Journal of Macromolecular Science, Part B
ISSN: 0022-2348 (Print) 1525-609X (Online) Journal homepage: http://www.tandfonline.com/loi/lmsb20
Thermal Phase Transitions of IOTA Carrageenan in
CaCl2 Solutions: A Fluorescence Study
Özlem Tari , Selim Kara & Önder Pekcan
To cite this article: Özlem Tari , Selim Kara & Önder Pekcan (2010) Thermal Phase Transitions
of IOTA Carrageenan in CaCl2 Solutions: A Fluorescence Study, Journal of Macromolecular
Science, Part B, 50:2, 306-318
To link to this article: http://dx.doi.org/10.1080/00222341003652286
Published online: 15 Dec 2010.
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Journal of Macromolecular Science
, Part B: Physics, 50:306–318, 2011
Copyright © Taylor & Francis Group, LLC
ISSN: 0022-2348 print / 1525-609X online
DOI: 10.1080/00222341003652286
Thermal Phase Transitions of IOTA Carrageenan
in CaCl2 Solutions: A Fluorescence Study
ÖZLEM TARI,1 SELIM KARA,2 AND ÖNDER PEKCAN3
1
Department of Physics, Istanbul Technical University, Maslak, Istanbul, Turkey
Department of Physics, Trakya University, Edirne, Turkey
3
Kadir Has University, Cibali, Istanbul, Turkey
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2
The fluorescence technique was employed to study thermal phase transitions of iota
(ι-) carrageenan (IC) in CaCl2 solution. IC gels underwent coil to double helix (ch) and double helix to dimer (h-d) transitions upon cooling. Upon heating IC gels
presented dimer to double helix (d-h) and double helix to coil (h-c) transitions, showing
hysteresis types of transition paths. Scattered light, Isc and fluorescence intensity, I, were
monitored against temperature to determine phase transitions. Transition temperatures
were determined from the derivative of the transition paths. The critical gel fraction
exponent, β, was measured and found to be in accord with the classic Flory–Stockmayer
model.
Keywords carrageenan, fluorescence, phase transition, polysaccharides, scattered
light, transition temperature
1. Introduction
Carrageenans are sulfated polysaccharides extracted from red seaweed. They are linear
polymers, with a backbone of alternating α-1,4 and β-1,3 linked galactose residues and
varying proportions and positions of sulfate groups. Various occurring arrangements of
components create three basic types of carrageenan, as kappa (κ-), iota (ι-), and lambda (λ) carrageenan.[1] Variations of these components influence gel strengths, texture, solubility,
synergisms, and melting temperature of the carrageenan.
κ and ι-carrageenan are gel-forming carrageenans, whereas λ carrageenan is a viscosity
builder. ι-carrageenan is a high molecular weight linear polymer consisting principally of
an alternating sequence of 3-linked β-D- galactose 4-sulfate and 4 linked 3,6-anhydro-βD-galactose 2 sulfate. Thus, each monosaccharide unit in the ideal polysaccharide carries
one sulfate group, and therefore ι-carrageenan behaves in aqueous solution as a highly
charged polyanion in the extended confirmation.[2] It’s well known that the κ-carrageenan
molecule contains one sulfate group and interacts well with potassium cations. On the
other hand, ι-carrageenan prefers to interact with 2+ valence cations, such as Ca2+ ions,
due to its two-sulfated nature.[3–5] It is known that the polysaccharide has a double helix
conformation in the solid phase, as shown by X-ray diffraction data, while in a calcium salt
solution it is converted to a three-fold right-handed double helix with parallel strands.[6–8]
Received 5 October 2009; accepted 14 January 2010.
Address correspondence to Önder Pekcan, Kadir Has University, Cibali, 34320, Istanbul, Turkey.
E-mail: [email protected]
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Thermal Phase Transitions of IOTA Carrageenan in CaCl2 Solutions
307
In solution, ι-carrageenan can be reversibly transformed from an ordered to a disordered
conformation. Naturally, at high ionic strength and low temperature, ι-carrageenan forms
an ordered, helical state. Upon heating, the helices dissolve and the ι-carrageenan takes on
a random coil conformation.[9]
Intermolecular double helix formation, investigated by several groups should result
in a doubling in the observed molecular weight of the ι-carrageenan.[10,11] However some
authors have proposed monomolecular single-helix formations.[12] It has been concluded
that the formation of the ι-carrageenan double helix follows second-order reaction kinetics
while the back reaction process is of first order. It has been shown that a decrease in polymer
concentration causes the change in the mechanism of ι-carrageenan conformational ordering
from an intermolecular to an intramolecular multistrand state.[13] More recently Morris and
coworkers proposed a model known as “fibrous network structure” for similar systems of
helix forming polysaccharides in which the junction zones act as sticky patches that connect
the chains together into fibers.[14–16]
A large number of studies have confirmed that the thermally induced gelation of carrageenans is accompanied by a change in the optical rotation.[17,18] It has been shown that
the molar rotations for ι-carrageenan in the two states closely corresponded to those calculated for a random coil and for a double-helix conformation, respectively,[19] in agreement
with the evidence from X-ray diffraction studies.[6]
A considerable amount of research has been performed on carrageenan and
carrageenan-like systems over the last several years to produce specific properties for
specific applications.[3] For example, the kinetics and equilibrium processes of the sol–gel
transitions of agar or agarose gels as well as the effect of gelation conditions on the gel’s
microstructure and rheological properties, have been studied in past few years.[20–22] It
was observed that gelation of agar molecules results in a large sigmoidal increase in the
magnitude of the sol’s shear modulus.[23,24] On reheating, the gel structure is destroyed
and during the gel–sol transition, the shear modulus follows another sigmoidal path back
to its initial value, forming a hysteresis loop.[25] The photon transmission technique was
employed to study the hysteresis phenomena during the sol–gel and gel–sol transitions in
carrageenan-water system.[26] The cation effect on the sol–gel and gel–sol phase transitions
of that system was also investigated by the same technique.[27]
The aim of this work was to study the thermal phase transitions of ι-carrageenan in
CaCl2 solution. Scattered light, I sc , and fluorescence intensity, I, were monitored against
temperature to determine phase transitions and transition temperatures. The gel fraction
exponent β was measured and found to be in accord with the classic Flory–Stockmayer
model, where Cayley tree type network structure is proposed.
2. Experimental
ι-carrageenan (Sigma C-1138) (2%) and pyranine (8-hydroxypyrene-1,3,6-trisulfonic acid
trisodium salt, Fluka 56360) were used to prepare gels by dissolving them in hot water with
CaCl2 solutions at the desired concentration. The pyranine concentration was kept at 2 ×
10−4 M. The CaCl2 contents were varied from 0.4 to 1.2%. These samples are named as
I2Ca04, I2Ca06, I2Ca08, I2Ca10, and I2Ca12. The compositions of the studied solutions
in various CaCl2 contents are presented in Table 1. The heated carrageenan solution was
continuously stirred by a magnetic stirrer. Then the solution was cooled down to room
temperature.
308
Ö. Tari et al.
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Table 1
The symbols and the transition temperatures of the studied gels with various CaCl2 content
Samples
CaCl2
(wt%)
T dh ± 0.5
(◦ C)
T hc ± 0.5
(◦ C)
T ch ± 0.5
(◦ C)
T hd ± 0.5
(◦ C)
I2Ca04
I2Ca06
I2Ca08
I2Ca10
I2Ca12
0.4
0.6
0.8
1.0
1.2
51.4
52.7
54.0
54.2
55.2
84.1
88.2
91.5
92.7
97.3
82.1
86.7
89.3
90.0
93.6
30.3
31.3
32.9
32.8
36.8
The fluorescence intensity measurements were carried out using a Varian Cary Eclipse
Fluorescence Spectrophotometer equipped with temperature controller. Pyranine was excited at 325 nm during in situ experiments and variation in the fluorescence intensity was
monitored at 515 nm as a function of temperature.
Thermal phase transitions observations were performed with a 1 × 1 × 4.5 cm glass
cell equipped with a heat reservoir. Before measurements, the sample was melted and then
cooled to ambient temperature so that the sample in the glass cell was distributed uniformly.
Then the ι-carrageenan gel was reheated up to 98◦ C with scan rate 0.65◦ C/min to obtain
the gel–sol transition. Cooling of the carrageenan sol from 98◦ C to room temperature was
then performed at the same rate to detect the sol–gel transition. Both scattered, I sc , and
fluorescence intensities, I, were monitored against temperature.
3. Results and Discussion
The variations in fluorescence, I, and scattered light, I sc , intensities between 20 and 98◦ C
for the samples I2Ca04 and I2Ca06, representative of all, are shown in Figs. 1(a), 1(b) and
2(a), 2(b), respectively. The heating and cooling runs are represented by open and closed
circles, respectively. The fluorescence intensity first decreased upon heating, indicating
that a low-temperature transition takes place. Further heating causes a dramatic increase
in I for both samples, corresponding to a high temperature transition. In reverse operation
the fluorescence intensity, I, decreased dramatically upon cooling the carrageenan samples
indicating that the high temperature back transition occurred. Then, with further cooling,
I increases, corresponding to the low temperature back transition. On the other hand, the
scattered light intensity first decreased during heating due to the dimer to helix (d-h)
transition, and then levels off without changing very much. At high temperatures, because
of the helix to coil transition, I sc decreased (See Fig. 2) showing a typical transition from
two phases to a single-phase system, that is, from a two to a one index of refraction system.
In order to elaborate the above results, the observed fluorescence intensity, I, has to be
corrected by taking into account the scattered light, to produce the real change in the
fluorescence intensity due to environmental variations, that is, thermal phase transitions.
The corrected fluorescence intensity Ic can be obtained from the I/Ik ratio where Ik acts
like a light source and is assumed to behave like 1/I sc . Since the turbidity of the gel varies
during phase transitions, one has to calculate the corrected fluorescence intensity, Ic to
eliminate the effect of the physical appearance of the gel and to obtain meaningful results
for the fluorescence quenching mechanisms. Here the observed fluorescence intensity, I,
is in fact the convolution of the exciting light intensity, Ik and the desired fluorescence
Fluorescence intensity, I (a.u)
Thermal Phase Transitions of IOTA Carrageenan in CaCl2 Solutions
210
200
190
180
170
160
(a)
Scattered intensity, Isc (a.u)
20
40
60
80
100
34
32
30
28
26
24
22
(b)
40
60
80
100
c
20
Corrected fluorescence int., I
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309
1.0
(d-h)
0.9
(h-d)
0.8
(h-c)
0.7
(c-h)
0.6
(c)
20
40
60
80
100
Temperature, T (oC)
Figure 1. Temperature variation of (a) fluorescence, (b) scattered, and (c) corrected fluorescence
intensities originating from I2Ca04 sample. The heating and cooling runs are represented by open
and closed circles, respectively.
intensity (corrected intensity, Ic ) from the excited pyranine, where it is assumed that Ik is
inversely proportional to the scattered light intensity, I sc . Figures 1(c) and 2(c) present the
corrected fluorescence intensity, Ic for I2Ca04 and I2Ca06 samples, respectively.
In order to interpret the results in Figs. 1(c) and 2(c), we have followed the Domain
model which was proposed by Morris et al.[10] According to this model there are two levels
of ordering of ι-carrageenan in solutions and gels. This ordering of the polysaccharides
can be named as double helices or as clusters of double helices that are called dimers. This
Fluorescence intensity, I (a.u)
200
Scattered intensity, Isc (a.u)
Ö. Tari et al.
65
Corrected fluorescence int., I
c
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310
180
160
140
(a)
20
40
60
80
100
20
40
60
80
100
60
55
50
45
40
(b)
1.1
1.0
(d-h)
0.9
0.8
(h-d)
(h-c)
0.7
0.6
(c-h)
(c)
0.5
20
40
60
80
100
Temperature, T ( oC)
Figure 2. Temperature variation of (a) fluorescence, (b) scattered, and (c) corrected fluorescence
intensities originating from I2Ca06 sample. The heating and cooling runs are represented by open
and closed circles, respectively.
model is represented by the following scheme:
[H2 ]2 ⇔ 2H2 ⇔ 4C,
(1)
where C is the random coil, H 2 is the double helix, and [H 2 ]2 is the double helix dimer.
The cartoon presentation of this model is given in Fig. 3.
According to this model, the high temperature transition during cooling corresponds
to a coil to double helix (c-h) transition. In other words, during the (c-h) transition, double
helix aggregates form a separate phase by excluding water from their domains; as a result
the ι-carrageenan-water system forms two phases with different network concentrations.
The decrease in Ic can be explained by greater quenching of the excited pyranine molecules
in this two-phase system than in the completely coiled medium. Probably most of the
Thermal Phase Transitions of IOTA Carrageenan in CaCl2 Solutions
[H2]2
2H2
311
4C
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Figure 3. Cartoon representation of Domain Model.
pyranines are located in water rather than trapped in the helices. Here we have to point out
that pyranines are quenched in water more than they are in helices when they are trapped.
In the low temperature region, further cooling causes the formation of double helix
dimers, that is, the double helix to dimer (h-d) transition occurs. Here the increase in
corrected fluorescence intensity, Ic , suggests a more rigid environment has been reached at
low temperature, which results in less quenching of excited pyranine molecules in this dimer
medium. When the dimers in the low temperature region are heated back, then the system
undergoes the dimer to double helix transition, where the Ic intensity, as a result of the
hysteresis, now decreases back to its minima. As seen in Figs. 1(c) and 2(c), (h-d) transition
occurs during cooling around 33◦ C, however (d-h) transition take place around 53◦ C during
heating, both in a very narrow region. So, (d-h) transition needs higher temperature to break
up the dimers into helices, however reverse happened at lower temperature to form dimers
from helices. In fact β values were calculated in a very narrow region, above the critical
temperatures where reduce temperature τ is in between 10−2 and 10−1.
Hysteresis naturally happens due to the temperature differences between (d-h) and (h-d)
transitions during heating and cooling processes, where system approaches (d-h) transition
gradually during heating due to higher temperature needs of dimer break up. Upon further
heating double helices are transformed to the coils and the system undergoes the double
helix-to-coil (h-c) transition. During the (h-c) transition, the Ic intensity increases back to
its previous location.
The behavior of the sigmoidal Ic curves during the heating and cooling processes
presented a perfect hysteresis loop, by showing fluorescence quenching of excited pyranine
during (d-h) transition. It is understood that pyranines are highly protected in dimers than
they are in helices, so that they quenched more in helix environment than they do in dimer
environment. As a result Ic curve monitors the (d-h) and (h-d) transitions during heating and
cooling processes by forming hysteresis loop. Then the following (h-c) transition causes
less quenching of excited pyranine molecules due to the coiled environment. The hysteresis
of the low temperature transition can be explained by the energetic needs of the (h-d) and
(d-h) transition. In other words, the (h-d) transition occurred at lower temperature because
formation of dimers from helices is energetically more possible than their dissolution, that
is, the (d-h) transition.
The coil to double helix transition temperatures, T ch and the double helix to dimer
transition temperatures, T hd was determined from the peak positions of the first derivatives
of Ic with respect to temperature. The measured transition temperatures, the curves for
which are shown in Figs. 4(a) and (b), are listed in Table 1.
312
Ö. Tari et al.
dIc / dT
0.06
(a)
I2Ca04
I2Ca06
I2Ca10
I2Ca12
0.04
Tch
0.02
0.00
70
75
80
85
90
95
100
(b)
-0.02
dIc / dT
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0.00
-0.04
-0.06
I2Ca04
I2Ca06
I2Ca10
I2Ca12
-0.08
-0.10
15
20
25
Thd
30
35
40
45
Temperature, T ( oC)
Figure 4. The first derivative of Ic curves vs. temperature upon cooling for the investigated samples.
The peak positions correspond to (a) coil to double helix, T ch and (b) double helix to dimer, T hd
transition.
The process of the sol–gel transition has been described in terms of the percolation
theory by several authors. In view of this theory, in the sol state molecules of the solute join
into small aggregates, namely clusters, which grow in size during gelation. The transition
from the sol state to the gel state occurs when the small clusters link together and create
one huge cluster, which fills most of the volume. The moment at which the huge cluster
just starts to appear indicates the gel point, p = pc , where the conversion factor p is the
fraction of the bonds which have been formed between the molecules compared to the total
number of crosslinks that can form. Thus, the system is called a gel for p > pc , a sol for
p < pc . Approaching the gel state, the number of finite clusters decreases during gelation,
whereas the size of the huge cluster grows, until all molecules are involved in the infinite
network. It is worthwhile noting that the size of the huge cluster, which is called the gel
fraction, plays the role of the order parameter in the Landau theory of the second-order
phase transitions.[28,29]
There are two groups of theories, which differ in their treatment of intramolecular
loops, namely space dimensionality, and excluded volume effects, used to describe the
sol–gel transition. These are the classic theories, like those of Flory–Stockmayer,[30,31] and
the scaling theories based on lattice percolation.[29,32]
The exact solution of the sol–gel transition was first given by Flory and Stockmayer
based on a special lattice, called a Bethe lattice, on which the closed loops are ignored. It
is known that the critical behavior of the gel fraction, G near the gel point is given by the
power law
G = A(p − pc )β ,
(2)
Thermal Phase Transitions of IOTA Carrageenan in CaCl2 Solutions
313
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where β is the critical exponent and A is the critical amplitude. The Flory–Stockmayer
theory gives β = 1 with a network in the form of a Cayley tree.[30,31] Using the relation
p − pc ≈ Tc − T and Eq. (2), the corrected fluorescence intensity, Ic can be written as a
power law near the sol–gel transition, where it is assumed that Ic is proportional to the G,
that is, as fluorescence molecules are trapped in the gelling environment, less quenching
occurs and Ic increases.
|I − Ich | = A |T − Tch |β , T → Tch− ,
(3)
−
|I − Ihd | = B |T − Thd |β , T → Thd
,
(4)
where A and B are new critical amplitudes, T ch is the coil to double helix transition
temperature, T hd is the double helix to dimer transition temperature, I ch is the critical value
of intensity at T ch , and I hd is the critical value of intensity at T hd . Here the assumption
was made that at low temperature (h-d) and (d-h) transitions, during cooling and heating,
respectively, correspond to sol–gel and gel–sol transition, respectively. On the other hand,
sol–gel and gel–sol transition at high temperature can be named as (c-h) and (h-c) transitions,
respectively, also during cooling and heating, respectively. In this work two distinct regions,
at low and high temperature, are separately taken to analyze the sol–gel and gel–sol
transitions in accord with Fig. 1. So, the formation of percolation clusters at each step is
different. First, the helices form clusters, then these helices are converted to dimer clusters
at the second stage during the cooling process.
In critical phenomenon, it is quite common to assume that the “inflection point” in a
sigmoidal phase transition curve can be taken as the critical temperature. Below and above
that point, carrageenan system can be considered in sol and gel state, respectively. The T ch
and T hd temperatures were determined by taking the first derivative of Ic with respect to the
temperature. The maximum peak positions indicate the critical temperatures T ch and T hd
on the temperature axis, as shown in Fig. 4. The produced T ch and T hd values for all the
samples are listed in Table 1.
The double logarithmic plots of the data for the (c-h) and (h-d) transition are presented
in Fig. 5 for the I2Ca04 sample. The critical exponent β was obtained by fitting the data to
the double logarithmic form of Eqs. (3) and (4). Table 2 presents the critical exponents, β,
c
= τ | < 10−1 ranges, where Tc = T ch for
in terms of reduced temperature, τ , 10−2 < | T −T
Tc
c-h and Tc = T hd for (h-d) transitions, over which the fitting procedure has been performed,
near the c-h and h-d transition for all samples. Moreover, the dimer to double helix (T dh )
Table 2
The critical exponents, β near the (c-h) and (h-d) transition for the investigated samples,
τ max is the maximum value of the reduced temperature
Coil-double helix transition
Double helix-dimer transition
Samples
β ch
τ max
β hd
τ max
I2Ca04
I2Ca06
I2Ca08
I2Ca10
I2Ca12
0.9327 ± 0.0078
0.9272 ± 0.0098
0.9017 ± 0.0080
0.9057 ± 0.0075
0.9576 ± 0.0056
0.0323
0.0162
0.0171
0.0246
0.0134
0.9199 ± 0.0101
0.9322 ± 0.0092
0.9416 ± 0.0089
0.9463 ± 0.0067
0.9512 ± 0.0073
0.0761
0.0466
0.0392
0.0410
0.0334
314
Ö. Tari et al.
log (I - Ic)
-1.2
-1.6
-2.0
β=0.9327
-2.4
-2.8
(a)
-3.2
-1.5
-1.0
-0.5
0.0
0.5
1.0
log (Tch - T)
log (I - Ic)
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-0.8
-1.2
-1.6
β=0.9199
-2.0
(b)
-2.4
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
log (Thd - T)
Figure 5. Log-log plots of the data for I2Ca04 sample near the (a) coil-double helix transition and
(b) double helix-dimer transition.
and double helix to coil (T hc ) transition temperatures were also determined from the first
derivative of the Ic curves upon heating. Figure 6 presents the placements of T dh and T hc
transition temperatures. The T hc , T hd , T dh , and T ch transition temperatures are listed in
Table 1 where it is seen that these temperatures are strongly affected by the CaCl2 content,
that is, temperatures increase by increasing CaCl2 content.
Most probably, high ion (Ca2+) content in the sol system causes a delay in the thermal
phase transition; that is, the transition occurs at relatively higher temperature. However, the
critical exponents for various CaCl2 content were found to be independent of the ion content
in the system. The critical exponents during the dimer to double helix and double helix to
coil transition can also be calculated by taking log-log plots of data at these transitions (Fig.
7). The list of the critical exponents and the maximum values of the reduced temperature
are presented in Table 3 for dimer to double helix and double helix to coil transitions.
Table 3
The critical exponents, β near the (d-h) and (h-c) transition for the investigated samples,
τ max is the maximum value of the reduced temperature
Dimer double helix transition
Double helix-coil transition
Samples
β dh
τ max
β hc
τ max
I2Ca04
I2Ca06
I2Ca08
I2Ca10
I2Ca12
0.9865 ± 0.0026
0.9724 ± 0.0030
0.9816 ± 0.0024
0.9715 ± 0.0031
0.9908 ± 0.0018
0.0977
0.9720
0.0995
0.0946
0.0993
0.9090 ± 0.0110
0.8938 ± 0.0115
0.9436 ± 0.0057
0.9578 ± 0.0060
0.9492 ± 0.0062
0.0225
0.0233
0.0161
0.0196
0.0124
Thermal Phase Transitions of IOTA Carrageenan in CaCl2 Solutions
315
0.000
dIc / dT
-0.004
-0.008
I2Ca04
I2Ca06
I2Ca10
I2Ca12
-0.012
10
20
30
(a)
Tdh
-0.016
40
50
60
70
80
dIc / dT
0.08
I2Ca04
I2Ca06
I2Ca10
I2Ca12
0.06
0.04
Thc
0.02
(b)
0.00
70
75
80
85
90
95
100
Temperature, T ( oC)
Figure 6. The first derivative of Ic curves vs. temperature upon cooling for the investigated samples.
The peak positions correspond to (a) dimer to double helix, T dh and (b) double helix to coil, T hc
transition.
log (I - Ic)
-0.5
(a)
-1.0
-1.5
β=0.9865
-2.0
-2.5
-3.0
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
log (Tdh - T)
-1.2
(b)
-1.6
log (I - Ic)
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Temperature, T ( oC)
-2.0
β=0.9090
-2.4
-2.8
-3.2
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
log (Thc - T)
Figure 7. Log-log plots of the data for I2Ca04 sample near the (a) dimer-double helix transition and
(b) double helix-coil transition.
316
Ö. Tari et al.
(a)
cooling
heating
Coils
Cayley tree with double helices
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(b)
cooling
heating
Double helices
Cayley tree with dimers
Figure 8. Cartoon presentation of thermal phase transition accord with the classical approach where
the formation of Cayley tree is shown for the (a) coil-double helix and double helix-coil transitions
and (b) double helix-dimer and dimer-double helix transitions.
The critical exponents, β, which are listed in Tables 2 and 3, have an average value
for β of 0.9436 which is very close to the value of the classic Flory–Stockmayer model
(β = 1). Similar results were obtained for the kappa carrageenan system studied using the
photon transmission method[33] and the fluorescence method.[34] It is important to note that
the value of β did not change by changing the type of carrageenan. All kappa and iota
carrageenan systems under consideration were found to belong to the same universality
class. In fact, these results are consistent with our recent studies on acrylamide-carrageenan
mixtures at high carrageenan concentrations, where the β exponents also obeyed the classic
Flory–Stockmayer model.[35]
4. Conclusions
Fluorescence probes such as pyranine have been known to be quite sensitive to their
environment. This paper has presented the fluorescence quenching mechanism that was
used to study thermal phase transitions in carrageenan system. It was shown that the
produced critical exponent β predicts the shape of the network in carrageenan gel in accord
with the classic Flory–Stockmayer model. From this we conclude that sol–gel transitions
from coil to helix and helix to dimer in iota carrageenan system obey fits the classic Bethe
lattice model, which is now presented in Cayley tree form in Fig. 8. Back transitions such
as helix to coil and dimer to helix also follow the classic Flory–Stockmayer model.
Thermal Phase Transitions of IOTA Carrageenan in CaCl2 Solutions
317
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