Biomacromolecules 2005, 6, 1623-1627
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Flory Temperature and Upper Critical Solution Temperature of Gelatin Solutions Amarnath Gupta, B. Mohanty, and H. B. Bohidar* School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India Received December 1, 2004; Revised Manuscript Received February 15, 2005
The Flory temperatures (θ) measured by turbidity experiments performed on gelatin solutions were found to be 12 ( 0.3, 13 ( 0.3, 14 ( 0.3, 14.5 ( 0.3, and 15 ( 0.3 °C for salt concentrations 0.1, 0.075, 0.05, 0.025, and 0 M (NaCl), respectively. Estimated persistence length (lp) of this weakly charged polyelectrolyte could be deduced from the Benoit and Doty (J. Phys. Chem. 1953, 57, 958) relationship with the approximation that this biopolymer assumes a compact near-globular shape at Flory temperature, implying lp ) 9(Rh)2/(5Lm), where Lm is the contour length and Rh is the hydrodynamic radius. It was found that lp ≈ 2.2 ( 0.2 nm at room temperature (20 °C), invariant of salt concentration. The Flory expansion factor (R ) Rh(T)/Rh(θ) ) 1.5(0.2) was found to be almost constant. θ-Composition for this biopolymer was deduced from turbidimitric titration of aqueous gelatin solutions with the alcohols methanol, ethanol, 2-propanol, and tert-butyl alcohol. It appears that hydrophobic interactions play a crucial role in causing chain collapse at θ-temperature and composition. I. Introduction Knowledge of the upper and lower critical solution temperatures (UCST and LCST) of polymer solutions is essential for the basic understanding of such solutions. This serves the purpose of providing a clear picture to the underlying interactions between the solvent medium and the polymer. Needless to say, from the application point of view, such information is essential. For synthetic polymers, establishment of UCST and LCST can be performed with ease in various solvent environments, which yields the Flory temperature, also called the θ-temperature.1-5 This has been done routinely for a wide range of polymers having different molecular conformations dissolved in a variety of solvents.6-10 The θ-temperature is a physical state where the binary interactions vanish or, equivalently, the second virial coefficient of osmotic pressure equals zero. For a given solvent(s), the polymer may have a θ-temperature that is uniquely defined by the thermodynamic environment of the polymer in the solvent. Similarly, for a given temperature there may be a θ-composition of the solvent mixture. It has been argued in the past that, due to the disappearance of all binary interactions, the static properties, such as the osmotic bulk modulus, are only sensitive to ternary interactions.11 An unusual manifestation of this is that at length scales smaller than the correlation length of a semidilute polymer solution the dynamics is linked to the local viscosity that showed concentration and temperature dependence.11 Thus, the behavior of the system at θ-temperature cannot necessarily be interpolated from normal temperature properties. Determination and understanding of such behavior in biopolymers such as proteins, polypeptides, nucleic acids, polysaccharides are even more intriguing, because these carry * Corresponding author. E-mail:
[email protected].
charged side groups and the net charge carried is a function of solution pH among other things. Due to this, the θ-temperature and composition determination remains elusive even today for many biopolymers. This is one of the areas in biopolymer science that has not attracted much attention in the past, despite of the fact that gathering such information is important for obvious reasons. The pertinent question to ask is, does LCST or UCST or both exist for all biological polyelectrolytes? Correspondingly, is there a well-defined Flory temperature for these biopolymers? In this paper, we address this problem for gelatin, a low charge density polyampholyte, and attempt to determine both Flory temperature and the θ-solvent composition for the binary solvent alcohol-water with the alcohols being methanol, ethanol, 2-propanol, and tert-butyl alcohol. This was achieved through turbidimitric titrations and dynamic light scattering measurements. II. Materials and Methods Materials. The alcohols used (methanol, ethanol, propanol, and tert-butanol) were obtained from Merck, Germany. Gelatin (Type-A, pI ≈ 5.1) was bought from Sigma Chemicals and sodium chloride was bought from E. Merck. All other chemicals used were bought from Thomas Baker. All of the chemicals were of analytic grade. The gelatin samples were used as supplied. The molecular mass of the gelatin sample was estimated from SDS/PAGE and was found to be 90 ( 10 kDa. Gelatin solutions of concentrations 1%, 0.75%, 0.5%, and 0.25% (w/v) were prepared in deionized water at 50 °C, and these were allowed to homogenize by resorting to continuous stirring for 4 h. Prior to this, the solvent ionic strengths were adjusted to the required value by dissolving the appropriate amount of NaCl.
10.1021/bm0492430 CCC: $30.25 © 2005 American Chemical Society Published on Web 03/22/2005
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Five different salt concentrations were chosen, namely, 0, 0.025, 0.05, 0.075, and 0.1 M for our experiments. The solution pHs were found to lie between 6.5 and 6.8. All the samples were optically clear and these remained transparent when cooled to room temperature (20 °C). We deliberately avoided performing experiments with samples having concentrations more than 1% w/v to remain within the solution phase for this biopolymer. There are two methods to reach the cloud point. The first approach is through cooling or heating of dilute polymer solutions of various concentrations and to determine the cloud temperature. This procedure is called the cloud temperature titration (CTT) method. We followed this procedure to obtain cloud points. The gelatin solution was kept in a thermally insulated chamber and the required temperature was maintained through a highly regulated refrigerated temperature controller providing a temperature accuracy of (0.1 °C. The solutions were cooled in steps of 0.3 °C from room temperature, and the turbidity of the solutions was measured by a high-resolution colorimeter (Brinkman-910, Brinkman Instruments) at 450 nm. In addition, the solution pH was monitored continuously and showed no change. This process was continued until the solution turned cloudy, corresponding to temperature TCT for a solution having biopolymer volume fraction φ2. In the second method, called cloud concentration titration (CCT), the cloud point is achieved at a given temperature by adding a nonsolvent to the dilute polymer solution. In our case, we titrated aqueous gelatin solutions with methanol, ethanol, 2-propanol, and tert-butyl alcohol at room temperature until the cloud point was reached, which yielded the volume fraction of the nonsolvent (φCP), corresponding to a biopolymer having volume fraction φ2. The solution pH showed a marginal increase to 7.0, which is being ignored. The particle sizing of the gelatin molecules at 20 °C and T ≈ θ was performed by dynamic light scattering measurements for CTT samples. The details about of the light scattering setup and instrument are discussed elsewhere.12 The Laplace inversion of the correlation spectra was performed to confirm unimodal relaxation time distribution, which guided the path to further analysis. This allowed determination of the translational diffusivity, D h z. According to Einstein relation, the D h z (the z-average diffusion coefficient at finite dilution) is inversely proportional to the translational frictional coefficient, ft at finite dilution by the relation, D hz ) kBT/ft where kB is the Boltzmann constant and T is absolute temperature. The value of ft obtained from above equation can be used for a direct estimation of the hydrodynamic radius (Rh) of the particles, provided they have a spherical shape, using the relation ft ) 6πηRh. We then get D)
kBT 6πηRh
(1)
where η is the solvent viscosity at temperature T. Since the size measurements were done at a finite concentration of biopolymers, it will be appropriate to refer to Rh as the effective hydrodynamic radius.
Figure 1. Turbidimitric observation of cloud point measurements performed on a 1% (w/v) aqueous gelatin solution at wavelength 450 nm. Notice that at higher ionic strength the cloud point temperature shifts to lower value. See the text for details.
Figure 2. Phase diagram of aqueous gelatin solutions as a function of ionic strengths determined through turbidimitric observation of cloud point. Notice the unusual shape of the curves, which is typical of polyelectrolytes. The Flory temperature decreases with increase in the ionic strength of the solution. See the text for details.
III. Results and Discussions (A) Cloud Temerature Titration (CTT) Studies. The CTT data gives the cloud point temperatures (TCT) at various volume fractions of the biopolymer (φ2). These are related through an empirical relation given by13 1/TCT ) 1/θ - BCT ln(Φ2)
(2)
Here BCT defines the polymer-solvent interactions with the limiting value defined at TCT ) θ giving BCT ) 0. Typical titration plots are shown in Figure 1, which revealed a shift in the observed Flory temperature to the lower temperatures as NaCl concentration was increased. The 1/TCT versus ln(φ2) plot yielded the Flory temperature and the values of the interaction parameter for gelatin solutions having different salt concentrations (Figure 2). The phase diagram shown in Figure 2 shows that TCT is not linearly dependent on polymer volume fraction as demanded by eq 2. The data were fitted to a quadratic volume fraction dependent equation like 1/TCT ) a + b ln(φ2) + c (ln(φ2))2, which always yielded c , b.
Flory Temperature and UCST of Gelatin Solutions
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Figure 3. Effect of Flory temperature on solution ionic strength. Experiments were performed on aqueous gelatin solutions and cloud points measured through turbidimitry.
Figure 5. Phase diagram of aqueous gelatin solutions as function of pH determined through turbidimitric titration of the solution with alcohol to observe the cloud point performed at wavelength 450 nm. The Flory composition concentration decreases with an increase in the size of the hydrocarbon chain of the aliphatic alcohols. See the text for details.
Figure 4. Effect of salt concentration on the interaction parameter. Notice that at 0.03 M NaCl there is a sudden change in BCT, which has been interpreted as the crossover from electrostatic to hydrophobic domain. See the text for details.
Hence, the data reduction was performed using eq 1 and both θ and BCT were deduced from the least-squares fitting of the first three data points in each curve. Figures 3 and 4 give plots of Flory temperature and interaction parameter as function of salt concentration, respectively. The interdependence between θ and BCT is shown in Figure 4. Figure 2 is actually an UCST phase diagram with an anomalous shape (concave upward), which owes its origin to intramolecular interactions (electrostatic and hydrophobic) prevailing between different segments of the gelatin chain. The signature of this is also evident from the fact that the θ-temperature decreased almost by 4 °C as the salt concentration increased from 0 to 0.1 M NaCl, as depicted in Figure 3. The corresponding interaction parameter, BCT, showed a very strong dependence on salt concentration but revealed almost no correlation to the θ-temperature data (the change was less than 10%, Figure 4). Figure 4 has two distinct domains, one for NaCl concentration less ≈0.03 M and one beyond going up to 0.1 M. The screened Coulombic interactions will have a DebyeHuckel screening length, κ-1 (κ ≈ 3.3I1/2 nm-1, where I is the monovalent salt concentration expressed in moles), which for the NaCl concentrations chosen for these experiments typically lies between 2 and 1 nm, whereas the typical mean interparticle distance (l) between two gelatin chains (ap-
proximated to be point particles) at the highest gelatin concentration (1% w/v) was ≈25 nm. Thus, qualitatively for κ-1 , l, the short-range intermolecular interactions were irrelevant. Since, a sizable chain segment of gelatin molecule is hydrophobic, we decided to concentrate on studying the intramolecular hydrophobic interaction mediated transition to the θ-state. This paved the way for CCT experiments to determine cloud point concentrations of binary solvents of water-alcohol. (B) Cloud Concentration Titration (CCT) Studies. The cloud points pertaining to the specific binary solvent composition (water-alcohol) were used in the empirical relation (eq 3) to determine the polymer-solvent interaction parameter BCP13 Φ3 ) Φ3,θ - BCP ln(Φ2)
(3)
where Φ3 is the volume fraction of nonsolvent (alcohol) and Φ2 is the volume fraction of polymer. Figures 5 and 6 reveal the pH and ionic strength dependence of Φ3,θ (concentration of nonsolvent corresponding to θ-composition) respectively for various alcohols. Two things are clear from this: (i) for alcohols with longer hydrophobic tails, Φ3,θ had lower values, and (ii) Φ3,θ was dependent on salt concentration. The variations in the value for Φ3,θ as a function of pH were more significant for methanol (20%), whereas the same for tert-butyl alcohol was only 5%. Similarly, the change in Φ3,θ for ethanol was ≈25% as I increased from 0 to 0.1 M, whereas the same for tert-butyl alcohol was only ≈10% (Figure 6). Figure 7 revealed a typical temperature dependence behavior of Φ3,θ, which indicates the requirement of higher Φ3,θ at higher temperatures for methanol. (C) Hydrophobic Interactions. Quantification of hydrophobic interactions is nontrivial, unlike Coulombic interactions. Hence, we will make a qualitative discussion based on experimental data. Figures 4-6 are quite revealing. The
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Figure 6. Phase diagram of aqueous gelatin solutions as a function ionic strength determined through turbidimitric titration of the solution with alcohol to observe the cloud point performed at wavelength 450 nm. The Flory composition concentration decreases with an increase in the size of the hydrocarbon chain of the aliphatic alcohols. For a given alcohol, this composition increases with salt concentration. See the text for details.
Figure 7. Dependence of temperature on the Flory composition. The experimental system comprised of 1% (w/v) aqueous gelatin solution that was titrated with ethanol at various temperatures.
lower molecular weight alcohols are more soluble in a polar solvent like water, as these can easily form hydrogen bonds with water molecules, but in higher alcohols the hydrophobicity increases, due to longer aliphatic chain length, which entropically hinders formation of hydrogen bonds for such alcohols. In fact, we found that beyond tert-butyl alcohol higher alcohols were immiscible with water. The fact that phase separation was induced at much lower Φ3,θ values for tert-butyl alcohol as compared to methanol implies that phase transition was indeed dependent on hydrophobic effects. Close to I ) 0.03 M, there is a small change in the slope in the curve shown in Figure 6 (more prominent for lower alcohols). This compares with Figure 4, where we observed identical features. Unlike short-range Coulombic interactions, hydrophobic interactions are known to increase with ionic strength of the solution. Thus, beyond I ) 0.03 M hydrophobic interactions are playing a definite role. Hydrophobic interactions are not very sensitive to pH, which explains the data in Figure 5, whereas it is very strongly dependent on temperature, which is in tune with the data in Figure 7. Alcohol, particularly ethanol-induced conformational phase transitions, have been observed in a variety of polyelectrolytes in the past. Arscott et al.14 studied DNA condensation induced by multivalent cations (Co3+) in ethanol-water
Gupta et al.
mixed solvent and observed a BfA conformational transition at ethanol concentration Φ3 ≈ 0.4. Piskur and Rupprecht15 have studied the thermal stability and structure of aggregated DNA in ethanol-water solution using a mechanochemical method. They observed that, at a threshold ethanol concentration (Φ3 ≈ 0.4), aggregation in DNA sets in with a marked increase in Tm, the double helix melting temperature. Further increase in ethanol concentration produced a BfA structure transition. In an earlier work,16 we reported ethanol-induced condensation of CT-DNA observed through static and dynamic light scattering, which occurred at ethanol concentration Φ3 ≈ 0.53. These observations raise a pertinent question: What happens to ethanol-water binary solvent in the ethanol concentration range Φ3 ≈ 0.4-0.5 that induces conformational phase transitions in polyelectrolytes? Yamaguchi performed SANS, X-ray diffraction measurements, and simulation studies on such a system17 and observed the anomalous behavior of this solvent in the ethanol concentration region Φ3 ≈ 0.45. It has been argued in the past18,19 that transfer of aliphatic (at least up to butanol) alcohols from its own bulk to water is favored energetically. The chemical potential change ∆µ thus encountered is positive with a value 0.76 kcal/mol for ethanol, 1.5 kcal/mol for n-propanol, and 2.4 kcal/mol for n-butanol.19 Interestingly, the corresponding entropy change is negative. Frank and Evans18 argued that water-bound alcohol molecules create a higher degree of order than that found in bulk water, which leads to lowering of entropy. The computer simulation results are in agreement with these contentions.17 Because of this affinity, the binary solvent becomes a marginal solvent for gelatin that leads to the phase separation at a threshold value of Φ3,θ. (D) Estimation of Persistence Length. The hydrodynamic radii (Rh) of the gelatin chains were measured at 20 °C and close to the Flory temperature by dynamic light scattering. Persistence length (lp) is the average projection of the endto-end vector on the tangent to the chain contour at a chain end in the limit of infinite chain length or the integral of the average projections of chain elements of the infinitely long chain on its initial direction.20 It is a measure of the stiffness of the polymer. It is an intrinsic property of a polymer molecule. For polyelectrolytes, lp ) (lo + le), where lo and le are bare and electrostatic persistence lengths. The later is a function of solution ionic strength and polyelectrolyte charge density. Benoit and Doty21 have derived the following expression relating the unperturbed radius of gyration (Rg) to lp and the contour length (Lm)21 (Rg2)/(lp2) ) Lm/3lp - 1 + 2lp/Lm - 2Lm2/lp{1 - exp(-Lm/lp)} (4) which can be approximated to eq 5 if Lm . lp lp ) 3(Rg2)/Lm
(5)
For spherical particles, Rg2 ) (3/5)Rh2, which gives lp ) (9/5)Rh2/Lm, yielding lp ≈ 2.0 ( 0.2 nm. This estimation required a priori knowledge about Lm, which was estimated as follows. Consider the gelatin primary structure to be a linear single strand polypeptide chain of monomeric repre-
Flory Temperature and UCST of Gelatin Solutions
Figure 8. The hydrodynamic radius and expansion factor as a function of the ionic strength of the solution. The expansion factor remained almost invariant of NaCl concentration. See the text for details.
sentation -(-Gly-X-Pro-)n-.Molecular weights of residues glycine, proline, and X (average of glutamic acid, 4-hydroxyproline, etc.) are 57, 97, 115, respectively. So, the average molecular weight per monomer is ≈ 270. There are four peptide bonds of bond length ) 1.32 Å each, three N-C bonds (bond length ≈ 1.47 Å each), and three C-C bonds (bond length ≈ 1.54 Å). Thus, the monomer length of the gelatin molecule is ≈14.31 Å. Since the average molecular mass established by SDS/PAGE was ≈100 kDa, the degree of polymerization comes out to be ≈370, giving a contour length Lm ≈ 520 nm. The persistence length determined in this approximate method compares rather well with the value reported in the literature (2 nm).22 The Flory expansion factor should be constant, because it is the ratio of the square of hydrodynamic radius at room temperature to the θ-temperature if the molecule folds to a near-spherical conformation at θ-temperature from its original random coil conformation at room temperature. Since, Reff defines a mean size at both these temperatures, the Flory expansion factor R ≈ Reff(T)/Reff(θ). This is plotted in Figure 8, which shows invariance with salt concentration. IV. Conclusions The θ-temperature was established for gelatin solutions. This was extended to include nonsolvent-driven phase transitions that yielded the cloud point concentrations of the binary liquid mixture, clearly indicating strong dependence on hydrophobic interactions over short-range electrostatic forces. It was also observed that the Flory temperature moved
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to lower temperatures as the ionic strength of the solution was increased. It was not possible to determine the UCST temperature explicitly for gelatin solutions because of the anomalous nature of these curves (Figure 2). It was found that hydrophobic interactions were dominant for salt concentration >30mM. It was possible to estimate the persistence length from the effective hydrodynamic radii measurements performed at close to θ-temperature, which was in agreement with literature data. The coil expansion factor was deduced from the molecular size measurements performed at 20 °C and close to θ-temperature. The coherent picture that emerges is that the maximum degree of intermolecular hydrogen bonding (in the vicinity of ethanol concentration Φ3 ≈ 0.5) is responsible for turning this binary solvent into a marginal one. In addition, the hydrophobic interactions play a definitive role in inducing phase separation. Acknowledgment. A.G. is thankful to Council of Scientific and Industrial Research, India, for a Junior Research Fellowship. This work was supported by a research grant from University Grants Commission, Government of India. References and Notes (1) Hunt, M. L. J. Phys. Chem. 1956, 60, 1278. (2) Patterson, D. Macromolecules 1969, 2, 672. (3) Saeki, S.; Kuwahara, N.; Konno, S.; Kaneko, M. Macromolecules 1973, 6, 589. (4) Rubinstein, M.; Colby, R. H. Macromolecules 1990, 23, 2753. (5) Raspaud, E.; Lairez, D.; Adam, M. Macromolecules 1995, 28, 927. (6) Cornet, C. F.; van Ballegoijen H. Polymer 1968, 7, 293. (7) Brown, W.; Stepanek, P. Macromolecules 1988, 21, 1791. (8) Saeki, S.; Konno, S.; Kuwahara, N.; Nakata, M.; Kaneko, M. Macromolecules 1974, 7, 521. (9) Adam, M.; Deslanti, M. Macromolecules 1985, 18, 1760. (10) Adam, M.; Deslanti, M. J. Phys. (Paris) 1984, 45, 1513. (11) Adam, M.; Leirez, D.; Raspaud, E.; Farago, B. Phys. ReV. Lett. 1996, 77, 3673. (12) Soni, S. S.; Sastry, N. V.; George, J.; Bohidar, H. B. J. Phys. Chem. 2003, 107, 5382. (13) Elias, Hans-G. In Polymer Handbook-II; Wiley-Interscience: New York, 1999; p VII/291. (14) Arscott, P. G.; Ma, C.; Wenner, J. R.; Bloomfield, V. A. Biopolymer 1995, 36, 345; Biopolymer 1990, 30, 619. (15) Piskur, J.; Rupprecht, A. FEBS Lett. 1995, 375, 174. (16) Roy, K. B.; Antony, T.; Saxena, A.; Bohidar, H. B. J. Phys. Chem. B 1999, 103, 5117. (17) Yamaguchi, T. Pure Appl. Chem. 1999, 71, 1741. (18) Frank, H. S.; Evans, M. W. J. Chem. Phys. 1945, 13, 507. (19) Arnett, E. M.; Krover, W. B.; Carter, J. V. J. Am. Chem. Soc. 1969, 91, 4028. (20) Micka, U.; Kremer, K. Europhys. Lett. 1997, 38, 279. (21) Benoit, H.; Doty, P. J. Phys. Chem. 1953, 57, 958. (22) Pezron, I.; Djabourov, M.; Leblond, J. Polymer 1991, 32, 3201.
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