study, state diagram of broccoli was developed considering freezing curve, glass line, maximal-freeze-concentration conditions, solids-melting and BET-monolayer line. The freezing point, glass transition and solidsmelting were measured and modeled by Chen’s model, Gordon-Taylor model, and Flory-Huggins model, respectively. The ultimate maximal-freeze-concentration conditions (Tm′)u (i.e. end temperature of freezing) and (Tg′′′)u [i.e. end glass transition at (Tm′)u] were found as −30.0 °C and −32.2 °C, respectively, and solids content (i.e. Xs′) at this point was 0.70 g/g sample. The solids-water interaction (χ) during melting was estimated as 0.69 (dimensionless) from Flory-Huggins model, and BET-monolayer was observed as 0.089 g/g dry-solids at 20 °C.

1. Contents lists available at ScienceDirect
Thermochimica Acta
journal homepage: www.elsevier.com/locate/tca
Thermal characteristics and state diagram of freeze-dried broccoli: Freezing
curve, maximal-freeze-concentration condition, glass line and solids-melting
Sithara Suresh
⁎
, Nasser Al-Habsi, Nejib Guizani, Mohammad Shafiur Rahman
Department of Food Science and Nutrition, College of Agricultural and Marine Sciences, Sultan Qaboos University, P.O. Box-34, Al-Khoud-123, Muscat, Oman
A R T I C L E I N F O
Keywords:
BET- monolayer
Glass transition
Maximal-freeze-concentration condition
Solids-melting temperature
A B S T R A C T
Stability of foods during processing and storage can be determined from their phase and state diagrams. In this
study, state diagram of broccoli was developed considering freezing curve, glass line, maximal-freeze-con-
centration conditions, solids-melting and BET-monolayer line. The freezing point, glass transition and solids-
melting were measured and modeled by Chen’s model, Gordon-Taylor model, and Flory-Huggins model, re-
spectively. The ultimate maximal-freeze-concentration conditions (Tm′)u (i.e. end temperature of freezing) and
(Tg′′′)u [i.e. end glass transition at (Tm′)u] were found as −30.0 °C and −32.2 °C, respectively, and solids content
(i.e. Xs′) at this point was 0.70 g/g sample. The solids-water interaction (χ) during melting was estimated as 0.69
(dimensionless) from Flory-Huggins model, and BET-monolayer was observed as 0.089 g/g dry-solids at 20 °C.
1. Introduction
A state diagram is a stability map presenting different states or
phases of a food or biomaterial as a function of water (or solids) content
and temperature [1–3]. This diagram helps in understanding the com-
plex changes that occur during treatments, processing and storage [4].
The possible processing path of extrusion, tempering or annealing
[5,6], drying [7–10], baking [11], sugar hydrolysis [12] and freezing
[7,4] processes could be easily visualized in the state diagram and can
be used to select the best possible processing path for achieving desired
properties.
Recently, broccoli has gained considerable attention due to its
health-promoting ability, such as prevention of carcinogenic and car-
diovascular disorders. It contains bioactive phytochemicals such as ni-
trogen-sulfur compounds (glucosinolates and isothiocyanates), phenolic
compounds (chlorogenic and sinapic acid derivates and flavonoids) and
nutrients (mainly vitamin C, E, A and K, and the essential minerals N, K,
Ca, Fe) [13]. State diagram of broccoli could help in determining the
stability of its active components during cooking, baking, drying and
freezing processes as well as during storage as fresh, cooked, dried or
frozen conditions. However, there is negligible information currently
available in the literature on the freezing point, glass transition and
state diagram of broccoli.
The first state diagram in the food science literature was most
probably proposed by Levine and Slade [1] by presenting glass line (i.e.
glass transition as a function of solids content), freezing curve (i.e.
freezing point as a function of solids content) and the maximal-freeze-
concentration conditions as an intersection point between glass line and
freezing curve. In the literature, mainly the state diagram of sugar
based foods or pure food components are presented as compared to
complex foods, such as vegetables (i.e. cellulose based), meat and fish
(i.e. protein based). The state diagram of sucrose [14], glucose [2],
onion, grape and strawberry [15], apple [16], pineapple [17], mango
[18], arabinoxylan [19], pomegranate peel water-extract [20], bac-
terial suspension [21], spaghetti [22], date-fruit flesh [23,24], and
gelatin [25] were developed by measuring freezing curve, glass line and
maximal-freeze-concentration conditions. In addition to the above
mentioned parameters, solids-melting line was included in the state
diagram for the gelatin [26], instant artificial rice [27]. Rahman [28]
proposed to combine glass transition and water activity concepts in the
state diagram by plotting BET-monolayer line in the state diagram, and
this could be a powerful tool since most significant theoretical concepts
(i.e. water activity and glass transition) for food stability are combined
in the proposed state diagram [3]. Zhao et al. [18] also emphasized to
include BET-monolayer line in the state diagram. To the best of our
knowledge, there is no state diagram developed for foods incorporating
glass line, freezing curve, maximal-freeze-concentrated conditions, so-
lids-melting, and BET-monolayer line. The main objective of this study
was to develop a state diagram for broccoli by measuring its freezing
curve, maximal-freeze-concentration conditions, glass and solids-
melting lines, and BET-monolayer line.
http://dx.doi.org/10.1016/j.tca.2017.06.015
Received 29 October 2016; Received in revised form 6 April 2017; Accepted 19 June 2017
⁎
Corresponding author.
E-mail addresses: sitharasuresh88@gmail.com, shafiur@squ.edu.om (S. Suresh).
Thermochimica Acta 655 (2017) 129–136
Available online 20 June 2017
0040-6031/ © 2017 Elsevier B.V. All rights reserved.
MARK

2. 2. Materials and methods
2.1. Materials
Five kg fresh broccoli (Brassica oleracea, variety: Calabrese) grown
in Oman were purchased from local super market and stored at re-
frigerated condition (4 °C). Only florets were cut from the bunch and
were placed into 50 ml plastic containers. These florets were then
frozen at −40 °C for at least 18 h. The frozen florets in the plastic
containers were freeze dried at 20 °C (i.e. process started from −40 °C
at the surface and ended at the 20 °C starting from surface to the center)
under a vacuum of 200 Pa for 4 days using an Edwards K4 Freeze Dryer
(Corawky, Crawley, England). Freeze-dried florets were then ground
into powder using a KMF grinder (KIKA Werke, Wilmington, USA). The
pH value was recorded using pH meter (EUTECH Cyberscan pH 11,
Singapore) from broccoli-water mixture (i.e., 10 g broccoli in 100 ml
distilled water). Moisture, protein, fat, ash, and crude fiber were ana-
lyzed using the standard methods of the International Official Methods
of Analysis [29]. Carbohydrate was calculated by subtracting total of
moisture, protein, fat, and ash contents from 100.
2.2. Moisture adsorption isotherm
Moisture adsorption isotherm of freeze-dried broccoli was measured
by static isopiestic method [30,31]. Freeze dried broccoli samples of
2–3 g were stored in 8 different air-tight aluminum cells maintained at
different relative humidity values. These cells were stored in chilled
room set at 5, 20, and oven set at 45, 60 and 80 °C. The desired relative
humidity in each cell was created using saturated salt solution in a
beaker placed inside the cells. The saturated salt solutions used to
maintain relative humidity were: lithium chloride, potassium acetate,
magnesium chloride, potassium carbonate, magnesium nitrate, sodium
bromide, strontium chloride and potassium chloride. The water activity
values of the saturated solutions were taken from Rahman [30]. The
saturated condition was ensured by maintaining a layer of salt crystals
at the bottom of the beaker. All samples in the cells were equilibrated
until a constant mass was achieved (i.e. 3–6 weeks). Thymol in a 5 ml
beaker was also placed inside the cells to prevent the mold growth.
Isotherm data within water activity of 0.05 and 0.45 were fitted to the
theoretical BET model to determine BET-monolayer moisture content
[31–33] using the following equation:
=
− + −
M
M B a
a B a[(1 )(1 ( 1) ]
w
b w
w w (1)
where Mw and Mb are the moisture content at any water activity (aw)
and BET-monolayer moisture content (g/g dry-solid), respectively and
B is a constant related to the net heat of sorption. The BET-monolayer
water was estimated by linearized regression of Equation (1). The va-
lues of Mb was calculated from the slope (S) and intercept (I) of the
linearized regression of aw/(1-aw)Mw against aw. The value of mono-
layer can be calculated from Mb = 1/(S + I) and B = (S + I)/I [34].
2.3. Differential scanning calorimetry (DSC)
Differential Scanning Calorimetry (DSC Q20, TA Instruments, New
Castle, DE, USA) was used to measure the thermal characteristics of
broccoli florets. Mechanical refrigerated cooling system capable to cool
the sample up to −90 °C and heat up to 500 °C was used. The instru-
ment was calibrated for heat flow and temperature using distilled water
(melting point 0 °C; enthalpy, ΔHm 334 kJ/kg), and indium (melting
point 156.5 °C; enthalpy, ΔHm 28.5 kJ/kg). Aluminum Tzero pan of
40 μl (model: T140818, TA Instruments, New Castle, DE, USA), which
could be sealed with lid (model: T130823, TA Instruments, New Castle,
DE, USA) was used in all experiments. This new pan showed more
sensitivity and provided linear base line as compared to the conven-
tional hermitical sealed pan. An empty sealed pan was used as reference
and nitrogen gas at a flow rate of 50 ml/min was used as a carrier gas.
Samples of 10 mg with moisture 85.0, 80.0, 75.0, 70.0 and 60.0 g/
100 g sample were initially scanned from −90 to 250 °C (according to
the protocol as discussed later) to determine the level of moisture loss
from the sealed aluminum pans. Broccoli samples with different
moisture were prepared by adding predetermined water to 5 g freeze
dried broccoli and equilibrated at 4 °C for 24 h after mixing these
thoroughly (Xw: from 0.10 to 0.95 g/g sample) or drying in infrared
moisture analyzer (Xw: from 0.05 to 0.01 g/g sample).
2.4. Thermal analysis of samples containing un-freezable water
Sample (10 mg) (Xw: 0.25–0.01 g/g sample) was placed in an alu-
minum pan as mentioned earlier and then sealed with its lid. The
sample within the pan was cooled to −90 °C at 5 °C/min, and then kept
for 1 min. It was then scanned from −90 °C to 250 °C at a heating rate
of 10 °C/min to generate the heating DSC thermogram and thermal
characteristics of broccoli samples with un-freezable water were then
determined. A shift in the thermogram line was considered as glass
transition, an exothermic peak was considered as crystallization or
molecular ordering, and an endothermic peak was considered as solids-
melting. The glass transition shift was characterized by onset (Tgi), mid
(Tgp) and end (Tge) points; and specific heat change (ΔCp) at the tran-
sition (as clearly discussed later using experimental data). The exo-
thermic peak was characterized by onset (Tei), peak (Tep) and end (Tee)
points; and area of the peak was considered as enthalpy (ΔHe).
Similarly, solids-melting endotherm was characterized as onset (Tmi),
maximum-slope (Tmm), peak (Tmp) and end (Tme) points; and area of the
peak was considered as enthalpy (ΔHm).
The glass transition temperature needs to be modeled as a function
of solids content in order to develop glass line in the state diagram. The
on-set glass transition temperature was commonly modeled using the
Gordon-Taylor equation as [35]:
=
+
+
T
X T kX T
X kX
gi
s gs w gw
s w (2)
where Tgi, Tgs and Tgw are the onset glass temperatures of broccoli, dry-
solids broccoli, and water respectively; Xw and Xs are the mass fraction
of water and dry-solids (g/g sample) respectively, and k is the Gordon-
Taylor parameter. The solids-melting peak temperature was modeled by
Flory-Huggins equation as [36]:
⎜ ⎟ ⎜ ⎟− = ⎛
⎝
⎞
⎠
⎛
⎝
⎞
⎠
−
T T
R
ΔH
V
V
ε χε
1 1
( )
mp sp u
u
w
w w
2
(3)
where, Tmp and Tsp are the peaks of melting temperature for the
polymer (i.e. broccoli) with diluent (i.e. water), and of pure polymer
(i.e., only dry solids) (K) respectively, R is the gas constant (8.314 J/
g mol K), ΔHu is the heat of fusion for repeated polymer units in the
diluent (J/g), Vw is the molar volume of the diluent (m3
/g mol), Vu is
the molar volume of polymer unit (m3
/g mol), εw is the volume fraction
of the diluent, and χ is the Flory–Huggins polymer-diluent interaction
parameter. The volume fraction of water was calculated from the fol-
lowing equation considering the volume of water and volume of solids
estimated from mass fractions and density values of water and solids
[9]:
=
+
ε
X ρ
X ρ X ρ
( / )
( / ) ( / )
w
w w
w w s s (4)
where, Xw is the mass fraction of water (w.b., g/100 g sample), ρw is the
density of water (kg/m3
), Xs is the mass fraction of solids content (g/
100 g sample), and ρs is the density of dry-solids (kg/m3
). The density of
freeze-dried broccoli (i.e. dry-solids) was considered as 1622 kg/m3
,
which was estimated from the proximate compositions (i.e. protein,
carbohydrate, fat and ash) of broccoli [30].
S. Suresh et al. Thermochimica Acta 655 (2017) 129–136
130

3. 2.5. Thermal analysis of samples containing freezable water
The procedure of thermal analysis for samples containing freezable
water (Xw
oo
: 0.30-0.95 g/g sample) was similar to Rahman et al. [26]. A
10 mg broccoli sample sealed in aluminum pan was cooled to −90 °C at
5 °C/min and kept for 1 min. The sample was then scanned from
−90 °C to 250 °C at a heating rate 10 °C/min in order to determine
glass transition, freezing point, apparent maximal-freeze-concentration
condition [(Tm′)a and (Tg′′′)a] and solids-melting. The solids-melting
data was considered acceptable up to moisture 0.80 g/g sample (i.e.
moisture loss up to 1%) as identified in preliminary experiments. The
glass transition was determined from the shift in the DSC thermogram.
The freezing point and apparent maximal-freeze-concentration condi-
tion were determined from the ice melting endothermic peak and shift
just before the endothermic peak. The freezing process was character-
ized by onset and maximum slope temperatures, and freezing enthalpy
from the area of the endothermic peak. The initial or equilibrium
freezing point was considered as the maximum slope in the ice melting
endotherm as suggested by Rahman [23]. It was observed earlier that
this point was very close to the measured value of the established
cooling curve method. Al-Rawahi et al. [20] also found that the max-
imum slope was close to the freezing point measured by commonly
established cooling curve method.
Samples with moisture 0.4 and 0.5 g/g sample were scanned simi-
larly as mentioned earlier with 30 min annealing at (Tm′)a −1 [37,38].
The annealed maximal-freeze-concentration [(Tm′)n and (Tg′′′)n] was
determined similarly from the shift just before ice melting endotherm.
The use of annealing condition allowed to maximize the formation of
ice before second heating cycle and to avoid the appearance of exo-
thermic or endothermic peak before glass transition [20]. The average
value of 4 replicates of (Tm′)n and (Tg′′′)n at moisture 0.4 g/g sample was
considered as ultimate maximal-freeze-concentration condition [(Tm′)u
and (Tg′′′)u]. The sample containing moisture of 0.4 g/g sample was
considered to determine ultimate (Tm′)u since it gave the lowest possible
value. The value of maximal-freeze-concentration solids content (i.e.
Xs′) was determined from the intersection point of the extended freezing
curve (TF versus Xs) by maintaining similar curvature as Chen [39]
model and drawing a horizontal line passing through ultimate (Tm′)u
[9]. Finally Xs′ was read on the x-axis by drawing a vertical line passing
through the intersection point and the intersection point on the glass
Fig. 1. A. Water adsorption isotherm as a function temperature, B: Plot of solids content at BET-monolayer as a function of temperature.
Fig. 2. DSC thermogram for the sample with un-freezable water (moisture: 0.067 g/g sample), A: DSC thermogram, B: Expansion of glass transition region for clear visualization, C: On-
set glass transition as a function of solids content (o, experimental point; − Gordon-Taylor model), D: Plot of ΔCp at glass transition as a function solids content.
S. Suresh et al. Thermochimica Acta 655 (2017) 129–136
131

4. line as Tg′. The intersection point of the extended freezing curve by
maintaining similar curvature as Chen’s [39] model and glass line was
termed as Xs′′ and Tg′′.
The commonly used Chen [39] model based on Clausius-Clapeyron
equation was used to model the freezing point data using the following
equation:
= − ⎡
⎣⎢
− −
− − +
⎤
⎦⎥
δ
β
λ
X CX
X CX EX
ln
1
1w
s
o
s
o
s
o
s
o
s
o
(5)
where δ is the freezing point depression (Tw-TF), TF is the freezing point
of food (°C), Tw is the freezing point of water (°C), β is the molar
freezing point constant of water (1860 kg K/kg mole), λw is the mole-
cular weight of water, Xs
o
is the initial solids mass fraction before
freezing (g/g sample), C is the un-freezable water (g/g dry-solids) and E
is the molecular weight ratio of water and solids (λw/λs).
3. Results and discussion
3.1. Moisture adsorption isotherm
The moisture contents of the fresh and freeze-dried broccoli were
90.2 and 6.7 g/100 g sample, respectively and the pH of the fresh
broccoli was 6.8. Similarly Koh et al. [40] reported the range of
moisture content of fresh broccoli from 83.9 to 90.3 g/100 g sample.
The protein, fat, crude fiber, ash and carbohydrate of freeze-dried
broccoli were respectively 24.3, 3.8, 8.7, 8.6 and 56.6 g/100 g sample.
These results are similar to those reported by Liu et al. [41] and Madhu
and Kochhar [42]. Fig. 1A shows that the equilibrium water content
increased with the increase of water activity (in most of the cases the
error bars were within the symbol). The BET-monolayer was calculated
based on Eq. (1) and Fig. 1B presents the solids content at the BET-
monolayer as a function of storage temperature. The BET-monolayer
value of broccoli was determined as 0.089 g/g dry-solids at 20 °C, thus
broccoli would be most stable at or below this moisture considering
theoretical water activity concept of foods’ stability. A linear regression
equation was developed as:
= −T X1003.20 903.63b bs (6)
where Tb is the temperature (°C) at BET-monolayer, and Xbs is the solids
content (g/100 g sample) at BET-monolayer. The regression correlation
(R2
) is 0.947. The above equation was used to develop BET-monolayer
line in the state diagram [28] as emphasized by Zhao et al. [18].
3.2. Moisture leak from the DSC pan
Preliminary experiments were conducted to check the evaporation
of water from the sample sealed in the pans during heating, especially
at temperatures above 100 °C. Heating above 100 °C can create high
pressure in the pans and may cause moisture leak from the pans. The
moisture losses were observed as 10.10, 0.77, 0.73, 0.68, and 0.58%
(i.e. as compared to the initial sample mass) for the samples containing
moisture 85.0, 80.0, 75.0, 70.0 and 60.0 g/100 g sample, respectively.
These results indicated that there was negligible leak or break of the
seal of the aluminum pan containing samples having moisture at or
below 80.0 g/100 g sample. The leakage at very high moisture sample
(i.e. above moisture 80.0 g/100 g sample) was due to the pressure build
up in the pan as compared to the low moisture samples. Therefore,
thermal characteristics above 100 °C were considered only for the
samples containing moisture at or below 80.0 g/100 sample.
3.3. Samples containing un-freezable water
A DSC thermogram of freeze dried sample with un-freezable water is
presented in Fig. 2. Fig. 2A shows a glass transition marked as G (i.e.
shift in the thermogrm line), an exothermic peak marked as E and an
Table1
ThermalCharacteristicsofbroccolicontainingun-freezablewater(HeatingRate:10°C/min).
XsTgi(°C)Tgp(°C)Tge(°C)ΔCp(J/kgK)Tei(°C)Tep(°C)Tee(°C)ΔHe(kJ/kg)Tmi(°C)Tmm(°C)Tmp(°C)Tme(°C)ΔHm(kJ/kg)
0.99043.6±4.372.6±6.385.7±2.7985±4123.9±0.5146.7±0.5159.4±0.845.6±1.2176.9±13.0177.1±12.8178.4±11.9207.8±14.391.0±4.0
0.97020.7±0.649.5±6.465.2±2.11009±31120.9±0.7143.1±0.7155.6±0.140.3±2.5170.0±12.2170.2±12.1171.3±11.0200.9±3.8121.3±9.3
0.950-2.6±0.710.4±1.840.5±4.11124±27120.9±1.7138.8±6.1150.8±13.523.3±20.7154.6±17.3159.0±16.4165.8±13.8218.2±25.0153.8±20.7
0.933-6.9±7.43.2±8.336.6±6.51211±315117.0±1.1137.3±0.6148.0±1.538.7±1.1158.9±0.5159.8±0.8174.2±3.1246.5±0.2254.6±26.1
0.900-4.9±1.56.8±2.132.3±1.81085±79113.9±0.5134.3±4.1145.0±8.923.3±17.4152.5±1.9153.8±1.8162.6±13.0193.8±15.0150.1±21.3
0.850-31.5±6.5-19.4±7.9-6.1±7.1836±215111.0±1.4134.8±1.3149.6±0.421.8±5.5164.8±10.0163.1±10.4168.8±5.4193.1±9.6191.5±37.8
0.800-49.4±0.8-43.0±1.3-32.6±1.1976±53110.4±0.6134.2±0.2148.2±1.717.8±2.4131.8±22.2131.2±18.2144.6±17.9182.9±13.3311.2±23.3
0.750-61.6±0.7-56.2±1.5-48.4±1.8879±20110.4±0.9133.4±0.6144.9±2.312.4±1.1149.1±5.3150.3±7.9157.2±7.0189.3±5.8390.9±13.5
S. Suresh et al. Thermochimica Acta 655 (2017) 129–136
132

5. endothermic peak marked as M for solids-melting. The exothermic peak
before melting indicated the crystallization or molecular ordering. The
glass transition region was expanded in Fig. 2B (i.e. onset, mid and end
points of glass transition, and ΔCp are marked). The ΔCp as shown in
Fig. 2B was calculated from the heat flow data (i.e. y-axis), sample mass
and heating rate. The onset glass transition temperature decreased
significantly with the decrease of solids mass fraction (Table 1) and it is
considered as the glass line. The decrease was due to the plasticization
of solids matrix with increasing water (i.e. decreasing solids) (Fig. 2C).
This type of plasticization was completely different in nature as com-
pared to that of gelatin [26], starch and instant rice [27]. In these cases,
the glass transitions decreased with decreasing solids and leveled off at
much higher temperature than Tm′, whereas broccoli’s glass transition
leveled off much below Tm′. Broccoli showed similar nature as sugars
and sugar based products [2,14–18]. The data were fitted to the
Gordon-Taylor model and the values of k and Tgs were observed as 4.31
and 42.8 °C, respectively (r2
: 0.961 and p < 0.001). The higher value
of k indicated the high plasticization of solids with water. This ob-
servation is supported by Rahman et al. [26] who reported that a k
value of 10 indicated very high plasticization of solutes. The k value for
broccoli was similar to the sugars or sugar based fruits, which varied
from 2.6 to 4.0 [24]. The glass transition temperatures of dry solids for
fructose, glucose and sucrose were with the range of 7–18, 20–31, and
52–70 °C, respectively [24]. The Tgs for broccoli solids was within the
range.
The ΔCp at the glass transition varied from 836 to 1211 J/kg K
(Table 1) and these variations were insignificant when fitted with linear
(r2
: 0.31, p > 0.15) and non-linear (r2
: 0.37, p > 0.31) correlations
(Fig. 2D), indicating that water did not affect the amount of amorphous
solids fraction of broccoli. The average value of ΔCp was
1013 ± 112 J/kg K. The high ΔCp indicated that solids contained
higher level of amorphous solids. In the case of gelatin, Rahman et al.
[26] observed relatively higher decrease of ΔCp with decreasing solids,
which were 2022 J/kg K at solids content 0.90 g/g sample and 490 J/
kg K at solids content 0.75 g/g sample. However, ΔCp of dry sucrose
(i.e. zero moisture) was observed as 700 J/kg K [14].
3.4. Samples containing freezable water
Fig. 3 shows DSC thermogram for sample containing freezable water
and the thermal characteristics of broccoli containing freezable water
are shown in Table 2. The apparent (Tm′)a and (Tg′′′)a decreased with
the increase of solids (i.e. increasing water) up to solids content of
0.6 g/g sample and then increased further with the increase of solids
(i.e. at solids 0.7 g/g sample) (Table 2). This indicated that the max-
imal-freeze-concentration condition was observed at water content
0.4 g/g sample, and sample at 0.3 g/g moisture content indicated re-
stricted ice melting in a very viscous medium. For the samples con-
taining moisture 0.5 and 0.4 g/g sample, the apparent (Tm′)a were ob-
served at −30.8 and −34.5 °C, while (Tg′′′)a were observed as −35.0
and −40.5 °C, respectively (Table 2). However annealing condition
gave a (Tm′)u value of −31.1 ± 0.3 and −30.0 ± 0.1 °C for samples
containing moisture 0.5 and 0.4 g/g sample, respectively. The close
values indicated that annealing for the samples containing moisture 0.5
or 0.4 g/g sample could provide maximal-freeze-concentration condi-
tion. The increased value of (Tm′)a at moisture 0.3 g/g sample indicated
the difficulty of forming ice and its growth during freezing cycle as
noticed in the melting cycle. In this work (Tm′)u was considered as
−30.0 °C from the sample containing moisture 0.4 g/g sample since it
gave lowest possible value. The (Tm′)u and (Tg′′′)u are most commonly
determined from moisture 0.4 g/g sample [26,20]. Additionally the
higher difference between values obtained from annealed and un-an-
nealed samples also supported the difficulty of ice formation in con-
centrated solid matrix. Similarly (Tg′′′)u were observed as −34.8 ± 0.3
and −32.2 ± 0.2 °C for samples containing moisture 0.5 and 0.4 g/g
sample, respectively.
The freezing point as a function of solids is plotted in Fig. 4A (i.e.
line ed) which shows that freezing point decreased with the increase of
solids content. The Chen’s model parameters E and C were estimated as
0.095 and 0.199 g/g dry solids, respectively (p < 0.0001). Freezing
point for sample containing moisture 0.3 g/g sample was not included
in the modelling due to their restricted freezing process in the con-
centrated solids matrix. The value of Xs′ was determined from the
Fig. 3. DSC thermogram for the sample with freezable water (moisture: 0.4 g/g sample), A: Complete thermogram (F: freezing exothermic peak for freezing of water during cooling, H:
endothermic peak for melting of ice during heating cycle, M: endothermic peak for solids melting), B: Expansion of ice melting endotherm (G1: glass transition at low temperature, G2:
glass transition before ice melting endotherm to determine apparent maximal-freeze concentration conditions, F: ice melting endotherm), C: Expansion of G1 for clear visualization, D:
Endothermic peak for solids melting.
S. Suresh et al. Thermochimica Acta 655 (2017) 129–136
133

6. intersection point (i.e. a) in Fig. 4A by extending the freezing curve (i.e.
ed) and maintaining the similar curvature as Chen’s model (Eq. (5)) and
a horizontal line passing through (Tm′)u = −30.0 °C. The Xs′ value (i.e.
0.70 g/g sample) was determined from the x-axis by drawing a vertical
line passing through point “a”. The un-freezable water content was
estimated as 0.30 g/g sample (i.e. Xw′ = 1- Xs′). The water represented
to the right side of the point was un-freezable water (i.e. unable to form
ice even at very low temperature). The values of Tg′ (i.e. point b, ver-
tical line passing through point a and crossing the glass transition line)
and Tg′′ (i.e. point c, by extending freezing curve as Chen’s model and
crossing the glass transition line) were determined as −73.5 and
−68.5 °C, respectively and Xs′′ (i.e. point c) was determined as 0.74 g/g
sample from the x-axis.
Fig. 4B is a plot of ice melting enthalpy as a function of solids
content and it showed two linear portions with different slopes. The
change of slope could be due to the change of ice melting as a function
of temperature and the binding nature of the water in broccoli. The
extended line to zero enthalpy (solids content: 0.68 g/100 g sample)
gave the un-freezable water as 0.32 g/g sample, which was close to the
un-freezable water determined from state diagram as 0.30 g/g sample
(i.e. solids content: 0.70 g/g sample). Similar extrapolation method was
also used for date-pits [43], gelatin [26], date-fruit flesh [23] and
mango [18].
3.5. Exothermic peak
The exothermic peak temperature and enthalpy are plotted in
Fig. 5A and B as function of solids content. The peak temperature and
the enthalpy decreased with the decrease of solids content (i.e. increase
of water), however a sharp decrease was observed at solids content
from 1.0 to 0.9 g/g sample. The decrease in enthalpy indicated a lower
fraction of disordered or amorphous component with increasing water
content that could be ordered before the solids-melting.
3.6. Solids-Melting
Fig. 5C shows that the solids-melting peak decreased with the de-
crease of solids content (i.e. increase of water), thus higher water
caused the onset of melting process at lower temperature. This could be
due to the nascent formation of the solids-polymers caused by water as
compared to the compact mass of the solids-polymers at low moisture.
Similar trend was also observed for cereal protein [44], gelatin [26],
date-pits [45] and instant rice [27]. The solids-melting peak tempera-
ture was modeled by Flory-Huggins equation (Equation 3) up to solids
content of 0.6 g/g sample as shown in Fig. 5C. The values of RVu/ΔHuVw
and χ for broccoli were estimated as 5.07 × 10−4
and 0.69, respec-
tively. The value of χ indicates the water-solids interaction during the
melting process and could be compared with the literature values for
other foods or food components. The melting point of dry solids was
observed at 178.4 °C. The values of χ were reported as 2.2 for gelatin
[26], 0.48-0.5 for starch [46], 0.0088 for artificial rice [27], and 0.0068
for date-pits [45]. This indicated that stiff molecules (i.e. artificial rice
and date-pits) showed low interaction with the water molecule during
the melting process. As compared to high (i.e. 2.2) and low (i.e. 0.0068)
values for gelatin and date pits respectively, the value of 0.69 obtained
for broccoli indicated that water was moderately interacted with the
solids during its melting process.
Fig. 5D shows that solids-melting enthalpy decreased with the in-
crease of solids content, thus higher melting energy was required for
higher water content. Similar result was observed for date-pits solids-
melting [45]. This could be due to the increased structural building by
hydrogen bonding within the solids matrix at higher level of water
[26], thus more energy was needed to melt the solids with higher water
content. In addition, there was a change in slope at solids content of
0.72 g/g sample (i.e. water: 0.28 g/g sample), which was close to the
un-freezable water (i.e. 0.30 g/g sample) determined from state
Table2
ThermalCharacteristicsofbroccolicontainingfreezablewater(HeatingRate:10°C/min).
XsTgi(°C)Tgp(°C)Tge(°C)ΔCp(J/kgK)(Tm′)a(°C)(Tg′′′)a(°C)ΔCp(J/kgK)(TF)m(°C)(ΔHF)m(kJ/kg)Tmi(°C)Tmm(°C)Tmp(°C)Tme(°C)ΔHm(kJ/kg)
0.70-67.9±2.9-63.8±3.0-56.8±4.2561±41-22.6±0.8-31.2±2.264±23-23.0±0.50.3±0.3138±27146±22155±17185±8335±25
0.60-66.8±0.2-62.6±0.2-56.8±0.9557±14-34.5±0.7-40.5±1.3412±25-19.2±2.124.8±3.2122±24131±18145±17173±10555±17
0.55-65.1±0.7-58.9±2.8-54.8±1.8529±22-34.1±0.6-39.6±0.9585±117-14.7±0.234.8±2.6122±28133±15150±17174±9568±43
0.50-64.1±0.3-59.5±0.5-54.2±0.8509±14-30.8±1.1-35.0±1.3941±153-11.5±1.851.4±8.3123±14132±6141±6165±1667±46
0.45-64.0±0.5-59.7±0.1-53.8±0.2519±10-28.8±0.4-32.8±1.01374±89-9.4±0.269.8±3.5149±4145±1157±1176±1763±32
0.40-63.0±0.3-56.7±0.1-51.1±0.2410±19-26.5±0.6-32.0±0.21361±220-6.7±0.887.4±10.2137±23144±21151±17169±13836±63
0.35-64.1±0.4-58.5±0.9-52.1±0.7391±24-25.1±0.5-31.1±0.71514±185-6.1±0.1105.0±4.5154±16151±10161±10177±10925±73
0.30-62.6±0.1-55.1±0.6-48.9±0.2381±9-22.1±0.7-29.0±0.81469±34-4.5±0.1118.8±1.5138±5143±3149±4164±51013±39
0.25-62.5±0.4-55.0±0.6-50.2±0.9345±8-19.4±0.5-31.7±0.71018±56-3.6±0.1136.8±1.3139±6143±5150±4165±31087±40
0.20-62.4±0.5-54.2±0.7-49.5±0.6321±22-17.9±0.1-32.5±0.7790±160-2.8±0.1153.1±3.9133±18129±1151±7165±71183±10
0.15-62.1±1.4-56.1±2.1-49.8±1.0271±27-14.5±0.7-32.9±1.1580±61-1.7±0.2177.9±7.7
0.10NDNDNDND-11.6±0.1-33.6±0.6419±94-1.2±0.2202.1±8.6
0.05NDNDNDND-7.9±0.4-39.8±0.5230±30-0.3±0.4234.7±11.3
S. Suresh et al. Thermochimica Acta 655 (2017) 129–136
134

7. diagram. In the case of starch granules, the shape of the melting peak
depended on the moisture content in the sample due to the presence of
different levels or types of organized structure [47–49].
4. Conclusion
Glass transition and solids-melting temperature of broccoli de-
creased with the decrease of solids content, while freezing point de-
creased with the increase of solids content. The ultimate maximal-
freeze-concentration temperature was observed as −30.0 °C at a char-
acteristic solids content 0.70 g/100 g sample (i.e. un-freezable water:
0.30 g/100 g sample). The intersection point of the glass line and
freezing curve as Chen’s [39] model was determined as −68.5 °C.
These thermal characteristics of broccoli were used to develop state
diagram, which showed different phases and state boundaries of broc-
coli. The developed state diagram could be used to determine the sta-
bility of bioactive components of broccoli during processing and sto-
rage. However, further research needs to be conducted in determining
stability kinetics of the active components of broccoli in the different
regions of the state diagram.
Acknowledgements
Ms. Sithara Suresh has received a Ph. D. scholarship from the Sultan
Qaboos University. Authors would like to acknowledge the supports of
the Sultan Qaboos University towards this research in the area of food
biophysics and food stability.
References
[1] H. Levine, L. Slade, A polymer physico-chemical approach to the study of com-
mercial starch hydrolysis products (SHPs), Carbohydr. Polym. 6 (1986) 213–244.
[2] Y. Roos, Characterization of food polymers using state diagrams, J. Food Eng. 24
(1995) 339–360.
[3] M.S. Rahman, Food stability beyond water activity and glass transition: macro–-
micro region concept in the state diagram, Int. J. Food Prop. 12 (4) (2009)
726–740.
[4] M.S. Rahman, Applications of macro-micro region concept in the state diagram and
critical temperature concepts in determining the food stability, Food Chem. 132 (4)
(2012) 1679–1685.
[5] A.G. Cnossen, T.J. Siebenmorgan, W. Yang, R.C. Bautista, An application of glass
transition temperature to explain rice kernel fissure occurrence during the drying
process, Drying Technol. 19 (8) (2001) 1661–1682.
[6] K. Srikaeo, C. Boonrod, M.S. Rahman, Effect of storage temperatures on the head
rice yield in relation to glass transition temperatures and un-freezable water, J.
Cereal Sci. 70 (2016) 164–169.
Fig. 4. A: Freezing and glass transition line, B: Freezing enthalpy (ΔHF)m as a function of solids content (–- −visual guide).
Fig. 5. The main building blocks of the device and the microfluidic cartridge.
S. Suresh et al. Thermochimica Acta 655 (2017) 129–136
135

8. [7] Y. Roos, M. Karel, Applying state diagrams to food processing and development,
Food Technol. 45 (1991) 66–71.
[8] A. Perdon, T.J. Siebenmorgen, A. Mauromoustakos, Glassy state transition and rice
drying: development of a brown rice state diagram, Cereal Chem. 77 (6) (2000)
708–713.
[9] M.S. Rahman, Food stability determination by macro-micro region concept in the
state diagram and by defining a critical temperature, J. Food Eng. 99 (2010)
402–416.
[10] A. Gianfrancesco, C. Smarrito-Menozzi, G. Niederreiter, S. Palzer, Developing
supra-molecular structures during freeze-drying of food, Dying Technol. 30 (2012)
1160–1166.
[11] B. Cuq, J. Abecassis, S. Guilbert, State diagrams to help describe wheat bread
processing, Int. J. Food Sci. Technol. 38 (2003) 759–766.
[12] C. Schebor, M.D.P. Buera, J. Chirife, M. Karel, Surcose hydrolysis in glassy starch
matrix, Food Sci. Technol. 28 (1995) 245–248.
[13] R. Dominguez-Perles, M.C. Martinez-Ballesta, M. Carvajal, C. Garcia-Viguera,
D.A. Moreno, Broccoli-derived by-products- A promising source of bioactive in-
gredients, J. Food Sci. 75 (4) (2010) C383–C392.
[14] G. Blond, D. Simatos, M. Catte, C.G. Dussap, J.B. Gros, Modeling of the water-su-
crose state diagram below 0 °C, Carbohydr. Res. 298 (1997) 139–145.
[15] M.M. Sa, A.M. Sereno, Glass transitions and state diagrams for typical natural fruits
and vegetables, Thermochim. Acta 246 (1994) 285–297.
[16] M.M. Sa, A.M. Figueiredo, A.M. Sereno, Glass transitions and state diagrams for
fresh and processed apple, Thermochim. Acta 329 (1999) 31–38.
[17] V.R.N. Telis, P.J.A. Sobral, Glass transitions and state diagram for freeze-dried
pineapple, Food Sci. Technol. 34 (2001) 1999–1205.
[18] J. Zhao, F. Liu, X. Wen, H. Xiao, Y. Ni, State diagram for freeze-dried mango:
freezing curve, glass transition line and maximal-freeze-concentration condition, J.
Food Eng. 157 (2015) 49–56.
[19] D. Fessas, A. Schiraldi, State diagrams of arabinoxylan-water binaries, Thermochim.
Acta 370 (2001) 83–89.
[20] A. Al-Rawahi, M.S. Rahman, M. Waly, G.J. Guillemin, Thermal characteristics of a
water soluble extract obtained from pomegranate skin: developing a state diagram
for determining stability, Ind. Crops Prod. 48 (2013) 198–204.
[21] F. Fonseca, J.P. Obert, C. Beal, M. Marin, State diagrams and sorption isotherms of
bacterial suspensions and fermented medium, Thermochim. Acta 366 (2001)
167–182.
[22] M.S. Rahman, W. Senadeera, A. Al-Alawi, T. Truong, B. Bhandari, G. Al-Saidi,
Thermal transition properties of spaghetti measured by Differential Scanning
Calorimetry (DSC) and thermal mechanical compression test (TMCT), Food
Bioprocess Technol. 4 (8) (2011) 1422–1431.
[23] M.S. Rahman, State diagram of date flesh using differential scanning calorimetry
(DSC), Int. J. Food Prop. 7 (3) (2004) 407–428.
[24] N. Guizani, G.S. Al-Saidi, M.S. Rahman, S. Bornaz, A.A. Al-Alawi, State diagram of
dates: glass transition, freezing curve and maximal-freeze-concentration condition,
J. Food Eng. 99 (1) (2010) 92–97.
[25] P. Diaz, D. Lopez, S. Matiacevich, F. Osorio, J. Enrione, State diagram of salmon
(Salmo salar) gelatin films, J. Sci. Food Agric. 91 (2011) 2558–2565.
[26] M.S. Rahman, G. Al-Saidi, N. Guizani, A. Abdullah, Development of state diagram of
bovine gelatin by measuring thermal characteristics using differential scanning
calorimetry (DSC) and cooling curve method, Thermochim. Acta 509 (2010)
111–119.
[27] H. Herawat, F. Kusnandar, D.R. Adawiyah, S. Budijanto, M.S. Rahman, Thermal
characteristics and state diagram of extruded instant artificial rice, Thermochim.
Acta 593 (2014) 50–57.
[28] M.S. Rahman, State diagram of foods: its potential use in food processing and
product stability, Trends Food Sci. Technol. 17 (2006) 129–141.
[29] AOAC, International Official Methods of Analysis, 17th ed., Association of Official
Analytical Chemists, Gaitherburg, MD, USA, 2000.
[30] M.S. Rahman, Food Properties Handbook, CRC Press, Boca Raton, FL, USA, 1995.
[31] M.S. Rahman, R.H. Al-Belushi, Dynamic isopiestic method (DIM): measuring
moisture sorption isotherm of freeze-dried garlic powder and other potential uses of
DIM, Int. J. Food Prop. 9 (2006) 421–437.
[32] S. Brunauer, P.H. Emmett, E. Teller, Adsorption of gases in multimolecular layers, J.
Am. Chem. Soc. 60 (1938) 309–319.
[33] T.P. Labuza, Sorption phenomena in foods, Food Technol. 23 (1968) 15–19.
[34] S.S.H. Rizvi, Thermodynamic properties of foods in dehydration, Engineering
Properties of Foods, CRC Press, Boca Raton, FL, 2005, pp. 239–326.
[35] M. Gordon, J.S. Taylor, Ideal copolymers and the second-order transitions of syn-
thetic rubbers. i: non- crystalline copolymers, J. Appl. Chem. 2 (1952) 493–500.
[36] P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY,
1953.
[37] M. Karel, S. Anglea, P. Buera, R. Karmas, G. Levi, Y. Roos, Stability-related tran-
sitions of amorphous foods, Thermochim. Acta 246 (1994) 249–269.
[38] Y. Bai, M.S. Rahman, C.O. Perera, B. Smith, L.D. Melton, State diagram of apple
slices: glass transition and freezing curves, Food Res. Int. 34 (2-3) (2001) 89–95.
[39] C.S. Chen, Effective molecular weight of aqueous solutions and liquid foods cal-
culated from the freezing point depression, J. Food Sci. 51 (1986) 1537–1553.
[40] E. Koh, K.M.S. Wimalasiri, A.W. Chassy, A.E. Mitchell, Content of ascorbic acid,
quercetin, kaempferol and total phenolics in commercial broccoli, J. Food Compos.
Anal. 22 (2009) 637–643.
[41] M.S. Liu, M.H. Ko, H.C. Li, S.J. Tsai, Y.M. Lai, Y.M. Chang, M.T. Wu, L.F.O. Chen,
Compositional and proteomic analyses of genetically modified broccoli (Brassica
oleracea var. italica) harboring an agrobacterial gene, Int. J. Mol. Sci. 15 (2014)
15188–15209.
[42] Madhu, A. Kochhar, Proximate composition, available carbohydrates, dietary fibre
and anti-nutritional factors of Broccoli (Brassica oleracea l var. Italica plenca) leaf
and floret powder, Biosci. Discov. 5 (1) (2014) 45–49.
[43] M.S. Rahman, S. Kasapis, N.S.Z. Al-Kharusi, I.M. AlMarhubi, A.J. Khan,
Composition characterization and thermal transition of date pits powders, J. Food
Eng. 80 (2007) 1–10.
[44] J.L. Kokini, A.M. Cpcero, H. Madeka, E. de Graaf, The development of state dia-
grams for cereal proteins, Trends Food Sci. Technol. 5 (1994) 281–288.
[45] S. Suresh, N. Guizani, M. Al-Ruzeiki, A. Al-Hadhrami, H. Al-Dohani, I. Al-Kindi,
M.S. Rahman, Thermal characteristics, chemical composition and polyphenol con-
tents of date-pits powder, J. Food Eng. 119 (2013) 668–679.
[46] A. Farhat, J.M.V. Blanshard, On the extrapolation of the melting temperature of dry
starch from starch-water data using the Flory-Huggins equation, Carbohydr. Polym.
34 (1997) 263–265.
[47] J.W. Donovan, K. Lorenz, K. Kulp, Differential scanning calorimetry of heat-
moisture treated wheat and potato starches, Cereal Chem. 60 (1983) 381–387.
[48] C.G. Biliaderis, C.M. Page, T.J. Maurice, B.O. Juliano, Thermal characterization of
rice starches: a polymeric approach to phase transitions of granular starch, J. Agric.
Food Chem. 34 (1986) 6–14.
[49] J.K. Jang, Y.R. Pyun, Effect of moisture content on the melting of wheat starch,
Starch 48 (1996) 48–51.
S. Suresh et al. Thermochimica Acta 655 (2017) 129–136
136