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Gel Network Structure of Methylcellulose in Water L. Li,*,† P. M. Thangamathesvaran,† C. Y. Yue,† K. C. Tam,† X. Hu,‡ and Y. C. Lam† School of Mechanical & Production Engineering, and School of Materials Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 Received June 18, 2001. In Final Form: October 2, 2001 Thermal gelation was studied for aqueous gelling solutions of a methylcellulose. An attempt was made to elucidate the gel network structure and the validity of scaling laws. Thermal gelation was observed on heating, and it reverted to the liquid state on cooling. The thermoreversibility was a heating/cooling rate dependent process. For isothermally stabilized samples, 42.5 °C was found to be the critical temperature differentiating the weak gels from the strong gels. Below 42.5 °C, the gel elasticity evolved by following a scaling law with temperature as Ge ∼ [(T - Tc)/Tc]2.93 where Ge is the equilibrium modulus of the gel and Tc is the critical temperature of 42.5 °C. In contrast, no single scaling laws could be found for Ge when the temperature was above 42.5 °C. In the temperature range from 42.5 to 70 °C, it was observed that the elasticity evolution was a linear function of temperature and the mean bridge length between junctions was independent of temperature. On the basis of the experimental results, we proposed the gel network structure formed from the methylcellulose, which consists of hydrophobically associating domains as the junctions and the mean chain length of 2.75 × 104 g/mol as bridges connecting the junctions.
Introduction Hydrogels are increasingly finding applications in many areas such as biomaterials, pharmaceutical devices, or controllable sensors.1-5 For example, controlled drug release is an important application of using hydrogels, where the drugs are dispersed or dissolved in a hydrogel and the drug release is controlled either by the molecular diffusion of the drug molecules through the hydrogel or by the shrinking and swelling of the gel.4,5 A hydrogel is defined as the system formed when a natural or synthetic polymer is cross-linked via either chemical or physical bonds, which can entrap a big volume of water. A physical hydrogel forms through ionic bonding, hydrogen bonding, or hydrophobic association. The physical gelation is usually a complex process due to the transient nature of the physical network junctions. A physical hydrogel may exhibit reversibility in that the gel can exist in a physical state of a liquid (solution) or a solid, responding accordingly to the external stimuli such as temperature, pH, electric field, surfactant, solvent composition, and light. The response is a function of the chemical structure and composition of the gel. Thermoreversibility refers to the reversibility responding to temperature.1 Typical examples of polymers for thermoreversible hydrogels are hydrophobically modified cellulose6-16 and poly(ethylene oxide) (PEO)-poly(propylene * To whom correspondence should be addressed. Tel: +65-790 6285. Fax: +65-791 1859. E-mail:
[email protected]. † School of Mechanical & Production Engineering. ‡ School of Materials Engineering. (1) Guent, J. Thermoreversible Gelation of Polymers and Biopolymers; Academic Press: London, 1992. (2) Osada, Y.; Gong, J. Adv. Mater. 1998, 10, 827. (3) Hu, Z.; Chen, Y.; Wang, C.; Zheng, Y.; Li, Y. Nature 1998, 393, 149. (4) Intelligent Materials for Controlled Release; Dinh, S. D., DeNuzzio, J. D., Comfort, A. R., Eds.; ACS Symposium Series 728; American Chemical Society: Washington, DC, 1999. (5) Eichenbaum, G. M.; Kiser, P.; Shah, D.; Simon, S. A.; Needham, D. Macromolecules 1999, 32, 8996. (6) Haque, A.; Morris, E. R. Carbohydr. Polym. 1993, 22, 161. (7) Desbrieres, J.; Hirrien, M.; Rinaudo, M. Carbohydr. Polym. 1998, 37, 145.
oxide) (PPO) triblock copolymers (PEO-PPO-PEO, PPOPEO-PPO, or their modified forms),17,18 which form gels in water through the hydrophobic association that is a function of temperature. This means that the strength of hydrophobic association is controlled by the different degrees of hydrophobic to hydrophilic phase separation at different temperatures. Overall, a gel system formed via the hydrophobic association can be affected by many factors such as the number of aggregates per unit volume of the system, the average size of hydrophobic aggregates (aggregation number), the structure of junctions (aggregates), and the association strength. Therefore, it is extremely difficult to control the gel network structure that is formed from such hydrophobic associations. For any polymeric gels, the difficulty in describing the gelation and rheological characteristics in the vicinity of the sol-gel transition can be simplified by using the power laws or scaling laws.19-22 Three scaling laws, which have been extensively applied for many types of polymeric gels (both chemical and physical gels), are established for (i) the zero-shear viscosity η0, (ii) the dynamic moduli G′ and (8) Desbrieres, J.; Hirrien, M.; Ross-Murphy, S. B. Polymer 2000, 41, 2451. (9) Kobayashi, K.; Huang, C.; Lodge, T. P. Macromolecules 1999, 32, 7070. (10) Ostravskii, D.; Kjoniksen, A.-L.; Nystrom, B.; Torell, L. M. Macromolecules 1999, 32, 1534. (11) Kjoniksen, A.-L.; Nystrom, B.; Lindman, B. Colloids Surf., A 1999, 149, 347. (12) Badiger, M. V.; Lutz, A.; Wolf, B. A. Polymer 2000, 41, 1377. (13) Chevillard, C.; Axelos, M. A. V. Colloid Polym. Sci. 1997, 275, 537. (14) Hirrien, M.; Chevillard, C.; Desbrieres, J.; Axelos, M. A. V.; Rinaudo, M. Polymer 1998, 25, 6251. (15) Sarkar, N. Carbohydr. Polym. 1995, 26, 195. (16) Sarkar, N.; Walker, L. C. Carbohydr. Polym. 1995, 27, 177. (17) Bromberg, L. Macromolecules 1998, 31, 6148. (18) Tuibers, P. D. T.; Bromberg, L.; Robinson, B. H.; Hatton, T. Macromolecules 1999, 32, 4889. (19) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953. (20) Stockmayer, W. H. J. Chem. Phys. (a) 1943, 11, 45; (b) 1944, 12, 125. (21) de Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (22) Stauffer, D. Introduction of Percolation Theory; Taylor and Francis: London, 1985.
10.1021/la010917r CCC: $20.00 © 2001 American Chemical Society Published on Web 12/01/2001
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G′′, and (iii) the equilibrium modulus Ge before, at, and beyond the sol-gel transition, respectively:23-30,34
η0 ∝ -γ
for p < pg
(1)
G′(ω) ∼ G′′(ω) ∝ ωn
at pg
(2)
Ge ∝ z
for p > pg
(3)
where ) |p - pg|/pg is the relative distance of a gelling variable p from the sol-gel transition point pg, and γ, n, and z are the three indexes for the scaling laws, which are always positive. The typical experimental values of γ are between about 1.3 and 1.7. n must be within 0-1, and the z values are typically reported to be 2.0-3.0.23-30,34 ω is the angular frequency. Although the above scaling laws provide convenient ways to characterize a gel, at least two difficulties can be demonstrated. First, there are no universal values of the three indexes that can be used to describe any gels. Second, the scaling laws are not always valid for all gels. While a number of publications can be found for the validity of the scaling laws,23-30,34 there are almost no reports directly investigating the invalidity of the scaling laws. In the family of thermoreversible gelling polymers for hydrogels, hydrophobically modified cellulose is one of the largest members.6-16 Cellulose that occurs naturally has a high hydrophilicity in chemical structure. However, unmodified cellulose is water-insoluble due to the strong intermolecular hydrogen bonding. When a certain fraction of hydroxyl groups are substituted by hydrophobic groups such as methyl groups or hydroxylpropyl groups, some hydrogen bonds are prevented and the resultant derivatives become water-soluble. However, the completely substituted cellulose (i.e., the degree of substitution, DS, is 3.0) is also insoluble in water due to the lack of any hydrophilic groups for water solubility. An optimum level of DS (typically, DS ) 1.7-2.0) is required for water solubility. The solubility of hydrophobically modified cellulose in water is usually within 10 wt %. In aqueous solutions, the gelation from a hydrophobically modified cellulose is considered to be due to the intermolecular association of the hydrophobic groups on the polymer chains, which is a function of temperature. At low temperatures (room temperature and below), water molecules are presumed to form enclosed structures to surround the hydrophobic groups, causing the derivatives to be water-soluble. Upon heating, these structures are distorted due to the increased phase separation between the hydrophobic and hydrophilic groups and they are broken, resulting in the formation of hydrophobic aggregates. One of the important derivatives of cellulose is methylcellulose made from the hydrophobic substitution by (23) Martin, J. E.; Adolf, D.; Wilcoxon, J. P. Phys. Rev. Lett. 1988, 61, 2620. (24) Martin, J. E.; Adolf, D. Annu. Rev. Phys. Chem. 1991, 42, 311. (25) Chambon, F.; Winter, H. H. Polym. Bull. 1985, 13, 499. (26) Winter, H. H.; Chambon, F. J. Rheol. 1986, 30, 367. (27) Chambon, F.; Winter, H. H. J. Rheol. 1987, 31, 683. (28) Scanlan, J. C.; Winter, H. H. Macromolecules 1991, 24, 47. (29) Izuka, A.; Winter, H. H.; Hashimoto, T. Macromolecules 1992, 25, 2422. (30) Mours, M.; Winter, H. H. Macromolecules 1996, 29, 7221. (31) Tanaka, F.; Nishinari, K. Macromolecules 1997, 29, 7571. (32) Tanaka, F. Physica A 1998, 257, 245. (33) Tanaka, F. Macromolecules 2000, 33, 4249. (34) (a) Li, L.; Aoki, Y. Macromolecules 1997, 30, 7835. (b) Li, L.; Uchida, H.; Aoki, Y.; Yao, M. L. Macromolecules 1997, 30, 7842. (c) Li, L.; Aoki, Y. Macromolecules 1998, 31, 740. (d) Aoki, Y.; Li, L.; Kakiuchi, M. Macromolecules 1998, 31, 8117.
methyl groups. Methylcellulose is water-soluble and is extensively used as a binder or thickener in pharmaceutical, cosmetic, and food applications. When heated, methylcellulose gels in water and it is of a thermoreversible nature. There are several studies conducted on the gelation of the methylcellulose solutions.6-16 The hydrophobically associative properties and the gelling mechanism have not been well understood for aqueous solutions of methylcellulose. In addition, the validity of the scaling laws (eqs 1-3) to the methylcellulose system has not been fully examined.6-16 In this work, rheological experiments were conducted for an aqueous solution of methylcellulose and the investigation focused on the thermoreversibility, the gel structure, and the validity of the scaling laws. Over a wide range of temperatures from 5 to 70 °C, the gel evolution of the methylcellulose solution was monitored and its thermoreversibility was rheologically determined. The validity of the scaling laws was discussed based on the experimental results, and a gel network structure was proposed. Experimental Section Materials and Sample Preparation. Methylcellulose (MC) used in this work was kindly provided by Shin-Etsu Chemical Co. Ltd., Japan, with the trade name of SM4000. The MC was in the form of a white fine powder. The weight-average molecular weight is reported by the supplier to be 380 000, determined using light scattering. The polydispersity of molecular weight for this methylcellulose was unknown due to the technical difficulty in determining it using gel permeation chromatography. The degree of substitution measured by the supplier was 1.8. The viscosity range was reported by the manufacturer to be 4.54 Pas at 20 °C for a 2 wt % aqueous solution. Prior to use, the MC polymer was dried at 55 °C under vacuum for 24 h to remove any moisture. The MC solutions with a concentration of 4.67 wt % (49.0 g/L or 0.049 g/mL) were prepared with deionized water from the Millipore water purifier. The solution preparation procedure was as follows: The MC powder was dispersed in water at room temperature (25 °C) and shaken well. As the MC could not be completely dissolved for a short period of time at room temperature, the dispersion was transferred to a refrigerator with a temperature below 10 °C and kept for a minimum of 48 h for getting a complete solution. The solutions were clear and transparent. Rhelogical Measurements. The MC solution was transferred from the glass bottle to the rheometer (ARES 100FRTN1, Rheometric Scientific). The rheometer was equipped with two sensitive force transducers for torque measurements ranging from 0.004 to 100 g cm. Parallel plates (25 mm) were used to measure the dynamic viscoelastic functions such as the shear storage modulus G′, loss modulus G′′, and complex viscosity η* as a function of gelling time, angular frequency, or temperature. To prevent dehydration from the solution, a thin layer of lowviscosity silicone oil was placed on the periphery surface of the solution held between the plates. The dynamic temperature sweep measurements were conducted from 5 to 70 °C at a constant shear strain amplitude of 5%, an angular frequency ω of 1 rad/s, and a heating rate of 2 °C/min. To observe thermoreversibility, cooling was applied at a cooling rate of 0.5 °C/min immediately after the sample reached 70 °C in the heating process (temperature sweep). The reason for choosing such a low cooling rate was that our preliminary experiments showed significantly slow thermoreversibility at the higher cooling rate of 2 °C/min. In other words, thermoreversibility is heating or cooling rate dependent. The small shear strain was chosen to ensure the linearity of dynamic viscoelasticity measured. Isothermal frequency sweeps in the frequency range from 0.01 to 100 rad/s were performed at various temperatures (5-70 °C) after the sample had reached the near plateau of G′ as monitored via the time sweep at the same temperature.
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Figure 1. Storage modulus G′ (triangles) and loss modulus G′′ (squares) as a function of temperature in heating and cooling processes for a 49.0 g/L methylcellulose solution. A shear strain amplitude of 5% and an angular frequency ω of 1 rad/s were used. The heating and cooling rates were 2 and 0.5 °C/min, respectively.The temperatures at which G′ crosses over G′′ in the heating and cooling processes are 41.1 and 17.0 °C, respectively.
Results and Discussions Thermoreversible Gelation. As the methylcellulose forms a physical gel in water, thermoreversibility is expected. To prove thermoreversibility, the gel was first developed via a heating process beginning from a low temperature of 5 °C at a heating rate of 2 °C/min, and the gel formed up to 70 °C was then cooled slowly to a low temperature (below 10 °C) at a cooling rate of 0.5 °C. The results are shown in Figure 1. Traditionally, the crossover of G′(ω) and G′′(ω) is used as an indication of the sol-gel transition point. This method is simple and convenient, but the gel point defined by this method is usually dependent on frequency used in the measurement. Equation 2 developed by Winter’s group25-27 defines the sol-gel transition as the point at which both G′ and G′′ scale with ωn and the ratio of G′′ to G′ (i.e., tangent δ) is independent of frequency ω. In other words, at the gel point with the frequency independence, G′ must be parallel to G′′. Although there have been many reports showing the validity of the frequency independence for various polymeric gels (chemical and physical gels),23-30,34 it has not been theoretically proven that any gelling systems should necessarily follow the rule. For the present methylcellulose solution, we choose the traditional definition for the gel point before we can prove if the scaling law in eq 2 is valid for this system. Another reason for not using the frequency independence method was the experimental difficulty in examining the frequency independence during an evolution process of the gel, such as the heating or cooling process shown in Figure 1. From the G′ and G′′ curves in the heating process, one finds that G′ crosses over G′′ at about 41.1 °C. The whole heating process can be divided into three parts. The first part is below 30 °C where G′ decreases as temperature increases, showing the common thermal behavior of a liquid. The gradual increase in G′ is observed from about 30 °C, which can be considered to be caused by the partial formation of aggregates or clusters through the hydrophobic association.6,9 On the other hand, G′′ slightly decreases with temperature until the crossover point while G′ has begun to increase. This difference between G′ and G′′ in this region suggests that the evolution of the
Li et al.
hydrophobic association mainly contributes to the increase in the elasticity of the system.9,35 The thermally induced increase in the number of hydrophobically associative aggregates makes the solution undergo the critical point at which G′ begins to override G′′ and the connectivity of the polymer chains across the system volume is then established. Just beyond the gel point, G′′ begins to increase gradually while the increase in G′ is still not sharp. The remarkable increase in G′ is observed in the temperature range of 50-60 °C, which is the range where the significant induction of the phase separation of the hydrophobic parts from the hydrophilic matrix by heating is occurring.6,9,14 G′ eventually reaches the onset of a plateau at about 68 °C. Starting from the plateau, the cooling process was conducted at a cooling rate of 0.5 °C/min, which was a quarter of the heating rate of 2 °C/min. The reason for choosing this cooling rate was that for a high cooling process at a cooling rate such as 2 °C/min, it was impossible to observe the crossover of G′ and G′′ in the measurable temperature range of 2-70 °C provided by the water bath. Thus, we can conclude that the thermal gelation is a process that is dependent on the heating or cooling rate applied. In contrast to the sharp increase in G′ from the heating process in the temperature range from 50 to 60 °C, the gradual decrease in G′ with temperature in the cooling process shows an outstanding deviation from the heating curve. This clearly indicates that the thermally induced hydrophobic dissociation is not an exactly reversal of the hydrophobic association in the heating process. Indeed, the crossover occurs at 17.0 °C in the cooling process, a much lower temperature than that (41.1 °C) determined from the heating process. Down to the lowest temperature investigated, it seems that the system has not completely recovered to the original state even though it is close. The difference in dynamic modulus between the heating and the cooling processes may be due to the existence of some associated aggregates or weak connections that have not completely disassociated. It is expected that a faster rate of cooling may cause the gel to recover more slowly. The observation in Figure 1 is a clear indication that there are kinetic factors with regard to the association and dissociation phenomena during the heating and cooling processes, respectively. The kinetic process of the dissociation would be much slower compared to the cooling rate used. Thermoreversibility of a physical gel is an important characteristic that is directly related to the energy involved in the gel network structure, particularly in the network junctions.27-29 The average energy required in forming a junction is a function of the molar bonding enthalpy and the number of hydrophobic units involved in the junction. The modified Eldridge-Ferry model by Tanaka and Nishinari31 described the gel junction structure to be composed of s chains and ζ monomers (repeat units) of each chain, where s is called the junction multiplicity and ζ is the junction length. Although it is uncertain for a physical gel to have a junction structure exactly like what is presented by the model, the model provides a useful way which allows the estimation of the junction energy or junction structure. The theoretical expression31,32 for the critical gelation concentration is given as
ln cg )
ζ∆h ln M + const kBT s - 1
(4)
(35) Ferry, J. D. Viscoelastic Properties of Polymers, 3rd ed.; John Wiley & Sons: New York, 1980.
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where ∆h is the bonding enthalpy per mole of repeating units participating in the junction, kB is the Boltzmann constant, T is the gelation temperature, and M is the molecular weight of the polymer. For a methylcellulose with a given M, if the bonding energy ∆h is only dependent on temperature and only the methyl groups can form the junction, one may assume a constant junction length ζ. Under this assumption, eq 4 can be rewritten as
ln cg ) -
const1 + const2 s-1
(5)
where const1 is positive and s g 1. Equation 5 indicates that cg is an exponential function of the junction multiplicity s. The higher the value of s, the higher the cg. This is true because more polymer chains are required to be involved to form a junction with a higher value of s.31,32,34d Furthermore, s can be directly correlated with the aggregation number of hydrophobic association. For a gel with a thermoreversibility where its cooling path does not follow the same trace as that in the heating process such as that shown in Figure 1, one gets a higher critical gelation temperature on heating and a lower temperature on cooling. The outstanding difference in the critical gelation temperature between the heating and cooling processes is due to the kinetics of association and dissociation or in other words the nonequilibrium conditions. If we conduct two gelation processes for the cellulose solution of 49.0 g/L at 17.0 and 41.1 °C, as shown later in this report, in a thermodynamic equilibrium state the solution will form a stronger gel at the higher temperature and a weaker gel at the lower temperature. This is attributed to the difference in the bonding energy at different temperatures. However, the disassociation or removal of hydrophobic association to release the hydrophobic groups from the junctions is a different process. This is because eq 4 only considers a static case and any kinetic factors are not directly involved. However, thermoreversibility is a kinetic behavior where the gelation constants in the heating and cooling processes may not be the same. Rubinstein and Semenov38 proposed a comprehensive way for explanation of the kinetic difference between association and dissociation by considering the presence of an additional potential barrier or activation energy of association, akBT, which restricts the dissociation. The kinetic properties of a given gelling system should decisively depend on both the bonding energy and the activation energy. Another factor that may affect the dissociation is the time for which the system has equilibrated at the highest temperature before starting the cooling process. In this work, the cooling process was initiated immediately as soon as the highest temperature had been reached in the heating process. However, if the sample is allowed to equilibrate for some time before cooling starts, the time should have a significant effect on the dissociation behavior in the following cooling process. And this effect should be determined by how close the system has been to reaching the gelation equilibrium. When the gel system has been developed with time to be near to its equilibrium state at the given temperature, the sample should be more difficult to dissociate in the cooling process because of the more perfect network formed, compared to a freshly formed gel at the same temperature. On the other hand, when the sample at the temperature is far from the equilibrium (36) Li, L. et al. To be submitted. (37) Meakin, P. Fractals, Scaling and Growth Far from Equilibrium; Cambridge University Press: Cambridge, 1998. (38) Rubinstein, M.; Semenov, A. N. Macromolecules 1998, 31, 1386.
Figure 2. Storage modulus G′ of a 49.0 g/L methylcellulose solution as a function of angular frequency ω at various temperatures indicated by the numbers in the box where C is the unit of degrees centigrade.
state, the dissociation should be easier, resulting a lower critical sol-gel transition. Gels Evolved at Different Temperatures. The temperature effect on gelation of the methylcellulose solution was studied using the dynamic viscoelastic method. As the methylcellulose solution does not gel at the storage temperature (∼10 °C), the gelation of the solution was promoted at a desired temperature by measuring the dynamic moduli G′ and G′′ as a function of time. As soon as the solution reached a plateau in G′, the dynamic frequency sweep was conducted to determine G′ and G′′. For comparison, the G′ and G′′ data below 25 °C (down to 5 °C) are also included. Figure 2 shows the storage modulus G′ at various temperatures as a function of angular frequency ω for the methylcellulose solution of 49.0 g/L. From the figure, it can be divided into two distinct groups. Below 25 °C (but excluding 25 °C), the solutions exhibit the liquidlike behavior in which G′ scales approximately with ω in the range of low frequency but the terminal behavior, G′ ∼ ω2, cannot be observed. The deviation of the methylcellulose solution from the terminal behavior at temperatures below 25 °C was explained by Kobayashi et al.9 to be due to a supermolecular structure maintained by weak reversible association. To investigate further this unusual behavior, we carried out the rheological experiments at 25 °C for a wide range of semidilute methylcellulose solutions (7.5-30.0 g/L) and found that the unusual terminal behavior (G′ > G′′) can be observed only in the concentration range of 10-17.5 g/L. A detailed report and discussion about the unusual terminal behavior and the supermolecular structure will be presented soon.36 Above 25 °C, all the G′ curves show a clear plateau at low frequencies, indicating the existence of long relaxation structure(s). The plateau height increases with temperature, and the width of each plateau also expands pronouncedly as temperature increases. In this frequency range, we observe the frequency-independent plateaus at temperatures above about 42.5 °C, while the system does
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Table 1. Dynamic Modulus G′ at 0.01 rad/s for a Methylcellulose Gel of 49.0 g/L, at Various Temperaturesa temp, °C
25
30
35
37.5
40
42.5
45
50
60
65
70
Ge, Pa 4.67 8.45 16.7 29.0 48.4 70.8 323 1700 5200 5970 7970 a
G′ has been defined as Ge in this report.
show the weak dependence of G′ on frequency when the temperature is below 42.5 °C but higher than 15 °C. We took all the G′ values at the lowest frequency of 0.01 rad/s and approximately defined them as Ge, the equilibrium modulus. These Ge values are given in Table 1, and they are plotted in Figure 3 (a) linearly and (b) semilogarithmically against temperature. Interestingly, in the linear scale the effect of temperature on Ge is observed only when temperature is higher than 42.5 °C, and it can be fitted by a straight line to show that Ge is linearly proportional to temperature. According to the classic rubber theory,35 the rubbery plateau GN at temperature T can be related to Me, the mean molecular weight between two neighboring crosslinking points:
GN )
FRT Me
(6)
where F is the density of the rubber and R is the gas constant. The linear fitting of the data above 42.5 °C in Figure 3a gives
Ge ) constant + 302T
(7)
From eq 6, we know that the slope of the straight line of Ge versus T is FR/Me. Therefore, one can directly obtain Me from the slope of 302 in eq 7, which is 2.75 × 104 g/mol. As the average molecular weight of the methylcellulose used in this work is 380 000, the mean number of “crosslinking points” per polymer chain is estimated to be 13.8. Another important piece of information from this linear relationship between Ge and T is that for a given polymer concentration Me is constant and independent of temperature. In other words, the enhancement of the plateau with temperature is attributed only to the increase in the number of cross-linked chains with the same Me. This effect can only be found when the temperature is higher than 42.5 °C. In terms of the classical rubber theory, the contribution to Ge is from the elastically effective chains. In the present case, one may consider that the measurable Ge is mainly attributed to the effective junctions from the hydrophobic groups on the chains. Similar to the effect of molecular weight on Ge for a polymer melt where Me is constant and independent of molecular weight, the formation of effective junctions and the increase in the number of effective junctions are a function of temperature, but the mean effective length (like Me) between two neighboring junctions remains the same when the temperature is above 42.5 °C. If one calculates the mean number of hydrophobic groups per methylcellulose chain based on the molecular weight of 380 000 and the degree of substitution of 1.8, approximately 4000 [)(380 000/ 170.4) × 1.8] is then obtained. If we further consider that (i) the hydrophobic association is attributed to the combination of 1.8 methyl groups on each glucose unit (ring) rather than individual methyl groups and (ii) each combination as one single hydrophobic unit is potentially able to contribute to the formation of a network junction, the total number of the so-defined hydrophobic units is 2230 ()380 000/170.4). This means that each methyl-
Figure 3. The quasi-equilibrium modulus Ge as a function of temperature for a 49.0 g/L methylcellulose system: (a) in a linear scale and (b) in a semilogarithmic scale. Ge is defined as the storage modulus at the angular frequency of 0.01 rad/s in Figure 2.
cellulose chain has hydrophobic units of 2230 on average. Compared to the mean number (≈14) of junctions per chain, we can conclude that only a small portion of hydrophobic groups participate in the effective junctions for the formation of the gel network. However, the assumption that each glucose unit (ring) has 1.8 methyl groups may not be completely true because the maximum degree of substitution can be 3. Since we can reasonably assume that the hydrophobicity of each glucose unit is determined only by the number of methyl groups (i.e., the degree of substitution, DS), the polydispersity in the DS along the cellulose chain may be the cause of the inhomogeneous fractals or multifractal structure as will be discussed later in this report. Furthermore, the effective junctions for a gel network may only be attributed to such units of a higher degree of substitution. The scaling law of eq 3 indicates that Ge is promoted by the polymer concentration when polymer concentration is used as a gelling variable. In other words, as the molecular weight of a given gelling polymer remains constant, a “denser packing” is observed for a more concentrated system. In this case, if the junction structure is not a function of polymer concentration, a more concentrated system will give a dense gel network with a shorter Me. In most cases, the scaling index of eq 3 is between 2.0 and 3.0. In the case of methylcellulose, as the polymer concentration is fixed, the evolution of Geq is attributed to the increase in the number of effective junctions induced by heating. There are few reports dealing with the thermoreversible gelation kinetics and the scaling
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Figure 4. Plots of the quasi-equilibrium modulus Ge values in Figure 3 against the relative temperature [)(T - Tc)/Tc] where Tc is defined as 42.5 °C.
law expression for the elasticity evolution (Ge) of MC aqueous systems.6,15 For example, Sarkar determined the gelation rate (dG′/dt) at the fixed gelling temperature of 65 °C and the maximum gelation rate was found to be proportional to the 3.3 power of the MC concentration.15 Sarkar also attempted to scale the elastic modulus of a 2 wt % MC aqueous solution, which was developed at various temperatures in the range from 55 to 80 °C for 1 h, with temperature. However, no single scaling law could be identified.15 Here, the plotting of the data in the semilogarithmic scale (Figure 3b) was to examine whether a scaling law is valid for the system. As shown in Figure 3b, however, it is clear that a single scaling law could not fit the data over the whole range of temperature. However, two distinct regions are observed: an approximate scaling behavior below 42.5 °C and the nonlinear region of Ge above 42.5 °C. It is interesting to have 42.5 °C as the boundary temperature between the two regions. The boundary temperature of 42.5 °C may be defined as a critical temperature from a weak gel to a strong gel as the Ge exhibits its sharp and linear increase from the point of 42.5 °C (Figure 3). By using 42.5 °C as the critical temperature, we replotted the Ge data against the temperature defined as (T - 42.5)/42.5 in Figure 4. Again, it is clearly shown that a single scaling law cannot express the entire Ge. However, we can divide it into three regions with the respective slopes as shown in the figure. Hence, the three scaling relations can be established as
Ge ∼ 2.93
for 25 °C e T < 42.5 °C
(8a)
Ge ∼ 7.82
for 42.5 °C e T < 51.0 °C
(8b)
Ge ∼ 0.78
for T g 51.0 °C
(8c)
In the first region, the methylcellulose solution evolves its elasticity by following eq 8a up to the critical temperature of 42.5 °C. This region corresponds to the weak gels because the estimated shortest mean length (1.14 × 106 g/mol) of bridges in this region is much higher than that (2.75 × 104 g/mol) beyond 42.5 °C. Ge evolves with the largest index of 7.82 in the second region, while the evolution of Ge slows down from the second critical temperature of 51.4 °C as the power index changes to 0.78 from 7.82. This significant drop in the power index may be explained by the approach to the low critical solution temperature (LCST) of MC, which has been determined to be about 75 °C for a 4.7 wt % solution.36 Above the LCST, a homogeneous MC gel will be phase-separated
into MC precipitates. When a gelling temperature is approaching the LCST, the further formation of junctions would be confined. Gel Structures and Validity of Scaling Laws. The gel structures formed in aqueous solutions of methylcellulose are complicated. The recent studies on the dilute and semidilute solutions of methylcellulose, conducted by Kobayashi et al.9 using dynamic light scattering, proved that at 20 °C in a dilute solution (c e 2.5 g/L) there existed only a single relaxation mode with a hydrodynamic radius of ca. 38 nm while the two relaxation modes appeared in the semidilute solutions (c g 5 g/L), where the slow mode was attributed to the formation of clusters. The formation of clusters in a semidilute solution of methylcellulose at the low temperature (20 °C) may explain why the plateau in G′ could be observed at room temperature (25 °C, Figure 2). On heating, a dilute solution, which cannot gel at all temperatures, could form large clusters with a hydrodynamic radius Rh of ca. 340 nm from individual coils with Rh ≈ 38 nm, suggesting the significance of the heatinduced aggregation of polymer chains. A dense sphere of 340 nm in radius may contain 716 small spheres with a radius of 38 nm. Since the same mechanism of heatinduced aggregation in a dilute solution should be applicable to a semidilute solution, a gel can be formed when the clusters grow in size to allow the formation of a threedimensional network. For the cellulose gels, however, the aggregation strength might not be a strong function of polymer concentration but it should be strongly dependent on temperature. Another difficulty in controlling the gel structure is that the gelation process usually has a significant effect on the structure. For instance, the gelation in a heating process can be different from that under isothermal conditions because of the nonequilibrium conditions existing during a kinetic process. Examination of validity of scaling laws should be made based on a thermodynamic equilibrium state, especially for a physical gel. In other words, the gel structure should be stable and is not a function of measuring time. The previous studies of poly(vinyl chloride) (PVC) gels, carried out by Li et al.,34 provide excellent examples for this concept. In the work,34 the PVC gels were prepared at room temperature and stabilized at 40 °C. This procedure was important because it ensured the formation of stable (in the thermodynamic equilibrium state) gel structures at the temperature. As a result, the scaling laws were found to be valid before, at, and beyond the sol-gel transition for the PVC gels. In this work, the gelation behavior obtained in Figure 2 is considered as the case close to the thermodynamic equilibrium condition so that the conclusion drawn based on such results should be meaningful. On the basis of our experimental results, we would like to propose the following gel network structure formed from the methylcellulose at temperatures above 42.5 °C: it consists of hydrophobic associating domains as the junctions and the connecting bridges with the mean length of 2.75 × 104 g/mol. These gels can be classified as the strong gels. On the other hand, below the critical temperature of 42.5 °C, the hydrophobic aggregates grow and the gel becomes stronger as temperature increases but the weak gels are formed. Figure 5 proposes a schematic structure for the gel formation from the heat-induced hydrophobic association. Since it is reasonable to consider that there is a dispersity in the degree of substitution along the cellulose chain, we here present the concept of “hydrophobic effective unit”, which means that the unit contains more hydrophobic groups of methyl and is effective for hydrophobic associa-
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of scaling.21 We would consider that Bromberg’s PAAgrafted PEO-PPO-PEO hydrogels have a similarity with our methylcellulose gels, when a single scaling law was not observed. The failure of a single scaling law may be due to the nonfractal gel structure over the whole temperature range. Alternatively, it may be considered that the fractal structures formed in the three regions (Figure 5) are not identical due to the different energy levels of thermally induced hydrophobic association (or phase separation). In other words, this inconsistency in the scaling law over the three regions may be explained by the concept of the inhomogeneous fractals or multifractals.37 However, further work on this hypothesis needs to be carried out. Figure 5. Schematic drawing showing gelation though the hydrophobic effective units of methylcellulose chains. At lower temperatures, the hydrophobic association is possible from the hydrophobic effective units. On heating, the gel is formed with the hydrophobic junctions consisting of such hydrophobic effective units and the mean length Me between two junctions remains constant when the gelling temperatures are higher than 42.5 °C.
tion. While the hydrophobic association is not strong at low temperatures, it becomes stronger at elevated temperatures, leading to the formation of junctions for a gel network. When the gelling temperature is above 42.5 °C, a strong gel is formed with a fixed mean bridge length of Me ) 27 500 g/mol. The invalidity of single scaling laws for the methylcellulose system in this study is considered to be due to a heterogeneous formation of the gel network. To form a physical gel in water from the hydrophobic association of methylcellulose, the polymer chains have to be close enough to allow the hydrophobic association as the cellulose glucose units (the ring structure) are modified just by methyl groups but not by a long hydrophobic side chain like cetyl hydroxyethyl cellulose.10-12 This chemical structure in methylcellulose would cause difficulty for the stiff cellulose chains to equally move to junction domains, resulting in a nonuniformity (polydispersity) or a nonfractal structure in the gel network. Bromberg17 reported the complex scaling behavior of the thermoreversible hydrogels of poly(ethylene oxide)b-poly(propylene oxide)-b-poly(ethylene oxide)-g-poly(acrylic acid), for which for example the zero viscosity η0 was scaled with the relative concentration with as many as four power indexes (η0 ∼ 1.26, 3.45, 6.15, and 1.11 in the range of from 0.1 to about 10). Although the author attempted to theoretically explain such complicated scaling laws, the lack of data points (three points to define a scaling law) to support the conclusions and the multiple scaling indexes are difficult to accept to satisfy the concept
Conclusions The thermoreversible gelation was studied for an aqueous solution of methylcellulose with a fixed concentration of 49.0 g/L. The temperature covered a wide range of rheological properties from a liquid state to a solid state. The most significant findings in this work are summarized as follows. The thermoreversibility depends on the heating and cooling rates. The thermal recovery in a cooling process does not follow the same path of the heating process. This reason is that the hydrophobic association and disassociation are kinetic processes with different kinetic constants. For isothermally stabilized samples, 42.5 °C is found to be a boundary between the weak gels and the strong gels. Below 42.5 °C, the evolution of gel elasticity follows a scaling law of Ge ∼ [(T - Tc)/Tc]2.93 where Ge is the equilibrium modulus of a gel and Tc is the critical temperature of 42.5 °C. However, any single scaling laws cannot be applied to Ge when the temperature is higher than 42.5 °C. In the temperature range from 42.5 to 70 °C, interestingly, the elasticity evolution is a linear function of temperature, resulting in a temperatureindependent mean length (27 500 g/mol) between junctions. For the strong gels, the gel network structure is proposed to consist of hydrophobically associating domains as the junctions and the mean chain length of 27 500 g/mol as bridges connecting the junctions. Finally, the invalidity of scaling laws to the thermal gelation of methylcellulose solutions is considered to be due to the polydispersity in the gel structure or a multifractal nature over the temperature range. Acknowledgment. This work was supported by a research grant from the Nanyang Technological University, Singapore. LA010917R
