Kinetics of "melting" of sucrose crystals - Crystal Growth & Design

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Kinetics of "melting" of sucrose crystals Akihiko Toda, Ryosuke Yamamura, Ken Taguchi, Tatsuya Fukushima, and Hironori Kaji Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.8b00234 • Publication Date (Web): 13 Mar 2018 Downloaded from http://pubs.acs.org on March 14, 2018

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Crystal Growth & Design

Kinetics of "melting" of sucrose crystals

Akihiko Toda a*, Ryosuke Yamamura b, Ken Taguchi a, Tatsuya Fukushima c, and Hironori Kaji c a

Graduate School of Integrated Arts and Sciences and b School of Integrated

Arts and Sciences, Hiroshima University, Higashi-Hiroshima 739-8521, Japan c

Institute for Chemical Research, Kyoto University, Uji 611-0011, Japan

* Corresponding author, [email protected], Tel: +81-82-424-6558

1 ACS Paragon Plus Environment

Crystal Growth & Design 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Abstract Kinetics of "melting" of sucrose crystals has been examined by conventional DSC and fast-scan calorimetry in terms of the possibility of clear distinction between physical melting and chemical decomposition processes by fast scan up to 10,000 K s-1.

On the

basis of a modeling of the crystal melting kinetics with superheating and possible influence of thermal lag, the heating rate dependence of "melting" was carefully examined. The equilibrium melting point TM of sucrose crystals at zero heating rate was estimated to be TM=188.91.2℃ by fast-scan calorimetry and the heat of fusion of 46 kJ mol-1 was determined by conventional DSC, which are in agreement with the reported values in literatures. The Kissinger plot of the peak temperatures by heating runs and the plot of characteristic times of isothermal runs against the inverse of absolute temperature suggested a kinetic diagram, in which the "melting" behaviors above and below TM are qualitatively different with purely physical melting above TM and "melting" initiated by chemical decomposition at active sites below TM.


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1. Introduction Sucrose crystal is known to have quite broad melting region of temperature [1-9]. Reported equilibrium melting points scatter below 190℃, and it can melt at much lower temperatures as 160℃ under isothermal conditions.

It has been supposed that the broad

melting region is basically due to chemical decomposition of sucrose molecules accompanying the physical melting of their crystalline state, which has been experimentally verified by chromatography and thermogravimetric analysis [3,6].

Eapp1

4 3  2

Eapp2

-1

T /K



Ln kLn c

TT0 



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

-1

Figure 1. Schematic drawing of an Arrhenius plot of reaction kinetics (the rate coefficient k inversely proportional to the characteristic time of kinetics c) with two processes coexisting in the temperature range. Dotted lines represent the passages by a temperature scan at constant rate, in the time-temperature domain.

Melting of organic and polymeric materials and of chemical compounds can be accompanied by degradation and/or decomposition, and hence the examination of physical melting process needs careful attention to make a distinction between physical and chemical processes.

Figure 1 shows a schematic drawing of an Arrhenius plot of

chemical reaction kinetics showing possible occurrence of two processes having different (apparent) activation energies of Eapp1 and Eapp2.

In this case, kinetics of those two

reactions shows a crossover behavior, depending on the isothermal temperature or on the applied rate of heating.

If the melting and decomposition processes behave in this

manner with the melting kinetics having an apparent activation barrier higher than that of decomposition (Eapp1>Eapp2), we can examine the meting process without the influence of decomposition by applying heating rate fast enough or isothermally at temperature high enough, as shown in Fig. 1. Some of recent studies [10-14] of melting by fast-scan calorimetry with chip sensor, with which heating rates in the range of 10,000 K s-1 can be 3 ACS Paragon Plus Environment


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applicable, are based on this expectation and successfully showed reliable melting data. Present examination of sucrose melting will be one more application of this strategy for the investigation of pure melting by fast scan. In prior studies of melting by thermal analysis in general, it has been assumed that the melting is completed at a constant temperature, i.e. equilibrium meting point, without superheating.

This expectation is not always correct and the melting velocity under

superheated states has been examined for some inorganic compounds [15]. In our recent studies [16-20], we have also reported superheated melting kinetics of a number of polymer crystals.

In the thermal analysis, the endothermic peak of polymer crystal

melting shifts to higher temperature in a predicted manner as superheating of the melting kinetics, and the melting under superheated state was in accordance with the direct observation of melting of polymer single crystals in the bulk melt [17].

In thermal

analysis, instrumental thermal lag is another factor causing an apparent shift of the peak to higher temperature.

Therefore, we need careful examination of the heating rate

dependence of the melting peak especially with fast scan for the determination of the equilibrium melting point, which should be the melting point at zero heating rate, so called zero-entropy-production melting point of the crystals in equilibrium with surrounding melt [21]. In terms of the melting and decomposition kinetics, it is usually supposed that the decomposition in the molten state is much easily activated than the process in the crystalline state in which molecules are regularly packed each other, so that it is not self-apparent whether those processes of melting and decomposition show similar crossover behavior as predicted from Fig. 1, namely whether the chemical decomposition can precede the physical melting at temperatures lower than the equilibrium melting point, as has been supposed for the sucrose melting at low temperatures. The aim of the present paper covers those subjects.

Firstly, by examining the

heating rate dependence of the physical melting kinetics on the basis of our modeling, we try to determine the equilibrium melting point of sucrose with a fast-scan calorimeter. Secondly, the "melting" behavior in the low temperature region is examined on the basis of the kinetic diagram such as shown in Fig. 1.


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2. Experimental Granular crystalline sucrose (≥99.5%) was purchased from Sigma-Aldrich. The melting behavior was examined by conventional differential scanning calorimetry (CDSC), DSC2920 (TA Instruments), and by fast-scan calorimetry (FSC), FlashDSC1 (Mettler-Toledo) with a chip sensor, UFS1; refrigerated cooling system was not used with both DSCs, and dry nitrogen gas with a flow rate of 50 and 30 mL min-1, respectively, was purged through the cell. In order to reduce sample size for FSC, powder samples were prepared by grinding granular sucrose with a mortar and pestle, and the powder samples were examined by conventional DSC as well as FSC.

The powder samples have been

stored under vacuum at 60℃ before the examination in order to reduce the influence of absorbed moisture. In order to set similar circumstances for CDSC and FSC and to avoid disturbance in CDSC signal by explosion or deformation on decomposition, powder sample in a pan was open for purge gas without crimping the pan, when examined by CDSC in the same way as FSC.

The heating rate ranges examined were  = 0.1–120 K

min-1 and 0.5–10,000 K s-1 by CDSC and FSC, respectively.

Melting of a standard

material, indium, was also examined as reference. Temperature calibration was done by the melting onset temperature of indium extrapolated to zero heating rate to be 156.6℃ for both of CDSC and FSC. Because indium only has a weak contact with sensor surface of FSC, we could easily remove it after the measurement of its melting on the chip sensor to be used for the melting of sucrose. By FSC, same chip sensor could be used repeatedly for sucrose melting if we raise temperature high enough above 400℃ for sucrose evaporation.

3. Results and Discussion Figure 2 shows typical results of isothermal and heating runs of sucrose by CDSC and FSC. The first endothermic peak corresponds to the "melting" of sucrose crystallites and the second one to decomposition, which are judged by the sample appearance and the measurement of mass loss after each run with preset time interval in the isothermal runs by CDSC.

The mass loss followed the following evolution: negligible mass loss after the

end of the 1st peak, about 2% at the peak position of the 2nd peak, and about 10% at the end of the 2nd peak. It is also noted that the second peak always followed the first one



with FSC as well as CDSC; in Fig. 2b, only the rising part of the second peak of FSC is

CDSC o iso.@165 C

0.05 mW

HF

shown.

(a)

0

100

200

t /min

HF /a.u.

300

-1

CDSC/K min 0.15 60 -1 FSC/K s (b) 6000

endo.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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150

200

250

o

300

350

400

T/C

Figure 2. Endothermic heat flow on "melting" of sucrose crystals examined by (a) isothermal and (b) heating measurements at the respective conditions indicated.

Both of the 1st and 2nd peaks appeared in the whole range of temperatures examined, including the range below the equilibrium melting point TM which is supposed to be at around 185–190℃ [1], as shown in Figs. 2a and 2b.

Therefore, the term

"melting" with quotation marks refers to both of purely physical melting above TM and the melting accompanied or possibly preceded by chemical decomposition below TM.

With

faster heating runs shown in Fig. 2b, both of the peaks shift to higher temperature, and the temperature interval between them becomes larger, as we expected from the schematic drawing of Fig. 1. It proves that the application of fast scan by FSC is effective in the separation of physical melting from chemical decomposition.

However, the

decomposition peak always follows subsequently after the 1st peak of "melting", so that purely chemical decomposition below TM does not precede as an endothermic peak, against the expectation of the kinetic diagram of Fig. 1; this subject will be discussed later in terms of the kinetic diagram. Figure 3 shows typical raw data obtained by FSC at several different heating rates. The peak shifts to higher temperature with faster applied heating rate with the shifts of both of the onset and peak temperatures. In other words, at slower heating rates, the onset


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and peak temperatures becomes close to each other, as we expect for the melting of a pure

HF/a.u.

one-component system having single melting point.

sucrose /Ks

-1

    

180

200

220

o

240

260

280

T/C

Figure 3. Endothermic heat flow on melting of sucrose crystals examined by FSC at the respective heating rates indicated. 230

CDSC peak onset

220 210

o

T/C

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

2 mg

200 190 180

FSC peak onset

170 160 10

-3

10

-2

10

-1

10

0

1

10 -1

10

2

10

3

10

4

 /Ks

Figure 4. Semi-logarithmic plot of the heating rate dependence of the onset and peak temperatures of the 1st peak of sucrose "melting" examined by CDSC and FSC; CDSC data are for samples with the mass indicated and FSC data are the extrapolated ones to zero sample mass in the plots as shown in Fig. 5.

Figure 4 shows the heating rate dependence of the 1st peak of "melting" obtained by CDSC and FSC. In the temperature region above TM ~185–190℃, we suppose the 1st peak representing purely physical melting. In this region, the data points obtained by FSC and CDSC are not in agreement; at the same heating rate, Fig. 4 suggests higher peak and onset temperatures with CDSC than with FSC.

We think that this behavior is simply

due to instrumental thermal lag Tlag with CDSC, which is represented as follows on the



basis of the Mraw's model of DSC describing it as a lumped parameter circuit of thermal resistances and heat capacities of the parts [19,22,23],

Tlag  Rs [ Cpan  m( csuc  f )]  i

(1)

where Rs represents the thermal contact resistance between sample pan and the stage, Cpan heat capacity of sample pan, m, csuc, and f sample mass, specific heat, and specific heat flux of kinetics, respectively, and i a time constant of instrumental delay of signal. In this expression, first of all, Rs of CDSC will be much higher than that of FSC because of poor thermal contact between sample pan and the stage in comparison with the direct contact of sucrose with the sensor surface in FSC. Second origin of larger thermal lag of CDSC will be the heat capacity of aluminum sample pan Cpan which is much larger than that of sucrose examined by CDSC; Cpan ~38 J K-1 in comparison with mcsuc ~2.5 J K-1 for the sucrose mass of 2 mg. Negligible difference of the data with 1 and 2 mg sucrose in CDSC results of Fig. 4 in the temperature range above 185–190℃ also confirms the strong influence of Cpan in thermal lag.

0.0

(a)

(b) 220

-1

-0.4

-0.6 200

o

o

1500 K s Hf /J 0.2 0.8 1.9 2.5 4.1 7.5

-0.2

T/C

HF /mW

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Tpeak

210

Tonset

200

-1

1500 K s

250

0

2

T/C

4

Hf /J

6

8

Figure 5. Typical examples of the sample mass dependence of (a) the raw data of melting peaks and (b) the onset and peak temperatures of the 1st peak of sucrose melting examined by the heating runs of FSC at 1500Ks-1.

The x-axis in (b) is the integrated heat of fusion in

proportion to sample mass; 1 J of heat of fusion corresponds to 7.5 ng of sample mass.

In terms of FSC, the results are also influenced by thermal contact between a sucrose powder particle and sensor surface. The resistance is uncontrollable and will be different for each powder particle examined in each run, and hence the quantitative evaluation of the resistance will be impossible. As an alternative method for the evaluation of instrumental thermal lag in FSC, we have examined a number of powder particles in terms of the mass dependence of the onset and peak temperatures and utilized the values linearly extrapolated 8 ACS Paragon Plus Environment

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to zero mass; on the basis of eq. (1) without the contribution of Cpan for FSC, the temperatures extrapolated to zero mass will be free from the thermal lag related to the thermal contact resistance.

Figure 5 shows typical results of mass dependence at a fixed

heating rate. As shown in Fig. 5a, with decreasing sample mass, peak height becomes smaller, while the peak keeps an intrinsic width characterizing the melting kinetics even approaching to zero sample mass.

We have done the same examination at each heating

rate, and the extrapolated temperatures are shown in Fig. 4 and utilized in the following analysis; all results of sample mass dependence are in Supporting Information.

Melting kinetics and the zero-entropy-production melting point 200

(a)

T/C

195 o

o

T/C

(b)

200

190

180

CDSC peak onset

170

160

0

20

40

60

80

 / K min

100

190

185

120

0.0

0.2

0.4

0.6

(/0)0.5

-1

0.8

1.0

0130 K min

-1

Figure 6. Heating rate dependence of CDSC results of Fig. 4 in (a) linear plot and (b) the plot against 0.5. 230

230

(a) FSC

(b) 220

210

o

o

T/C

220

T/C

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


210

200

200

peak onset

190 0

2000

4000

6000

 /Ks

8000

190

10000 0.0

0.2

0.4

0.6 0.4

-1

(/0)

0.8

1.0 -1

011,000 K s

Figure 7. Heating rate dependence of FSC results of Fig. 4 in (a) linear plot and (b) the plot against 0.4.



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Figures 6 and 7 show the examination of the melting kinetics based on the following expressions of our modeling [19], Tonset  TM  Ao  z  Bo  Tpeak  TM  Ap  z  Bp  w

(2)

where the 2nd and 3rd terms in the right hand side represent the shifts due to superheating of melting kinetics and due to thermal lag, respectively. Firstly, based on our modeling of melting kinetics, the power z and coefficients Ao and Ap, which characterize the  dependence of Tonset and Tpeak, are determined by the superheating dependence of the melting rate coefficient R of a 1st-order kinetic equation in terms of crystallinity  on melting, expressed as follows [16-20],

ɺ  R   y R  a (T )

(3)

where T represents the degree of superheating, and a and y are the coefficient and power characterizing the melting kinetics; y =1 means proportional dependence corresponding to an ideal melting without kinetic barrier, and increasing y from unity represents larger kinetic barrier, such as of a nucleation. On heating at a constant rate , eq. (3) with T = t can be integrated, and the endothermic melting peak which is in proportion to ɺ of eq. (3) is expressed as follows with the characteristic time c t y  1  y 1 /( y 1) ɺ  a ( t)y 0 exp[( ) y 1 ] with c  (  ) a c

(4)

Then, the shift Tshift in the melting peak to higher temperature due to superheating of the kinetics is given as,

Tshift  c  (

y  1 1 /(y 1) )  A z a

(5)

which corresponds to the second term in the right hand side of eq. (2). Therefore, for the range of y ≥1, eq. (5) predicts z ≤1/2. On the other hand, on the basis of the Mraw's model of DSC [19,22-24], the third term of the onset temperature in eq. (2) is linearly dependent on the applied heating rate, while the power w of Tpeak is predicted to be in the range between 1/2 and 1 depending on sample mass; w =1 with smaller sample mass and w =1/2 with larger mass due to the influence of latent heat on melting [19].

Those

behaviors have been confirmed with crystal melting of a number of polymers [18-20] and a 10 ACS Paragon Plus Environment

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standard material, indium [19] which is supposed to melt without superheating, examined by CDSC and FSC. When we examine the heating rate dependences of Tonset and Tpeak plotted against the x-axis in the form of z, as shown in Figs. 6b and 7b, we utilize this power z as an adjustable parameter for the best fit linear straight lines. Then, the determined power will be an effective power including both of the effects of melting kinetics and thermal lag, so that the acceptable range of the power will be in between zero and unity.

It is noted that

for the fitting in Fig. 6b by CDSC, only the data points with heating rates above the vertical straight line were utilized in order to examine purely physical melting kinetics, though we admit that there is an ambiguity in the choice of the lower limit. On the other hand, in Fig. 7b by FSC, all data were utilized because we suppose that the lower limit of heating rate 0.5 K s-1 = 30 K min-1 will be fast enough. As shown in Figs. 6b by CDSC and 7b by FSC, both of Tonset and Tpeak could be well fit by the same powers of 0.5 and 0.4, respectively; the best fit values of z for Tonset and Tpeak are 0.47 and 0.64 in Figs. 6b by CDSC, and 0.43 and 0.34 in Figs. 7b by FSC, respectively. Considering the scatter in the data points especially with FSC, those values are close to each other but the power of CDSC is slightly larger most probably due to the influence of the 3rd term in eq. (2), i.e. thermal lag. Then, in terms of the melting kinetics suggested by the power z =0.40.5, the T dependence of the melting rate R in eq. (3) will be slightly stronger than linear dependence of y =11.5.

It means that the melting

kinetics of sucrose has small kinetic barrier, but is basically close to that of ideal melting. The y-axis intercept of the plots in Figs. 6b and 7b is the melting temperature at zero heating rate, so-called zero-entropy-production (ZEP) melting point, which is the melting point of crystals under equilibrium with surrounding melt, TM in eq. (2).

Figures 6b by

CDSC and 7b by FSC, give TM ~184.9, 185.8℃ in Figs. 6b and 187.7 and 190.1℃ in Figs. 7b, as the extrapolated temperatures of Tonset and Tpeak, respectively; when utilizing the best fit values of z for Tonset and Tpeak, TM ~184.5, 187.6℃ in Figs. 6b, 188.1, and 188.1℃ in Figs. 7b, respectively. Those extrapolated temperatures of Tonset and Tpeak as well as the power z for the fitting by straight lines are in good agreement in Figs. 6b and 7b, suggesting the successful application of the analysis to sucrose melting, which will have a single equilibrium melting point. This behavior is in clear contrast to polymer crystal melting, in which the extrapolated temperature of Tpeak is much higher than that of Tonset 11 ACS Paragon Plus Environment


[19], because the ZEP melting point of polymer crystals is the melting points of chain-folded lamellar crystals and is supposed to have a broad distribution. The reason for the discrepancy of about 4℃ between TM determined by CDSC and FSC may be possibly due to the choice of the lower limit of heating rate for the linear fitting in Fig. 6b of CDSC data. If it is the case, we should rely on the value obtained by FSC, and hence in concluding the analysis of purely physical melting, present results suggest TM ~188190℃ by FSC, which is in the ranges of the reported value in literatures [1-9]. In one of the prior trials of the determination of melting point of the substances which decompose [1], quick temperature jump was applied by placing the sample on a hot plate with temperature gradient, and concluded TM =189℃ of sucrose.

Obviously, quick

temperature jump will be the reason for the agreement with the present result determined by fast scan. In terms of the heat of fusion, it is determined from the integrated 1st peak of CDSC to be 130 J g-1 = 46 kJ mol-1, which is also in good agreement with the reported values [25].

Kinetic diagram of sucrose "melting" 200

-5

-2

-1

o

160 C

Heating 10 FSC CDSC C 2nd Isothermal FSC 5 CDSC C 2nd

(TM)-1

-1

Ln[(Tpeak) /K min ]

0

180

-10

0

(a)

(TM ) 1

Ln kLn 

220

Ln[ /min]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Physical melting

Chemical decomposition

‘‘Melting’’

(b)

-15

-5 2.0

2.1

T

-1

3

10 /K

2.2 -1

2.3

-1

-1

T /K

Figure 8. (a) Kissinger plot of heating runs and the semi-logarithmic plot of characteristic time of isothermal runs against the inverse of temperature, obtained by the respective measurements indicated; "C 2nd" means the 2nd peak obtained by CDSC. corresponding kinetic diagram.

(b) Schematic drawing of

The logarithmic y-axes in (a) are set to be in the same scale.

Figure 8a includes the replot of the data shown in Fig. 4: the Kissinger plot [26] of the peak temperatures obtained by heating runs and the semi-logarithmic plot of the 12 ACS Paragon Plus Environment

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characteristic time  obtained by isothermal runs against the inverse of absolute temperature. It is noted that the characteristic times of isothermal runs are the peak times of CDSC as shown in Fig. 2a, which are obtained below the physical melting point TM ~188190℃, and the relaxation time of endothermic heat flow on melting examined by FSC above TM; the details of isothermal melting by FSC will be discussed later. As shown in the schematic kinetic diagram of Fig. 8b, the results clearly indicate that the 1st peak of "melting" behaves in a different manner above and below TM.

Above TM,

physical melting kinetics does not follow a straight line predicted for a chemical reaction kinetics in the Kissinger plot and seems to completely halt at TM. Hence, the melting behaviors above TM should be analyzed on the basis of purely physical melting kinetics, as done in the above. On the other hand, below TM, both of the 1st and 2nd peaks seem to follow straight lines. In addition, the temperature dependences of the Kissinger plot of heating runs and of the peak time peak of isothermal runs are in good agreement, indicating the same activation barriers for heating and isothermal runs.

The slopes of the fitting straight lines

of the 1st peak below TM and the 2nd peak in the whole temperature range correspond to apparent activation energies Eapp as follows: 220, 224, 144, and 161 kJ mol-1 for the 1st peak with heating and isothermal runs, and the 2nd peak with heating and isothermal runs, respectively. There are small difference in Eapp between the 1st and 2nd peaks, but it seems that the "melting" kinetics below TM is mainly driven by the chemical decomposition kinetics, as schematically shown in the diagram of Fig. 8b.

As mentioned

in Introduction, it is usually supposed that the decomposition in the molten state is much easily activated than in the crystalline state. Then, for the "melting" below TM initiated by chemical decomposition of crystalline state, we would suppose relatively higher activation barrier and the role of crystal surface, crystal defects, and inclusions as active sites for decomposition process [7,8]. The decomposed molecules will be in a molten state, and can behave as solvent for sucrose crystal dissolution below TM, as has been hypothesized in literatures [7,8]. Present results shown in Fig. 8 in terms of the behaviors of the 1st peak of "melting" below TM and the 2nd peak of chemical decomposition will support this scenario. It is finally noted in terms of the influence of thermal lag that the Kissinger plot is against the inverse of absolute temperature, while several degrees of superheating is analyzed in the melting kinetics.

Therefore, in comparison with the



analysis of melting kinetics, that of Kissinger plot will not be seriously influenced by thermal lag. Isothermal physical melting above TM Crystal melting has been mostly examined under heating conditions by thermal analysis, because of quite fast process of melting under isothermal conditions with negligible degrees of superheating.

By fast-scan calorimetry, with the applicability of nearly

instantaneous temperature jump in the order of ms, we have an access to the isothermal melting if the melting undergoes appreciable superheating on heating runs, as in the case of sucrose crystal melting. 0

HF /W

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 18

-10

-20

-30 0.0

0.5

t /s

1.0

Figure 9. Typical examples of the endothermic heat flow on isothermal melting at 195℃. Broken lines are the fitting by an exponential decay function.

Figure 9 shows three examples of endothermic heat flow on isothermal melting. Due to uncontrollable thermal contact resistance between a sucrose powder particle and sensor surface, the time evolution of melting differs substantially for each particle. But the general trend suggests the endothermic heat flow starting from the beginning of isothermal runs, which indicates no induction time for melting and shows a remarkable contrast with the isothermal behavior of "melting peak" below TM as shown in Fig. 2a. The kinetic equation of eq. (3) with constant rate coefficient R(T) under isothermal conditions with constant T predicts an exponential decay with time of the heat flow in proportion to ɺ , as follows,

ɺ  R0 exp[Rt]

(6)

In Fig. 8, as a rough estimate, the mean relaxation time =1/R is plotted against the inverse of absolute temperature with error bars representing large scatter in the relaxation times probably due to the uncontrollable thermal contact. Nevertheless, the plots of the mean 14 ACS Paragon Plus Environment

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time in Fig. 8 show good agreement with the results of peak temperatures in the heating runs of the Kissinger plot by utilizing the same y-axis adjustment as the peak times of isothermal runs below TM.

4. Conclusions For the "melting" of sucrose crystals with broad melting region, we have tried to determine the equilibrium melting point at zero heating rate by examining the heating rate dependence of melting peak with a fast-scan calorimeter. TM ~188190℃ determined by fast-scan calorimetry is in agreement with the reported value in literatures.

By utilizing

fast scan and on the basis of our modeling of the melting kinetics, it is confirmed that the melting rate is nearly proportional to the degree of superheating, which is the kinetics without large barrier as an ideal melting. In terms of the "melting" behaviors above and below TM, a kinetic diagram is constructed from the Kissinger plot of peak temperatures by heating runs and the Arrhenius plot of characteristic times by isothermal runs, which are semi-logarithmic plots against the inverse of absolute temperature. The diagram clearly suggests the "melting" below TM controlled by a chemical reaction kinetics, and supports the scenario of "melting" initiated at active sites of decomposition, i.e. probably at crystal surface, crystal defects, and inclusions, as has been hypothesized in literatures. Above TM, the melting should be analyzed as a physical 1st-order phase transition kinetics, which is characterized by the degree of superheating, i.e. by the distance from TM, not by the inverse of absolute temperature of chemical reaction kinetics.

Supporting Information Sample mass dependence of the onset and peak temperatures of the 1st peak of sucrose melting examined by the heating runs of FSC at the heating rates shown in Fig. 4.

Acknowledgements Part of this work was supported by the Collaborative Research Program of Institute for Chemical Research, Kyoto University [2014-86] and by the Grants-in-Aid for Scientific Research -KAKENHI- from the Ministry of Education, Culture, Sports, Science and Technology of Japan [JP16H04206]. 15 ACS Paragon Plus Environment


References: [1] Kofler, L; Sitte, H; Zur Schmelzpunktbestimmung von Substanzen, die unter Zersetzung schmelzen. Monatsh. Chem. 1950, 81, 619–626. [2] Kumaresan, R; Babu, S.M.; Crystal growth and characterization of sucrose single crystals. Mater. Chem. Phys. 1997, 49, 83-86. [3] Hurtta, M.; Pitkänen, I.; Knuutinen, J.; Melting behaviour of D-sucrose, D-glucose and D-fructose. Carbohydr. Res. 2004, 339, 2267–2273. [4] Kishihara, S.; Okuno, M.; Fujii, S.; Kawasaki, K.; Nishiura, T.; An opinion on structure of sucrose crystal. Proc. Res. Soc. Jpn. Sugar Refin. Technol. 2001, 49, 1-8. [5] Lee, J.W.; Thomas, L.C.; Schmidt, S.J.; Investigation of the Heating Rate Dependency Associated with the Loss of Crystalline Structure in Sucrose, Glucose, and Fructose Using a Thermal Analysis Approach (Part I) . J. Agric. Food. Chem. 2011, 59, 684–701. [6] Lee, J.W.; Thomas, L.C.; Jerrell, J.; Feng, H.; Cadwallader, K.R.; Schmidt, S.J.; Investigation of Thermal Decomposition as the Kinetic Process That Causes the Loss of Crystalline Structure in Sucrose Using a Chemical Analysis Approach (Part II) . ibid. 2011, 59, 702–712. [7] Roos, Y.H.; Franks, F.; Karel, M.; Labuza, T.P.; Levine, H.; Mathlouthi, M.; Reid, D.; Slade, L.; Comment on the Melting and Decomposition of Sugars. ibid. 2012, 60, 10359–10362. [8] Roos, Y.H.; Karel, M.; Labuza, T.P.; Levine, H.; Mathlouthi, M.; Reid, D.; Shalaev, E.; Slade, L.; Melting and Crystallization of Sugars in High-Solids Systems. J. Agric. Food. Chem. 2013, 61, 3167-3178. [9] Magoń, A.; Wurm, A.; Schick, C.; Pangloli, Ph.; Zivanovic, S.; Skotnicki, M.; Pyda, M.; Heat capacity and transition behavior of sucrose by standard, fast scanning and temperature-modulated calorimetry. Thermochim. Acta 2014, 589, 183–196. [10] Cebe, P.; Hu, X.; Kaplan, D.L.; Zhuravlev, E.; Wurm, A.; Arbeiter, D.; Schick, C.; Beating the heat - fast scanning melts silk beta sheet crystals. Sci. Rep. 2013, 3, 1–7. [11] Furushima, Y.; Nakada, M.; Takahashi, H.; Ishikiriyama, K.; Study of melting and crystallization behavior of polyacrylonitrile using ultrafast differential scanning calorimetry. Polymer 2014, 55, 3075–3081. [12] Corvis, Y.; Wurm, A.; Schick, C.; Espeau, P.; Vitreous state characterization of pharmaceutical compounds degrading upon melting by using fast scanning calorimetry. J. Phys. Chem. B 2015, 119, 6848–6851 [13] Cebe, P.; Partlow, B.P.; Kaplan, D.L.; Wurm, A.; Zhuravlev, E.; Schick, C.; Fast scanning calorimetry of silk fibroin protein: sample mass and specific heat capacity 16 ACS Paragon Plus Environment

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determination, in: C. Schick, V. Mathot (Eds.), Fast Scanning Calorimetry, Springer International Publishing, Cham, 2016, pp. 187–203. [14] Abdelaziz, A.; Zaitsau, D.H.; Mukhametzyanov, T.A.; Solomonov, B.N.; Cebe, P.; Verevkin, S.P.; Schick, C.; Melting temperature and heat of fusion of cytosine revealed from fast scanning calorimetry. Thermochim. Acta 2017, 657, 47–55. [15] Fang, C.Y.; Uhlmann, D.R.; The process of crystal melting II. Melting kinetics of sodium disilicate. J. Non-Cryst. Solids 1984 64, 225–228. [16] Toda, A.; Hikosaka, M.; Yamada, K.; Superheating of the melting kinetics in polymer crystals: a possible nucleation mechanism. Polymer 2002, 43, 1667–1679. [17] Toda, A.; Kojima, I.; Hikosaka, M.; Melting kinetics of polymer crystals with an entropic barrier. Macromolecules 2008, 41, 120–127. [18] Toda, A.; Taguchi, K.; Nozaki, K.; Konishi, M.; Melting behaviors of polyethylene crystals: An application of fast-scan DSC. Polymer 2014, 55, 3186–3194. [19] Toda, A.; Heating rate dependence of melting peak temperature examined by DSC of heat flux type. J. Therm. Anal. Calorim. 2016, 123, 1795–1808. [20] Toda, A.; Androsch, R.; Schick, C.; Feature article: Insights into polymer crystallization and melting from fast scanning chip calorimetry. Polymer 2016, 91, 239–263. [21] Wunderlich, B.; Macromolecular physics, vol. 3. Academic Press, New York, 1980, Ch. 9. [22] Mraw, S.C.; Mathematical treatment of heat flow in differential scanning calorimetry and differential thermal analysis instruments. Rev. Sci. Instrum. 1982, 53, 228–231. [23] Saito, Y.; Saito, K.; Atake, T.; Theoretical analysis of heat-flux differential scanning calorimetry based on a general model. Thermochim Acta. 1986, 99, 299-307. [24] Illers, K-H.; Die ermittlung des schmelzpunktes von kristallinen polymeren mittels warmeflusskalorimetrie (DSC) . Eur. Polym. J. 1974, 10, 911–916. [25] Sopade, P.A.; Kearsley, M.W.; Legrys, G.A.; Heat of melting of sucrose. Int. Sugar J. 1988, 90 (1070), 38–38. [26] Kissinger, H.E.; Reaction kinetics in thermal analysis. Anal. Chem. 1957, 29, 1702–1706.



For Table of Contents Use Only

Kinetics of "melting" of sucrose crystals

Akihiko Toda*, Ryosuke Yamamura, Ken Taguchi, Tatsuya Fukushima, and Hironori Kaji

220

200 -1

(TM)

-5

-2

-1

-1

Ln[(Tpeak) /K min ]

0

180

o

160 C

Heating 10 FSC CDSC C 2nd Isothermal FSC 5 CDSC C 2nd

-10

0

-15

Ln[ /min]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 18

-5 2.0

2.1

T

-1

3

10 /K

2.2 -1

2.3

Synopsis: Kinetics of "melting" of sucrose crystals showed distinctive behaviors below and above the equilibrium melting point TM; the examination of the melting kinetics could be achieved by utilizing fast-scan calorimetry (FSC) up to 10,000 K s-1.


Kinetics of "melting" of sucrose crystals - Crystal Growth & Design

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