Kinetics and Thermodynamics Study of Ultrasound-Assisted Depolymerization of k-Carrageenan in Acidic Solution

K-carrageenan is a natural polymer with high molecular weight ranging from 100 to 1000 kDa. The oligocarrageenan with low molecular weight is widely used in biomedical application. The aim of this work was to depolymerize -carrageenan in an acidic solution with the assistance of ultrasound irradiation. The ultrasonication was conducted at various pH (3 and 6), temperatures (30-60 °C), and depolymerization time (0-24 minutes). The results show that the depolymerization reaction follows pseudofirst-order kinetic model with reaction rate constant of 1.856×10-7 to 2.138×10-6 s-1. The reaction rate constant increases at higher temperature and lower pH. The Q10-temperature coefficients of the depolymerization are 1.25 and 1.51 for pH 6 and 3, respectively. The enthalpy of activation (ΔH‡) and the Gibbs energy of activation (ΔG‡) are positive, while the entropy of activation (ΔS‡) is negative, indicating that the activation step of the ultrasound-assisted depolymerization of -carrageenan is endothermic, non-spontaneous, and the molecules at the transition state is more ordered than at the ground state. The ΔH‡ and the ΔS‡ are not affected by temperature, while the ΔG‡ is a weak function of temperature. The ΔH‡ and ΔS‡ become smaller at higher pH, while the ΔG‡ increases with the increase of pH. The kinetics and thermodynamics analysis show that the ultrasound-assisted depolymerization of -carrageenan in acidic solution is possibly through three mechanisms, i.e. bond cleavage due to cavitational effect of microbubbles, hydroxyl radical and hydrogen peroxide, as well as proton. Copyright © 2020 BCREC Group. All rights reserved


Introduction
K-carrageenan is a natural hydrocolloid with an average molecular weight of 100-1000 kDa extracted mainly from red seaweed Many researchers have attempted to apply low molecular weight -carrageenan in biomedical field as tumor growth inhibitor [2], antivirus [3], anticoagulant, antioxidant [4], and cancer growth inhibitor [5]. The biological activity of carrageenans is influenced by the degree of sulfation, distribution of sulfate groups in the carbohydrate backbone, and the molecular weight [3]. It is hypothesized that the bioactivity of the low molecular weight -carrageenan against virus is due to the negative charge of the molecule which may effectively inhibit reverse transcriptase enzyme activity of the virus [1]. Furthermore, -carrageenans with lower molecular weights have better antioxidant activity and potential for cancer prevention [5].
K-carrageenan can be depolymerized using various techniques, such as thermal depolymerization [6], acid-catalyzed hydrolysis [7][8][9][10][11], enzymatic hydrolysis [2], ozone oxidation [12], and ultrasound irradiation [13]. When a polysaccharide solution is subjected to an ultrasound irradiation, the ultrasound wave will cause a cavitation which consists of the nucleation, growth, and collapse of microbubbles. This special acoustic cavitation effect is able to cleave the polymer chain at the midpoint [14]. The collapse of the bubbles also generates instantaneous hotspot with a temperature of 5000 K and pressure of 1000 atm inside the bubbles, while the temperature in the vicinity of the collapsing bubbles can reach 1000 K. This hotspot is able to induce dissociation of water molecules to hydrogen and hydroxyl radicals [15].
Ratnawati et al. [13] investigated the effect of temperature on the thermodynamics and kinetics of depolymerization of -carrageenan at pH 9 with the assistance of ultrasound irradiation. There has been no researcher concerned on the effect of pH on the ultrasound-assisted of hydrolysis of k-carrageenan. Therefore, this research is aimed to study the effect of pH along with the temperature on the kinetics and thermodynamics of ultrasound-assisted hydrolysis of -carrageenan.

-carrageenan Refining
Prior to the depolymerization experiment, the -carrageenan was refined. Semirefined -carrageenan powder was dispersed in distilled water to form a 1% (w/v) mixture which was then heated at 80 °C for 15 minutes by constant stirring. The mixture was filtered using a vacuum filter to remove the undissolved matter. Isopropyl alcohol was added to the filtrate to coagulate the carrageenan which was then separated from the liquid by vacuum filtration. The carrageenan was dried in an airforced dryer at 70 °C for 24 h and milled into 80 mesh and stored in a closed-tight container for the experiment.

Ultrasonication
The refined carrageenan powder was dispersed in distilled water to form a 0.5% (w/v) mixture. The mixture was heated and stirred at 70 °C for 15 minutes. The solution was adjusted to a certain temperature required for the ultrasonic experiment (30,40,50, and 60 °C). A dilute HCl solution was added to the -carrageenan solution to adjust the pH to 3 and 6. The solution was transferred to a glass vessel, which was then placed in an ultrasound device, Krisbow type KLS 303365 with a frequency of 42 kHz. The sonication was conducted for 24 minutes, and a sample was withdrawn in every 8 minutes for viscosity determination using a Canon-Fenske capillary viscometer. Each viscosity determination was conducted in triplicate.

Molecular Weight Determination
The viscosity of each sample was determined at various concentration, and the ηsp/c was plotted against c according to Huggins equation as written in Equation (1) [16]: (1) where c (g.mL -1 ), ηsp (dimensionless), [η] (mL.g -1 ), and kH (dimensionless) are the concentration, specific viscosity, intrinsic viscosity, and Huggins constant of the solution, respectively. The intrinsic viscosity was deduced from the intercept of the plot. The intrinsic viscosity is related to the number-average molecular weight (M) according to Mark-Houwink equation as presented in Equation (2)

Kinetics Model Development
The derivation of the kinetics model for ultrasound-assisted depolymerization of -carrageenan is based on the assumption that both glycosidic bonds, i.e. (1→3) and (1→4), have similar susceptibility to breakage by ultrasound and acid hydrolysis [17]. The model to describe the kinetics of the depolymerization of -carrageenan under the influence of ultrasound irradiation follows pseudo-first order kinetic is represented by Equation (3) where k is the rate constant, m is the molecular weight of the structural unit and M0 and Mt are the number-average molecular weight of the polymer at t = 0 and t, respectively. The repeating unit in -carrageenan consists of G4S and AG units with molecular weights of 241 and 144, respectively. Since both the (1→3) and (1→4) links have similar susceptibility to breakage, an average of the molecular weights of both structural units is used here, i.e. 192 [6,17].
The rate constant (k) can be related to temperature according to Arrhenius equation as presented in Equation (4), (4) where A is the pre-exponential factor (s -1 ), Ea is the activation energy (kJ.mol -1 ), and R is the universal gas constant (8.314×10 -3 kJ.mol -1 .K -1 ).

Kinetics of -carrageenan Depolymerization
Equation (3) is used to correlate the number-average molecular weight of -carrageenan and time of ultrasonication. The rate constant (k) can be obtained by plotting of 1/Mt versus t as depicted in Figure 1. The values of k for various pH and temperatures of this work are presented in Table 1. The Arrhenius plot of ln (k) versus 1/T is depicted in Figure 2. The preexponential factor A and the activation energy Ea are obtained from the intercept and slope of the plot, respectively, and are presented in Table 2 along with the results for pH 9 calculated using the data from the literature [13].

Effect of temperature on the rate constant
The results presented in Table 1 show that To examine the effect of temperature on the reaction rate constant, the Q10-temperature coefficient is commonly used [19], which is defined in Equation (6), (6) where k1 and k2 are the reaction rate constants at temperatures T1 and T2, respectively. The rate constant for pH 3 increases from 6.24×10 -7 s -1 at 30 °C to 2.138×10 -6 s -1 at 60 °C, or the Q10temperature coefficient is 1.51. Meanwhile, the rate constant for pH 6 rises from 1.856×10 -7 s -1 at 30 °C to 3.648×10 -6 s -1 at 60 °C, or the Q10temperature coefficient is 1.25. The Q10temperature coefficients obtained in this work along with those calculated from the literature for the ultrasound-assisted depolymerization [13] and those for thermal and acid hydrolysis without the assistance of ultrasound [6,8,9] are presented in Table 3.
Many groups of researchers revealed similar results to this work, in which the rate constant increased as the temperature became higher [13,18,20,21]. Ratnawati et al. [13] depolymerized -carrageenan at 30-60 °C and pH 9 and found that the Q10-temperature coefficient was 1.16. The mechanism possibly occurred causing the reaction became faster when the temperature increased was through the radical formation [13]. During cavitation of microbubbles, accompanied with instantaneous extremely high temperature (up to 5000 °C) and pressure (up to 1000 atm) [15], the water molecule may experience homolytic bond breaking to hydrogen radical (H•) and hydroxide radical (OH•) leading to the formation of hydrogen gas (H2) and hydrogen peroxide (H2O2) [22]. The hydroxyl radical and hydrogen peroxide are strong oxidizing agents [23]. Both oxidants are able to depolymerize organic polymer by cleaving the glycosidic bond [24,25]. This oxidation reaction is accelerated as the temperature rises [25].
Wang et al. [18], Waghmare and Rathod [20], and Prajapat et al. [21] conducted sonoenzymolysis to starch at 25-65 °C, waste cooking oil at 40-60 °C, and guar gum at 30-50 °C, respectively. The Q10-temperature coefficient value of 1.47 can be calculated from the data of Wang et al. [18], 1.16 from Waghmare and Rathod [20], and 1.14 from Prajapat et al. [21]. They explained that a higher temperature could reduce the viscosity of the reaction mixture that would enhance the interactions between the enzyme and the substrate. This would make the reaction proceed faster and hence higher value of the rate constant at higher temperature was observed [20,21].
However, there are different results reported by other researchers. Mahalik and Madras [26] degraded poly(butyl acrylate) in o-dichlorobenzene and found that the rate constant decreased from 2.95×10 -7 mol.g -1 .min -1 to 1.38×10 -7 mol.g -1 .min -1 as the temperature increased from 30 to 70 °C, or the Q10temperature coefficient was 0.83. Chakraborty et al. [27] found that the Q10-temperature coefficient for degradation of isotactic polypropylene and polybutadiene were also less than uni-  Table 2. Activation energy and pre-exponential factor of ultrasound-assisted depolymerization of -carrageenan at various pH.  1 ty, i.e. 0.85 and 0.77, respectively. These groups of researchers explained that the reduction of depolymerization rate as the temperature rise was possibly due to the nature of the mechanism causing the polymer chain scission at the midpoint. As the temperature increases, more solvent evaporates and enters the cavitation bubbles. This will cause a cushioning effect on the collapsing bubbles and a diminishing of the intensity of the shock wave. It eventually lessens the degradation rate of the polymer at higher temperatures. Furthermore, these researchers used organic solvents instead of water. It is possible that the organic solvent does not experience cleavage as water, so there are no oxidizing agents, such as: hydroxyl radical and hydrogen peroxide formed during the ultrasonication. As the results, the only reaction that might happen was due to the mechanical effect of collapsing microbubbles, which is negatively affected by temperature. It is presented in Table 3 that the Q10temperature coefficients for chemical depolymerization of -carrageenan in aqueous solution with the assistance of ultrasound range from 1.16 to 1.51 while those without ultrasound vary from 3.19 to 3.54. Meanwhile, the Q10-temperature coefficients of the ultrasoundassisted depolymerisation of various polymers in organic solvents are less than unity. It indicates that the chain scission mechanism happening in organic solvent, i.e. midpoint scission due to solvatodynamic effect of the collapsing microbubbles, also occurs in the ultrasoundassisted depolymerisation of -carrageenan in aqueous solution [13].

Effect of pH on the rate constant
The results presented in Table 3 indicate that pH also affects the rate constant. At the same temperature, the rate constant increases as the pH decreases. At 30 °C the rate constant increases from 1.856×10 -7 s -1 at pH 6 to 6.240×10 -7 s -1 at pH 3. The same effects are ob-served for other temperatures. At pH lower than 7, another mechanism, i.e. acid hydrolysis, may also occur. According to Yoon et al. [28], the proton (H + ) readily attacks oxygen in the glycosidic bond causing cleavage at the bond. The concentration of proton at pH 3 is higher than that at pH 6, hence the reaction is faster at pH 3 than at pH 6.
It is presented in Table 1 that pH affects the Q10-temperature coefficients. At the same range of temperature (30-60 °C), the Q10temperature coefficients increases from 1.25 at pH 6 to 1.51 at pH 3. Meanwhile, a value of 1.16 for the Q10-temperature coefficients at pH 9 (at 30-60 °C) can be calculated based the work of Ratnawati et al. [13]. It indicates that the Q10-temperature coefficient increases as the pH decreases. A similar effect in acid hydrolysis of -carrageenan without ultrasound can also be deduced based on the data in the literature [8,9] as presented in Table 3. At almost the same range of temperature (54-78 °C), the Q10-temperature coefficients are 3.19 at pH 4.7 [9], 3.36 at pH 3 [9], and 3.54 at pH 2 [8]. The increase of the Q10-temperature coefficient at lower pH is most possibly due to the difference in proton concentrations. The concentration of proton at pH 2 is 2.7-order of magnitude higher than that at pH 4.7. With a higher concentration of proton, more glycosidic oxygens are attacked by the proton. This reaction proceeds faster as the temperature becomes higher [29]. As a result, the Q10temperature coefficient becomes higher at lower pH. The Q10 lowering effect of pH on the ultrasound-assisted depolymerization of -carrageenan is most possibly through the mechanism happens in the depolymerization without the assistance of ultrasound. As pH lowers, the concentration of proton increases causing more cleavage of carrageenan molecules as a result of proton attack to oxygen at the glycosidic bond. This reaction, as other chemical reactions, proceeds faster as the temperature becomes higher. As a result, the Q10-

Effect of ultrasound on the rate constant
The Q10-temperature coefficients for hydrolysis with the assistance of ultrasound at pH 3 and 9 are 1.51 and 1.16, respectively as presented in Table 3. Meanwhile, for hydrolysis without ultrasound, the values are 3.54 at pH 2 [8] and 3.19 at pH 4.7 [9]. In general, the Q10temperature coefficients for the ultrasoundassisted depolymerisation are lower than that of the depolymerisation without the assistance of ultrasound. It indicates that ultrasound lowers the Q10-temperature coefficients. Choi and Kim [30], who hydrolyzed starch in 3% H2SO4 solution, also found a similar effect in which ultrasound lowered the Q10-temperature coefficient from 3.10 for hydrolysis without ultrasound to 2.40 for hydrolysis with ultrasound. The occurrence of the polymer bond cleavage due to physical effect of the shear stress of the collapsing bubble in the ultrasound-assisted hydrolysis is possibly the cause of the lower value of the Q10-temperature coefficient compared to that of the hydrolysis without the assistance of ultrasound. It means that the cleavage of -carrageenan through cavitational effect of the microbubble possibly occurs in the ultrasound-assisted acid hydrolysis of -carrageenan [13].

Effect of ultrasound on activation energy
The results presented in Table 2 show that the value of Ea for ultrasound-assisted hydrolysis of -carrageenan at pH 3 and 6 are 32.63 kJ.mol -1 and 19.04 kJ.mol -1 , respectively. The value of 12.39 kJ.mol -1 was calculated for the pseudo-first-order kinetic model using the data of hydrolysis of -carrageenan at pH 9 [13]. Most of the chemical reactions, without the assistance of ultrasound, have activation energy which varies from 40 to 400 kJ.mol -1 . A reaction is categorized as a very fast reaction when its Ea is less than 40 kJ.mol -1 [21].
To evaluate the effect of ultrasound on the thermodynamics parameters of hydrolysis of -carrageenan, this work is compared to that reported by Lai et al. [6] who performed thermal hydrolysis of -carrageenan at pH 7 without ultrasound. They found that Ea and A were 97 kJ.mol -1 and 7.010 7 s -1 , respectively. Comparing the result of this work at pH 6, with Ea equals 19.04 kJ.mol -1 and A as low as 3.566×10 -4 s -1 , to those obtained by Lai et al. [6], it is obvious that ultrasound lowers both the activation energy and the pre-exponential factor. A similar effect was reported by Wang et al. [18] who conducted an enzymolysis to starch with and without ultrasound. They reported that Ea for the enzymolysis at 25-55 °C without and with ultrasound were 46.71 kJ.mol -1 and 40.92 kJ.mol -1 , respectively. The reduction of the activation of energy in the ultrasound-assisted hydrolysis means that ultrasound may reduce the energy barrier for reaction. According to transition state theory, a chemical reaction proceeds through the formation of a transition complex. This step needs an amount of energy, known as the activation energy. The scission of the polymer molecules by cavitation effect of ultrasound does not go through the formation of the activated complex, so it does not have any energy barrier [21].
The activation energy of the ultrasoundassisted depolymerization of -carrageenan obtained in this work and that obtained from the literature [13] are higher than those of the ultrasound-assisted depolymerization of polymers in organic solvents, but less than those of most of the chemical reactions without the assistance of ultrasound. The activation energy for ultrasound-assisted depolymerization of polypropylene, polybutadiene, poly(n-butyl acrylate), and poly(butyl methacrylate) were all negative [26,27,31]. The negative value of the activation energy would not have any physical meaning, but it is similar to that observed for mechanical breakage of polymer [27]. It also indicates that the mechanism through cavitation effect, which is a physical process, dominates the ultrasound-assisted depolymerization in organic solvents. The activation energy obtained in this work is 19.04-32.63 kJ mol -1 . It is obvious that mechanism other than the physical effect of cavitation could possibly occur as well, i.e. oxidation by hydroxyl radical and hydrogen peroxide as explained previously, as well as the attack of the glycosidic oxygen by the proton.

Effect of pH on activation energy
At pH 9, the activation energy of ultras o u n d -a s s i s t e d d e p o l y m e r i z a t i o n o f -carrageenan calculated from the data reported by Ratnawati el al. [13] is 12.39 kJ.mol -1 . The positive value of the activation energy could be due to the contribution of the chemical reaction. At pH 9, the concentration of proton is extremely low, i.e. 10 -9 mol.L -1 , that the mechanism through protonation of O in glycosidic bond is very likely not the case. The chemical reaction that most possibly occurs is the attack of -carrageenan molecules by hydroxyl radical and hydrogen peroxide as the results of homolytic cleavage of water molecules.
As it is shown in Table 2, the activation energy becomes higher at lower pH. It is possible that another mechanism with higher activation energy also works in this depolymerization. i.e. through the protonation of oxygen in glycosidic bond. As pH becomes lower, the number of proton increases causing more proton-catalyzed depolymerization, with high activation energy, to occur. The effect of all mechanisms is that the activation energy rises as the pH decreases. However, the pre-exponential factor is much lower for higher pH. Hence, the overall effect of pH on the rate constant is that the rate constant increases as pH decreases. Similar results were reported by L'homme et al. [32] for the hydrolysis of fructooligosaccharides in mineral-buffered aqueous solutions. The activation energy for the hydrolysis of 1-kestose increases from 75.4 to 80.9 kJ.mol -1 as the pH decreases from 7.0 to 4.0, while those for nystose and fructofuranosylnystose increase from 60.9 and 56.7 kJ.mol -1 to 76.2 and 84.6 kJ.mol -1 , respectively.

Effect of pH on ΔH ‡ , ΔG ‡ , and ΔS ‡
The values of ΔG ‡ , ΔH ‡ and ΔS ‡ calculated from the data of this work along with those from the literature [6,10,13] are presented in Table 4. The values of ΔH ‡ and ΔS ‡ are not af-fected by temperature, while ΔG ‡ is a weak function of temperature as presented in Table  4.
The enthalpy of activation (ΔH ‡ ) of the ultrasound-assisted acid hydrolysis of -carrageenan obtained in this work is positive. It means that the formation of the activated complex is an endothermic reaction. As presented in Table 4, the ΔH ‡ of the ultrasoundassisted depolymerization at pH 6 is 48% lower than that at pH 3. Meanwhile, from the pseudo-first-order kinetic model of the ultrasoundassisted depolymerization at pH 9 as reported by Ratnawati et al. [13], the ΔH ‡ can be calculated, i.e. 9.74 kJ.mol -1 . These results show that pH affects the ΔH ‡ . The ΔH ‡ becomes lower as the pH becomes higher. At pH 9, the possible reaction mechanisms are through physical scission by shear stress in the vicinity of the collapsing microbubbles [15] and oxidative scission by hydroxyl radical and hydrogen peroxide [22]. The physical reaction does not need activation energy, but the oxidative reaction is most likely the mechanism that needs the activation energy, and as the result is that the ΔH ‡ of the depolymerization at pH 9 is as low as 9.74 kJ.mol -1 . As the pH lowers, more protons exist in the solution, which promote another mechanism, i.e. acid-catalyzed hydrolysis of carrageenan with a higher value of activation energy, as well as the enthalpy of activation. As the result, the overall effect is that the ΔH ‡ is higher as pH becomes lower.  Table 4. Thermodynamic parameters for hydrolysis of -carrageenan.
Hjerde et al. [8] (120 kJ.mol -1 ) and Lai et al. [6] (97 kJ.mol -1 ) who conducted thermal hydrolysis of -carrageenan at pH 2 and 7, respectively. The value of ΔS ‡ is smaller (larger negative) as pH becomes higher as presented in Table 4. The negative value of ΔS ‡ indicates that the molecules at the transition state is more ordered than at the ground state [33]. At pH 9, as explained previously, the depolymerization is possibly through cavitation and radical reaction mechanisms. The bond cleavage by cavitation effect can only occur when the -carrageenan molecules is in a precise position relative to the shear stress induced by the collapsing bubbles, i.e. the midpoint of the polymer is close enough to the collapsing bubbles [14]. As pH becomes lower, the protoncatalyzed mechanism is more pronounced. It is most likely that the transition state of species involved in this mechanism is less ordered than that in the mechanical scission mechanism by microbubbles collapse. As the result, the overall activation entropy change is higher at lower pH.
To evaluate the effect of ultrasound on the activation entropy, the ΔS ‡ at pH 6 of this work is compared to that calculated from the data reported by Lai et al. [6]. The activation entropy calculated from the data of Lai et al. [6] (-0.10 kJ.mol -1 .K -1 ) is much larger than the value obtained in this work (-0.322 kJ.mol -1 .K -1 ). It indicates that ultrasound lowers the activation entropy, which means that more molecules are in ordered configuration during the depolymerization reaction, i.e. through the mechanical scission mechanism by microbubbles collapse.
The values of ΔG ‡ of the ultrasound-assisted depolymerization, as presented in Table 4, are all positive. It means that the ultrasoundassisted depolymerization of -carrageenan is a non-spontaneous and endergonic process [33]. At the same temperature, ΔG ‡ decreases with pH. On average, the values of ΔG ‡ at pH 3 is 3.1% lower than those of pH 6. The same effect is also observed in the depolymerization of -carrageenan without the assistance of ultrasound [6,9] as presented in Table 4.

Conclusions
The ultrasound-assisted of acid hydrolysis of k-carrageenan has been conducted. The depolymerization reaction follows a pseudo-first order reaction. It is found that the higher temperature increases the reaction rate constant. The effect of temperature on the reaction rate constant can be measured by the Q10-temperature coefficient of which the value is greater than unity. It is also concluded that as the pH lowers, the reaction rate constant becomes higher as well as the Q10-temperature coefficient. Based on kinetics and thermodynamics a n a l y s i s , t h e d e po l y me r i z a t i o n o f -carrageenan in acidic solution with the assistance of ultrasound is most possibly through three mechanisms, i.e. bond cleavage due to cavitational effect of microbubbles, hydroxyl radical and hydrogen peroxide, as well as proton. The reaction rate constant has a positive correlation to temperature. Lower pH gives a higher value of the Q10-temperature coefficient. At higher pH, the values of ΔH ‡ and ΔS ‡ become smaller while ΔG ‡ becomes slightly higher. The ΔH ‡ is positive, indicating that the activation reaction is endothermic. The ΔG ‡ is a weak function of temperature and positive, indicating that the activation reaction is nonspontaneous and endergonic.