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Reversible Gelation in Isotropic Solutions of the Helical Polypeptide Poly(γ-benzyl-L-glutamate): Kinetics and Formation Mechanism of the Fibrillar Network† Rafael Tadmor,‡ Rafail L. Khalfin,§ and Yachin Cohen*,§ Department of Chemical Engineering, TechnionsIsrael Institute of Technology, Haifa, Israel 32000, and Materials Research Laboratory, University of California at Santa Barbara, Santa Barbara, California 93106 Received February 4, 2002. In Final Form: April 25, 2002 Poly(γ-benzyl-L-glutamate) (PBLG) is a synthetic polypeptide with a rigid helical conformation in several solvents. Small-angle X-ray and neutron scattering measurements were used to study the reversible gelation process in semidilute isotropic solutions of PBLG in benzyl alcohol. Time-resolved measurements of the scattering signal due to aggregation of PBLG helices into a network of microfibrils show characteristics of a nucleation and growth process with an incubation period which is extremely sensitive to the gelation temperature. Analysis by the Avrami equation yields an exponent of about 2. A mechanism of homogeneous nucleation and one-dimensional growth of fibrils, which incidentally merge or branch to form the network, is proposed. The thermodynamic transition temperature controlling fibril nucleation seems to be below the gel melting temperature. This transition may be an incongruent melting point of an ordered crystalline phase, which lies within the wide biphasic region of the phase diagram.
Introduction Poly(γ-benzyl-L-glutamate) (PBLG) is a synthetic polypeptide which assumes a rigid helical conformation in a variety of organic solvents where solubility is due to favorable interactions between the solvent and the pendant benzyl side groups.1 Its intrinsic rigidity in the organic solvents, due to stable intramolecular hydrogen bonding,2 results in lyotropic liquid crystalline behavior at elevated concentrations.3 Solutions of PBLG have thus been a useful model in the research of phase behavior of rigid polymers. Some of the phenomena which have been at the focus of intensive research are the transition between the isotropic to the liquid crystalline (LC) states with increasing polymer concentration, thermoreversible gelation by decreasing temperature, and the structure and dynamics of rigid polymer solutions in both isotropic and LC states.4,5 Equilibrium between isotropic and LC phases, predicted theoretically by Flory6 has been verified experimentally with PBLG as a model system.7 The predicted phase boundaries for liquid-liquid separation of isotropic and LC phases exhibit a narrow biphasic region at high temperature (negative values of the Flory interaction parameter χ) which transform at a critical value of χ near zero to a wide biphasic region.8 Different theoretical approaches as well as modifications of Flory’s original * To whom correspondence should be addressed: e-mail,
[email protected]. † This article is part of the special issue of Langmuir devoted to the emerging field of self-assembled fibrillar networks. ‡ University of California at Santa Barbara. § Technion. (1) Uematsu, I.; Uematsu Y. Adv. Polym. Sci. 1984, 59, 37. (2) Doty, P.; Bradury, J. H.; Holtzer, A. M. J. Am. Chem. Soc. 1956, 78, 947. (3) Cifferi, A. In Polymer Liquid Crystals; Ciferri, A., Krigbaum, W. R., Meyer, R. B., Eds.; Academic Press: New York, 1982; p 63. (4) Frey, M. W.; Cuculo, J. A.; Ciferri, A.; Theil, M. H. J. Macromol. Sci.-Rev. Macromol. Chem. Phys. 1995, C35, 287 and references therein. (5) Odijk, T. In Light Scattering Principles and Development; Brown, W., Ed.; Clarendon Press: Oxford, 1996; p.103 and references therein. (6) Flory, P. J. Proc. R. Soc. (London) 1956, A234, 73. (7) Wee, E. L.; Miller, W. G. J. Phys. Chem. 1971, 75, 1446.
approach to include effects such as polydispersity and semiflexibility were introduced, as reviewed recently.4 The focus of this work is on the gelation process that occurs upon cooling a semidilute isotropic solution of PBLG. The ability of low concentration solutions to form thermoreversible gels has been known for many years, and despite intensive research on this phenomenon, it still poses challenging questions.9 The gel structure revealed by transmission electron microscopy of freezefracture replicas1,10,11 or vitrified thin films11,12 depicts an interconnected network of microfibrils, the lateral dimensions of the microfibrils are polydisperse, ranging from a few nanometers to several tens of nanometers. Small-angle scattering measurements of X-rays (SAXS) and neutrons (SANS) also indicate aggregation of PBLG helices into microfibrils of this nanometer scale during gelation.12-15 The length of the microfibrils between junction points, and indeed the detailed nature of the junctions, is not well determined. The gel structure also exhibits larger scale inhomogeneities,16 as evident from visible-light microscopy16,17 and light scattering (either directly16,18,19 or using probe particles20). The interconnected network structure as well as the appearance of (8) Flory, P. J. Adv. Polym. Sci. 1984, 59, 1. (9) Schmidtke, S.; Russo, P.; Nakamatsu, J.; Buyuktanir, E.; Turfan, B.; Temyanko, E.; Negulescu, L. Macromolecules 2001, 33, 4427. (10) Tohyama, K.; Miller, W. G. Nature 1981, 289, 813. (11) Cohen, Y.; Talmon, Y.; Thomas, E. L. In Physical Networks; Burchard, W., Ross-Murphy, S. B., Eds.; Elsevier Applied Science: London, 1990; p 147. (12) Cohen, Y. J. Polym. Sci.: Polym. Phys. 1996, 34, 57. (13) Dadmun, M. D.; Muthukumar, M.; Schwahn, D.; Springer, T. Macromolecules 1996, 29, 207. (14) Tadmor, R.; Cohen, Y. J. Phys. IV 1993, C8, 103. (15) Izumi, Y.; Takezawa, H.; Kikuta, N.; Uemura, S.; Tsutsumi, A. Macromolecules 1998, 31, 430. (16) Russo, P. S.; Magestro, P.; Miller, W. G. In Reversible Polymeric Gels and Related Systems; Russo, P. S., Ed.; Am. Chem. Soc. Symp. Ser. 350; American Chemical Society: Washington, DC, 1987; p 152. (17) Chowdhury, A. H.; Russo, P. S. J. Chem. Phys. 1990, 92, 5744. (18) Tipton, D. L.; Russo, P. S. Macromolecules 1996, 29, 7402. (19) Shukla, P. Polymer 1992, 32, 365. (20) Oikawa, H.; Nakanishi, H. J. Chem. Phys. 2001, 3785.
10.1021/la0256026 CCC: $22.00 © 2002 American Chemical Society Published on Web 07/25/2002
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a wide biphasic region in the phase diagram led early models of the gelation process, which occurs when isotropic solutions are cooled, to be associated with liquid-liquid phase separation by spinodal decomposition (SD).10,16,21 Recent light scattering measurements support this model for PBLG-toluene gels,22 although a previous study did not.18 An alternative gelation mechanism, considered by several researchers, is nucleation and growth (NG) of a crystalline phase.23-27 Involvement of crystals in the gel structure is also supported by measurements of enthalpic endotherms during gel melting.15,25 Formation of so-called “crystal-solvate” phases, in which PBLG cocrystallizes with solvent molecules, have been suggested as the basis for the gel microfibrils.23,24,27 X-ray diffraction from concentrated PBLG gels from the LC phase showed clear evidence for crystal solvates.23,28 Solvent-mediated interactions between PBLG helices aggregating to form the microfibrils of the gel network are also supported by recent SAXS measurements.15 The phase diagram presented for PBLG in benzyl alcohol over a wide concentration range is consistent with formation of two crystalline phases, at least one of which is a crystal solvate.27 Mixed mechanisms, whereby liquid-liquid phase separation first ensues (either by SD or by NG), followed by crystallization in the concentrated phase have also been suggested.25,26 Gelation due to association of PBLG helices in solution to form a network was termed a “connectivity transition”18 following a similar concept in analysis of gelation in associating flexible polymers.29 The interplay between the hypothesized connectivity transition and phase separation and its effect on the structure of the resultant gel has been presented. It was shown to depend on a variety of experimental conditions such that a universal model may not be applicable.18 The objective of this study is to elucidate the gelation mechanism of isotropic PBLG solutions in benzyl alcohol, by following the kinetics of molecular aggregation as a function of temperature, using SANS and SAXS. Understanding self-assembly of rigid polymers to form a microfibrillar network is also relevant to technological applications. High-performance fibers, spun from rigid polymer solutions, are composed of a microfibrillar network. Manipulation of the microfibrillar structure by controlling its formation kinetics is a current challenge.30 Rigid polymer gels can be used to fabricate new membranes or lightweight foam,25 where structural control may be important. Self-assembled fibrillar networks from small molecules are of current interest, as organogelators and other applications.31 Kinetic studies on network formation are only recently being reported.32 Insight on gelation of rigid polymers may be helpful in understanding the mechanism by which self-assembled rodlike supramolecules form gels at very low concentrations. (21) Miller, W. G.; Kou, L.; Tohyama, K.; Voltaggio, V. J. Polym. Sci., Polym. Symp. 1978, 65, 91. (22) Korenaga, T.; Oikawa, H.; Nakanishi, H. J. Macromol. Sci.Phys. 1997, 36, 487. (23) Sasaki, S.; Hikata, M.; Shiraki, C.; Uematsu, I. Polym. J. 1982, 14, 205. Sasaki, S.; Tokuma, K.; Uematsu, I. Polym. Bull. 1983, 10, 539. (24) Ginzburg, B.; Siromyatnikova, T.; Frenkel, S. Polym. Bull. 1985, 13, 139. (25) Jackson, C. L.; Shaw, M. T. Polymer 1990, 31, 1070. (26) Horton, J. C.; Donald, A. M. Polymer 1991, 32, 2418. (27) Tadmor, R.; Dagan, A.; Cohen, Y. Macromol. Symp. 1997, 114, 13. (28) Cohen, Y.; Dagan, A. Macromolecules. 1995, 28, 7638. (29) Tanaka, F.; Stockmayer, W. H. Macromoleules 1994, 27, 3943. (30) Tsabba, Y.; Rein, D. M.; Cohen, Y. J. Polm. Sci., Part B: Polym. Phys. 2002, 40, 1087. (31) Terech, P.; Weiss, R. G. Chem. Rev. 1997, 97, 3133. (32) Liu, X. Y.; Sawant P. D. Appl. Phys. Lett. 2001, 79, 3518.
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Figure 1. SANS patterns from 1% (w/w) PBLG in d-BA in solution at 70 °C (O) and in the gel state obtained by quenching to 28 °C (b).
Experimental Section PBLG was obtained from Sigma Chemical Co. Ltd., having nominal molecular weight of 86 000. Spectroscopic grade benzyl alcohol (BA, Merck) and deuterated benzyl alcohol (C6D5CD2OH) (d-BA, MSD Isotopes) were distilled under vacuum and kept over molecular sieve to eliminate traces of water. The polymer concentration in the solutions studied was 1% (w/w). SANS measurements were performed at the LOQ beam-line of the ISIS spallation source, Rutherford Appleton Laboratory (U.K.), using a two-dimensional position-sensitive detector with time-of-flight measurement. Data reduction to scattering vector h ) 2π sin θ/λ (2θ being the scattering angle and λ the wavelength) and background subtraction and normalization with respect to a reference standard were performed using the Colette procedure.33 To maximize signal, a wide beam (14 mm diameter aperture) and thick quartz cuvettes (2 mm path) were used. Gelation kinetics were followed by time-resolved SANS measurements. Samples in cuvettes were heated by a circulating water bath to 70 °C and transferred to a sample holder held at a fixed gelation temperature by another circulating water bath. The first measurement was performed after about 90 s, and for the fastest gelations (at 26 and 28 °C) a reliable scattering signal could be recorded with 30 s counting time. Kinetic measurements for the slowest gelation (33 °C) were obtained by SAXS. These were performed with Ni-filtered Cu KR radiation using a compact Kratky camera equipped with temperature control by Peltier elements (KPH-A. Paar) and a linear position-sensitive detector (Raytech, with pulse-height discrimination). Reduction to absolute intensity units was performed with a secondary glass standard calibrated with a moving slit device. Correction for the slit geometry (length and width) was done by the procedure of Glatter for indirect Fourier transformation in reciprocal space (ITR).34
Results and Discussion The gelation process can be readily followed by SAXS or SANS measurements that reflect microstructural changes on the length scale of about 1-100 nm that are particularly relevant to the aggregation of helices into the microfibrillar network. The SANS patterns from 1% PBLG in the solution and gel states are shown in Figure 1 as the open and filled circles, respectively. The scattering pattern from the gel exhibits a significant increase in intensity at small angles, relative to the solution state. This is due to aggregation of PBLG helices into the microfibrils forming the gel network.12-14 The functional (33) King, S. M.; Heenan, R. K. The LOQ Instrument Handbook Vol. 1, Technical Report RAL-TR-96036; Rutherford Appleton Laboratories, Didcot, 1996. (34) Glatter, O.; Gruber, K. J. Appl. Crystallogr. 1993, 26, 512.
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Figure 3. SANS patterns during gelation of a 1% (w/w) PBLG/ d-BA solution quenched to 28 °C. The elapsed time (min) after quenching is indicated in the figure. Bottom to top: solution, 2.5, 4, 8, 11, 14, 20 min, and final gel.
Figure 2. The Bragg reflection in SAXS patterns from a gel quenched to 20 °C (lower curve) and upon subsequent heating to 30, 40, 50, and 60 °C (plots displaced vertically for clarity).
form of the gel scattering pattern is sensitive to the gelation process. Often a power-law relation of intensity to scattering vector is observed, especially in quenched gels,13,14 which has been interpreted as reflecting a selfsimilar fractal structure. However, due to the rather limited h-range over which the power law is observed, this may be due to a broad distribution of microfibrillar dimensions. Quenched and slowly cooled gels also differ in the higher angle part of the scattering patterns. We reported previously that quenched gels exhibit a Bragg reflection at spacing of about 2 nm, even at the low concentration of 1%. However, such a peak was not observed in slowly cooled gels. Figure 2 shows the high-h part of SAXS patterns from a 1% PBLG gel quenched to 20 °C and annealed at increasing temperatures, after correction for the dimensions of the incident beam (“desmearing”). The Bragg peak suggests a relatively high degree of order in the parallel packing of PBLG helices in the microfibrils, and thus its appearance only in quenched gels was puzzling. It is evident that annealing below the gel melting temperature decreases the peak intensity, which is barely noticeable above 40 °C. The large increase in scattering at small angles during the sol-gel transition can be used to follow the gelation kinetics. The large difference in scattering length densities of PBLG and d-BA, and the high flux of the spallation source allow time-resolved SANS patterns to be collected at different gelation temperatures. Figure 3 shows SANS patterns from the 1% PBLG/d-BA system during gelation by quenching the solution (at 70 °C) to 28 °C. The most prominent sign of the gelation process is the increase in the scattered intensity at small angles, which is due to aggregation of PBLG helices into the gel microfibrils. To evaluate the gelation kinetics from SANS patterns such as in Figure 3, and at other gelation temperatures, we need to establish a relation between the recorded intensity, in excess of the solution scattering, to the extent of gelation as a function of time XT(t). We rather arbitrarily choose the integrated intensity at small-angles QT′, in the
format of the scattering invariant,35 evaluated in the experimentally significant range of 0.08 < h < 1.0 nm-1
QT′(t) )
1.0 2 h [iT(h,t) - isol(h)] dh ∫0.08
(1)
where isol(h) and iT(h,t) are the intensities at scattering vector h from solution and at time t after a quench to temperature T, respectively. The basis for this choice is an assumption that during gelation, the scattering pattern contains additive contributions from the solution and aggregated states, weighted by their respective volume fractions. The integrated representation of eq 1 is preferred since in the framework of analysis of a two-phase structure, it is proportional to the volume fraction of aggregates (for small values) and is not sensitive to the aggregate structure.35 We thus represent the extent of gelation as a function of time XT(t) as
XT(t) )
QT′(t) QT′(tf∞)
(2)
The extents of gelation as a function of time, evaluated from the time-resolved SANS measurements, are shown in Figure 4a for different temperatures (SAXS measurements were used for the highest temperature due to the long time required). The characteristic “S”-shaped curves, with an incubation period that is very sensitive to temperature, are strong indications of a nucleationcontrolled process. The temperature dependence of the gelation rate is striking. The gelation half-time (τ1/2) is a few minutes at 26 °C, whereas it is several days at 33 °C. It may therefore be instructive to evaluate the gelation kinetics as shown in Figure 4b, using the Avrami equation36
1 - XT(t) ) exp(-ktn)
(3)
The exponents obtained from the slope of the linear fits in Figure 4b, listed in Table 1, are approximately 2, except for the highest temperature where it is closer to 1. An exponent of 2 is in accord with one-dimensional (fibrillar) (35) Porod, G. In Small-Angle X-ray Scattering; Glatter, O., Kratky, O., Eds.; Academic Press: New York, 1982; p 17. (36) Wunderlich, B. Macromolecular Physics; Academic Press: New York, 1976; Vol. 2, Chapters 5 and 6.
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Figure 5. Schematic representation of a critical nucleus of the ordered phase within an isotropic solution.
Figure 4. Gelation kinetics at different temperatures: (a) time evolution of the gel fraction, (b) fit of the Avrami equation (eq 3); solid line, SANS; dashed line, SAXS. Table 1. The Avrami Exponent as a Function of the Gelation Temperature T (°C)
n
T (°C)
n
26 28 30
2.2 2.1 1.9
32 33
2.3 1.2
growth controlled by homogeneous (thermal) nucleation.36 If we assume that the microfibrils are the entities that undergo nucleation and growth, then it is reasonable to expect homogeneous nucleation due to the small scale of the nucleated entity (a few nanometers). At 33 °C, the rate of homogeneous nucleation is so slow that heterogeneous nucleation can also play an important role, which may explain the lower exponent at this temperature. It is instructive to compare the present analysis to that presented recently for formation of networks by selforganization of the small molecule gelling agent GP-1 (Nlauroyl-L-glutamic acid di-n-butylamide).32 Gel images of both systems show some similarities in the overall appearance of a fibrillar network, although the scale of the PBLG network is smaller by at least an order of magnitude. The gelation kinetics of GP-1 solutions are characteristic of a nucleation and growth process, exhibiting an incubation time for nucleation having a characteristic relation to the solution supersaturation37 (analo(37) Liu, X. Y. J. Chem. Phys. 2000, 112, 9949.
gous to undercooling in this case). A fractal object of dimension Df grows in 3D space from a single heterogeneous nucleation site by a process of “initial nucleationgrowth-branching-growth-branching- - -by self-epitaxial nucleation of daughter branches on a growing parent branch”.32 For this mechanism, theory and measurements show that the fractal dimension of the gel is equal to the Avrami exponent of its growth kinetics.32 It so happens that the SANS power laws (“apparent fractal dimensions” in the range of 2.2-2.5)11-14 reported for PBLG/BA gels are close to the Avrami exponents reported here, as well as to that of the GP-1 gel (2.4). Nevertheless, we maintain that significant differences exist between these systems so that different mechanisms play a dominant role. PBLG gels form from pre-existing rigid polymers and the fibril length between network junctions may be on the order of a few polymer lengths. In GP-1 gels the small molecules in solution can crystallize directly onto the growing network, in which the fibril length is much larger then the molecular dimensions. For the current system we suggest the mechanism of homogeneous nucleation and one-dimensional growth of fibrils, which incidentally merge or branch to form the network, rather than heterogeneous nucleation and 3D growth of a fractal branched network. The currently proposed mechanism may also apply to small molecule systems, in which supramolecular rods are first formed and only subsequently aggregate to a network. The striking temperature sensitivity of the nucleation rate is indicative of homogeneous nucleation. More work is needed, however, to verify this suggestion. If the gelation kinetics are controlled by the rate of homogeneous nucleation, then the gelation half-time τ1/2 may be related to temperature (T), as36
ln τ1/2 )
8πσs2σeTx2 ∆H2kT(Tx - T)2
(4)
where ∆H is the enthalpy of fusion per volume of the ordered PBLG phase within the microfibril and Tx is the thermodynamic transition temperature. σs and σe are the surface energies of the sides and ends of a cylindrical nucleus of the PBLG microfibril, as shown schematically in Figure 5. Neglecting differences of absolute temperature between different gelations (in the Boltzmann factor kT), the transition temperature that controls nucleation of microfibrils can be evaluated from a linear plot of ln-1/2(τ1/2) as a function of T, as shown in Figure 6. The transition temperature obtained by extrapolation to infinite time is about 41.5 °C, significantly lower than the gel melting temperature, about 55 °C. Finally, we attempt to interpret the findings reported above with regards to the equilibrium phase diagram of the PBLG/BA system under study. The phase diagram,
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Figure 6. The gelation half-time as a function of gelation temperature, a linear approximation of eq 4.
Figure 7. The phase diagram for PBLG (MW 86 kDa) in benzyl alcohol, from ref 27. The dotted line represents schematically the “connectivity transition”.
as reported previously,27 is shown in Figure 7. It was determined by evaluating the temperature at which the small-angle scattering signal from PBLG aggregates disappears upon slow heating. At concentrations below about 60%, the melting transition is only weakly dependent on concentration, whereas at higher concentrations it increases sharply. This indicates two different crystalline forms that differ in both melting temperature and fusion enthalpy. We suggest that an incongruent transition to an ordered crystalline phase (Tx of eq 4) exists within the wide biphasic region, as shown by the dotted line in Figure 7. For 1% PBLG Tx is about 42 °C. The fusion enthalpy of this phase is significantly higher than that of the liquid crystal or crystal solvate phases. Therefore, a shallow quench below the gel melting temperature but above Tx
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does not significantly nucleate these less ordered phases, whereas a deeper quench below Tx nucleates the ordered crystalline phase, from which PBLG microfibrils grow to form the gel network. However, the equilibrium sate of the microfibrils is the crystal solvate, such as the complex A phase in Figure 7. This suggestion is also in line with the behavior of the diffraction peak at larger scattering vectors shown in Figure 2, which appears only in quenched gels and becomes less prominent upon heating until it is barely visible at 40 °C. The transition denoted Tx may thus serve as the “connectivity transition” described by Tipton and Russo,18 and gives it a particular meaning: it is the temperature at which the microfibrils forming the gel network can nucleate. The gelation scenario suggested by our results is similar to the second type of percolation transition discussed by these authors.18 The temperature of the connectivity transition is below that of the equilibrium boundary defining the isotropic phase from the wide biphasic region and yet can be easily reached in practice due to kinetic reasons. We differ in the identification of the wide biphasic region as liquid-solid equilibrium in the current case (PBLG/BA) rather than liquid-liquid equilibrium in the PBLG/toluene case.18 Spinodal decomposition, therefore, does not play a role in the gelation mechanism proposed for this system. It was shown on the basis of Flory’s theory that a rather deep metastable region exists between the binodal and the spinodal for isotropic solutions of rigid polymers.25 Conclusion The gelation kinetics of isotropic PBLG solutions, followed by the SANS signal due to aggregation of helices, show conclusive evidence for a nucleation and growth mechanism: large hysteresis between gelation and gelmelting temperatures and characteristic “S-shaped” kinetic curves with an incubation period which is highly temperature dependent. An Avrami exponent of about 2 suggests a mechanism of homogeneous nucleation and one-dimensional growth of fibrils. These may incidentally merge or branch to form the network. The thermodynamic transition temperature controlling fibril nucleation, obtained by extrapolation to infinite incubation period, is below the gel melting temperature. We suggest that this transition is an incongruent melting point of an ordered crystalline phase, which lies within the wide biphasic region of the phase diagram. Acknowledgment. The authors thank the council for the Central Laboratories of the Research Councils (U.K.) for supporting neutron scattering studies. We are grateful to Dr. R. K. Heenan and Dr. S. M. King of the ISIS facility for invaluable assistance. LA0256026
