-water system (see supplementary material18).
(ii) Assignment of
(iii) Experimental procedure: BoLo report that they could not reproduce the Tg of bulk aqueous citric acid solutions with citric acid weight fractions of 0.70 and 0.75. When we prepared these solutions, we took care that no impurities that may provide surfaces for heterogeneous nucleation entered the vial during the preparation. For the same reason, we did not use stir bars and held the temperature of the solution above its solubility for some time to ensure that no undissolved citric acid crystals invisible to the eye were left in the solution. It is not unusual that aqueous solutions can be supercooled with respect to the solid phase of the solute. Both Refs. 9 and 16 observed Tg of aqueous citric acid solutions with w2 > 0.70. The calorimetric thermograms of the relevant aqueous citric acid solutions observed from both bulk and emulsified samples reported by LZZKP are displayed in Fig. 1(c).
The same procedure was applied for the aqueous malonic acid solutions. Additionally, as described by LZZKP, the emulsified aqueous malonic acid droplets with w2 = 0.750 were heated to the melting temperature of pure malonic acid after Tg was observed, to make sure that no crystal was formed in the cooling cycle (not shown).
(iv) Uncertainty of
(v) Classification of the glass transition: In addition to points (i) to (iv), BoLo state that the entropy excess discontinuities found by LZZKP imply that the glass transition is a first order transition. However, our work does not warrant such a conclusion. The data and evaluation with regard to the excess entropy discontinuity suggest only that the glass transition is not a classical second order phase transition according to the Ehrenfest classification. Additionally, the shape of the heat flow curves at the glass transition indicates that the transition is not a first order transition. Note that the glass transition occurs between two metastable states (supercooled liquid to amorphous solid) and is at least partially a dynamic phenomenon, hence the transition temperature depends on the cooling rate.6 Therefore, it is not a purely thermodynamically controlled phase transition, which complicates the classification according to Ehrenfest.
To summarize, we thank BoLo for a series of new measurements, which, as far as the conclusions of LZZKP are concerned, corroborate our findings. The ETH Research Grant ETH-0210-1 is acknowledged.