Comment on “ Experimental evidence for excess entropy discontinuities in glass-forming solutions ” [ J . Chem . Phys . 136 , 074515 ( 2012 ) ]

Lienhard et al.1 report that the difference between the molar excess mixing entropies of supercooled 3and 4component liquids, Smix, and glasses, Smix, might not be zero at the glass transition temperature, Tg. The authors (i) measure the Tg and heat capacity change Cp of bulk and emulsified 2-, 3-, and 4-component solutions using differential scanning calorimetry (DSC) and (ii) calculate the Tg of 3and 4-component solutions using two approaches from Refs. 8 and 28 cited in Ref. 1. The difference between the calculated and measured Tgs is accounted for by SmixSmix =0.1 However, although the authors promise “Experimental evidence. . . ” they do not present thermograms from which their data are extracted. Neither do they give sufficient information about the materials and experimental procedure used. This complicates reproduction of their results and verification of the validity of the conclusion on entropy excess discontinuity, which essentially states that the glass transition is a first order transition, a notion which goes against the current view of glass transition as a dynamic phenomenon.2 In this Comment, we show that our Tgand Cp-data, including a quasiinvariant point,3 (C′g,T′g), of aqueous citric acid (CA) differ from those reported in Ref. 1. We measured bulk (∼5.5 mg) and emulsified (∼20-30 mg) CA/H2O solutions of a concentration up to ∼63.5 wt.% CA between 278 and 133 K using Mettler Toledo DSC 822. We employed an emulsification procedure and a matrix of 77 wt.% mineral-oil4 + 23 wt.% lanolin (thereafter the ML-matrix) similar to that used in Ref. 1 in order to reproduce the results of Lienhard et al.. We also used a matrix of 80 wt.% halocarbon-oil+20 wt.% lanolin, (HLmatrix),5, 6 which produces a straight baseline between 278 and 133 K7 and therefore does not perturb the Tg and Cp of emulsified solutions. The droplet diameter in emulsions was ∼0.5–30 μm. More information about our measurement technique is given elsewhere.5, 6 We employed a cooling/warming rate (3 K/min) lower than the 10 K/min used in Ref. 1. Earlier we showed5, 6 that the Tg of a freeze-concentrated solution (FCS) observed at 3 K/min is similar to that observed at the atmospheric temperature change of ∼2 K/h. However, it is unclear whether this is the case for 10 K/min (600 K/h) used in Ref. 1. The fact that our ice melting temperatures, Tms,

molar excess mixing entropies of supercooled 3-and 4component liquids, S l mix , and glasses, S g mix , might not be zero at the glass transition temperature, T g .The authors (i) measure the T g and heat capacity change C p of bulk and emulsified 2-, 3-, and 4-component solutions using differential scanning calorimetry (DSC) and (ii) calculate the T g of 3and 4-component solutions using two approaches from Refs. 8 and 28 cited in Ref. 1.The difference between the calculated and measured T g s is accounted for by S l mix -S g mix =0. 1 However, although the authors promise "Experimental evidence. . ." they do not present thermograms from which their data are extracted.Neither do they give sufficient information about the materials and experimental procedure used.This complicates reproduction of their results and verification of the validity of the conclusion on entropy excess discontinuity, which essentially states that the glass transition is a first order transition, a notion which goes against the current view of glass transition as a dynamic phenomenon. 2 In this Comment, we show that our T g -and C p -data, including a quasiinvariant point, 3 (C g ,T g ), of aqueous citric acid (CA) differ from those reported in Ref. 1.
We measured bulk (∼5.5 mg) and emulsified (∼20-30 mg) CA/H 2 O solutions of a concentration up to ∼63.5 wt.% CA between 278 and 133 K using Mettler Toledo DSC 822.We employed an emulsification procedure and a matrix of 77 wt.% mineral-oil 4 + 23 wt.% lanolin (thereafter the ML-matrix) similar to that used in Ref. 1 in order to reproduce the results of Lienhard et al..We also used a matrix of 80 wt.% halocarbon-oil+20 wt.% lanolin, (HLmatrix), 5,6 which produces a straight baseline between 278 and 133 K 7 and therefore does not perturb the T g and C p of emulsified solutions.The droplet diameter in emulsions was ∼0.5-30 μm.More information about our measurement technique is given elsewhere. 5,6 e employed a cooling/warming rate (3 K/min) lower than the 10 K/min used in Ref. 1. Earlier we showed 5,6 that the T g of a freeze-concentrated solution (FCS) observed at 3 K/min is similar to that observed at the atmospheric temperature change of ∼2 K/h.However, it is unclear whether this is the case for 10 K/min (600 K/h) used in Ref. 1.The fact that our ice melting temperatures, T m s, a) E-mail: anatoli.bogdan@uibk.ac.at are similar to those reported in Ref. 1 indicates that solution concentrations are similar in both studies.The origins of the inconsistencies between our and Lienhard et al.'s results are discussed below.(i) ML-matrix or HL-matrix: Fig. 1(a) demonstrates that the ML-matrix vitrifies at T g ML ≈ 176.3 K.The T g ML is similar to the T g ≈ 176.5 K of 55 wt.% CA droplets embedded into the ML-and HL-matrix, (Figs. 1(a) and 1(b)), and the T g ≈ 176.6 K of 55 wt.% CA reported in Ref. 1.This similarity indicates that: (a) there is no effect of the ML-matrix on T g for the case T g ≈T g ML , (b) the mineral oil used in this work and Ref. 1 is the same (see Ref. 4).However, the ML-matrix perturbs the C p of 55 wt.% CA droplets because it includes the C p ML of the ML-matrix which is about twice as large as the C p of droplets.Further, the 60 wt.%CA thermogram demonstrates that the ML-matrix perturbs T g s which are in the vicinity of the T g ML .The perturbed T g ≈ 187 K is ∼7 K warmer than the unperturbed T g ≈ 180 K of 60 wt.%CA droplets in the HL-matrix, Fig. 1(b).Our bulk 60 wt.%CA also produces T g ≈180 K (not displayed) which is ∼3 K colder than that of 60.1 wt.% CA in Ref. 1. Thus, the ML-matrix perturbs C p when T g ≈ T g ML and T g when it is in the vicinity of the T g ML .(ii) Assignment of T g : As diluted solutions are cooled, the maximum freeze concentration, C g , and, consequently, the glass transition temperature of the maximally FCS, T g , are constant and independent of the initial solution concentration 3,6 and can be reached at an infinitely slow cooling rate. 8In Ref. 1, the authors report only about the T g = 214.3K and T g = 218.8K of emulsified 20.4 and 50.1 wt.% CA. 1 However, the fact that these temperatures differ from each other by 4.5 K and the experimental accuracy is ±0.9K 1 suggests that they are not true T g .This is confirmed by our thermograms displayed in Fig. 1(c) which show that only 20 wt.% CA droplets in the HL-matrix produce a subtle glass transition at ∼206 K.The thermogram of 20 wt.% droplets in the ML-matrix shows no indication of a glass transition.50 wt.%droplets embedded in both ML-and HLmatrixes also do not produce a glass transition but instead a double exothermic event at ∼206 and 218 K which is not mentioned in Ref.The authors provide neither information on the temperature at which the concentrated solutions were prepared and then loaded into the calorimeter, nor on the temperature region of the measurements.Our experiments with such solutions prepared at ∼85 o C show that MA crystallizes during emulsion preparation, (Fig. 1(e)), and CA crystallizes upon cooling both at 3 and 10 K/min (not shown).We therefore believe that the T g s reported in Ref. 1 are perturbed by the crystallization of solute (not only CA).The MA-crystallization together with the ML-matrix (see above) can be responsible for the nonmonotonous behavior of the T g of MA/H 2 O in Ref. 1. (iv) Uncertainty of S l mix -S g mix : The authors do not present its value.Their Eq. (12) shows that the values and uncertainty of S l mix -S g mix depend mainly on the C p W = c 1 1 -c 1 g of water and weakly depend on the scattering of experimental T g s.From extrapolation in a dilution series in Fig. 3(c) in Ref. 1 they determine a C p W of 34 J mol −1 K −1 , which is much larger than the C p W of ∼0.7 J mol −1 K −1 measured directly on glassy water samples. 11Also when using the approach of extrapolating to zero concentration, we arrive at a much lower value of the C p W of 18 J mol −1 K −1 from the data in Fig. 3(c) in Ref. 1. Using this latter value instead of 34 J mol −1 K −1 we find a deviation of 7.4 J mol −1 K −1 from the S l mix -S g mix ≈ 4 J mol −1 K −1 reported for 60.1 wt.% CA in Fig. 4 in Ref. 1 and an even a much larger deviation when using the directly measured C p W . Based on this uncertainty in C p W it cannot be decided whether the S l mix -S g mix difference is zero or different from zero using the approach presented by Lienhard et al.
In conclusion, the material presented in this Comment shows that T g and c l -c g data reported in Ref. 1 for the CA/H 2 O are not persuasive, which casts doubt on the validity of their estimation of S l mix -S g mix .The thermograms presented here do not require evocation of a discontinuity in entropy at the glass transition, but are in agreement with the glass transition representing a continuous slow-down of dynamics and continuous change in entropy.This work is funded by the Austrian Science Fund (project P23027) and the ERC (Starting Grant SULIWA).

FIG. 1 .
FIG. 1.(a) Cooling and warming thermograms of ML-matrix (0 wt.% CA) and only warming thermograms (shown for clarity) of emulsified CA/H 2 O droplets embedded into ML-matrix.(b) Thermograms of emulsified droplets embedded into HL-matrix.(c) Thermograms of emulsified 20 and 50 wt.%CA droplets embedded into ML-and HL-matrices.Arrows mark a double exothermic event.(d) Thermograms of bulk CA/H 2 O samples.(e) Optical microscope picture of emulsified 70 wt.%MA before measurement.Diameter of the droplets is less than ∼3 μm and the size of MA-crystals less than ∼15 μm.Glass transition temperatures, T g , are determined as the intersection of a baseline and a line drawn along a step of heat capacity change, C p .T i,cr marks the crystallization of ice upon warming and T 1 and T 2 the two thermal events of (M)FCS (see text).The skewed lines truncate ice melting peaks, T m , to fit the figure.The concentration of samples is indicated.Scale bars denote heat flow through samples.
3,8Thus, in contrast to what is stated in Ref. 1, the value of T g cannot be derived from emulsion experiments.Yet, T g is derived from bulk experiments which reveal two thermal events, T 1 ≈ 204 K and T 2 ≈ 218 K, Fig.1(d).The T 1 is close to the intersection point of the extrapolated T g -and T m -curves which define the quasiinvariant point, (C g ,T g ).3,8Our T m s are similar to those reported in Ref. 1 only for concentrations up to 55 wt.% CA but colder by ∼2 and 5 K for 60 and 63 wt.% CA (not shown).Also our T g of 63 wt.% CA is ∼3 K colder than that in Ref. 1. Using our T m -and T g -values, the extrapolated T m -and T g -curves intersect between ∼203 and 205 K that is similar to T g ≈ 205 K reported in Ref. 9. (iii) Experimental procedure: The authors report the T g s of bulk 70.2 and 75 wt.%CA and emulsified 70 and 75 wt.%MA (malonic acid).The solubility limit of CA is ∼62 wt.% at 298 K 10 and that of MA is not known.