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Gelation Mechanism of Thermoreversible Gels of Poly(vinylidene fluoride) and Its Blends with Poly(methyl acrylate) in Diethyl Azelate Asok K. Dikshit and Arun K. Nandi* Polymer Science Unit, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700032, India Received December 8, 2000. In Final Form: February 28, 2001 Poly(vinylidene fluoride) (PVF2) and its blends with poly(methyl acrylate) (PMA) produce thermoreversible gels in diethyl azelate. SEM studies indicate a fibrillar network structure, and WAXS/FTIR studies indicate the presence of R-polymorphic crystals of PVF2 in the gels. Some newer X-ray diffraction peaks are observed in the dried gels than those in the melt-crystallized PVF2 samples, and the intensity ratios (I°hkl/I°II0) of the diffraction peaks of the dried gels are also different from those of the melt-crystallized sample. The gelation rates of these systems are measured by the test tube tilting method. At a particular isothermal temperature the gelation rates of the blends decrease and the critical gelation concentrations / ) of the blends increase with an increase in PMA concentration. In terms of PVF2 concentration the (Ct)R / Ct)R values are also higher for the blends than that of the pure PVF2 at a given gelation temperature. The -1 gelation rate (t-1 gel) has been analyzed from the equation tgel ∞ f(C) f(T). At a constant temperature analysis of the concentration function f(C) indicates three-dimensional percolation is a suitable model for gelation of both PVF2 and its blends, supporting that blending does not alter the macroscopic mechanism. The microscopic mechanism, determined from f(T), is however affected due to blending. The gelation process is considered as a two-step process: coil f TGTG h conformer f fibrillar crystallization (gelation). The free energy of activation (∆F) of the conformational ordering increases, and the free energy of formation of the critical size nucleus (∆G*) decreases with increasing PMA concentration of the blend. A possible explanation for this difference has been offered. A comparison of ∆F and ∆G* of the two processes indicates that transformation of the coil f TGTG h conformer is the rate-determining step of the gelation process for all the samples. The lower gelation rate of the blends may be due to its increased ∆F value.
Introduction The mechanisms of thermoreversible gelation of polymers are an important area of research for the past two decades.1-2 The mechanism of gelation depends on both the polymer and the solvent, and it may be caused from liquid-liquid phase separation, mesomorphic phase transition, conformational ordering, and crystallization.1-3 Among these, one or sometimes more than one process may be responsible for gelation. Poly(vinylidene fluoride) (PVF2) is a technologically important polymer because of its piezo- and pyroelectric properties.4 It produces gels in different solvents5-9 and also produces miscible blends with different commodity plastics.4 In our previous studies it has been argued that three-dimensional percolation is a suitable mechanism for gelation of PVF2 in different solvents.5-7 Also, conformational ordering and fibrillar crystallization are the main processes responsible for gelation.5-7 Here we report how the gelation mechanism of PVF2 is affected due to blending with a miscible polymer. Though the gelation mechanism of a single polymer is widely studied, the gelation mechanism of the blends is (1) Reversible Polymer Gels and Related Systems; Russo, P. S., Ed.; ACS Symposium Series; American Chemical Society: New York, 1986. (2) te Nijenhuis, K. Adv. Polym. Sci. 1997, 130, 1. (3) Berghmams, H. In Integration of Fundamental Polymer Science and Technology; Lemstra, P. J., Kleintjens, L. A., Eds.; Elsevier Applied Science: London, 1988; Vol. 2, p 296. (4) Lovinger, A. J. In Developments in crystalline polymers-1; Bassett, D. C., Ed.; Applied Science Publishers: London, 1981; p 195. (5) Mal, S.; Maiti, P.; Nandi, A. K. Macromolecules 1995, 28, 2371. (6) Mal, S.; Nandi, A. K. Polymer 1998, 30, 6301. (7) Dikshit, A. K.; Nandi, A. K. Macromolecules 1998, 31, 8886. (8) Dikshit, A. K.; Nandi, A. K. Macromolecules 2000, 33, 2616. (9) Cho, J. W.; Song, H. Y.; Kim, S. Y. Polymer 1993, 34, 1024.
not studied much, particularly for synthetic polymers. Recently, Cho et al.10 have studied the thermoreversible gelation of blends of PVF2 and poly(vinylidene fluoridetetrafluoroethylene) in γ-butyrolactone and have suggested that multidimensional growth of the gel occurs in such polymer blend solutions. They have also observed the existence of separate crystals of the components in the gels. Asnaghi et al.11 have studied the gelation mechanism of poly(acryl amide) in the presence of poly(ethylene glycol) and observed a competition between gelation and spinodal decomposition in the system. However, to our knowledge, there is no gelation study reported in the literature for the miscible blends of synthetic polymers, and we report here the gelation mechanism of a miscible blend. In our earlier works we discussed the mechanism of thermoreversible gelation in two ways:6,7 (a) macroscopic mechanism and (b) microscopic mechanism. The former deals with the nature of connectedness as a whole, whereas the later sheds light on the molecular mechanism by which the physical cross-linking occurs. The mechanisms of the gelation processes have been elucidated from the gelation rate measurements, substantiated from the structural and thermodynamical investigations. The gelation rate (t-1 gel) is usually expressed as a combination of a concentration function f(c) and a temperature function f(T):5-7,12
t-1 gel ∝ f(C) f(T)
(1)
where tgel is the gelation time and is usually expressed as (10) Cho, J. W.; Lee, G. W. J. Polym. Sci. 1996, B34, 1605. (11) Asnaghi, D.; Giglio, M.; Bossi, A.; Righetti, P. G. J. Chem. Phys. 1995, 102, 9736.
10.1021/la001718v CCC: $20.00 © 2001 American Chemical Society Published on Web 05/18/2001
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Figure 1. SEM picture of gels of PVF2 and PVF2-PMA blend in DEAZ where the PVF2 concentration is 4.5 g/dL: (a) WPVF2 ) 1.0; (b) WPVF2 ) 0.75; (c) WPVF2 ) 0.5; (d) WPVF2 ) 0.25.
the gelation rate. At constant temperature the variation of t-1 gel with f(C) helps to elucidate the macroscopic mechanism of gelation, and at constant concentration variation of t-1 gel with temperature yields the microscopic mechanism. In this work we have chosen poly(methyl acrylate) (PMA) to produce blends with PVF2 and diethyl azelate [(CH2)7(COOC2H5)2] as a medium of gelation. The blending has been done at three different compositions of PVF2 and PMA. We have chosen these blends because the interaction between the polymers and its dependence on composition is well-known.13 So, a critical analysis of the gelation mechanism with blend composition can be made. The gelation rates of PVF2 and its blends are measured, and the influence of blending on the gelation mechanism of PVF2 is delineated here. Experimental Section Materials. A commercial PVF2 sample (KY-201 Pennwalt Corporation, USA) was used in the work. The polymer had a weight average molecular weight (M h w) ) 8.81 × 105, polydispersity index (PDI) ) 2.82, and head to head (H-H) defect ) 5.31 mol %.7 The sample was recrystallized from a dilute solution in acetophenone (0.3%, w/v), washed with methanol, and dried in a vacuum at 60 °C for 3 days. PMA was prepared by a solution polymerization technique using 2,2′-azobisisobutyronitrile (AIBN) (12) Ohkura, M.; Kanaya, T.; Kaji, K. Polymer 1992, 33, 5044. (13) Maiti, P.; Nandi, A. K. Macromolecules 1995, 28, 8511.
as initiator and dodecyl mercaptan as the chain transfer agent.14 The polymer was fractionated by a liquid-liquid phase separation technique from its benzene solution using methanol as nonsolvent.14 The second fraction was used to make blends with PVF2. The blends were prepared by a solvent cast method from N,Ndimethyl acetamide.15 The molecular weight for the second fraction of PMA (M h ν ) 3.7 × 105) was measured from intrinsic viscosity measurements in benzene at 25 °C. The solvent diethyl azelate (DEAZ) was purchased from Lancaster, London, and was used as received. Preparation of Gel and Its Characterization. The gels were prepared in two ways. For structural and morphological investigations, the gels were prepared in test tubes by taking appropriate amounts of polymer and solvent. They were sealed under vacuum (10-3 mm) by repeated freeze thaw techniques.5-7 They were then homogenized at180 °C for 20 min and quenched at room temperature (30 °C) to prepare the gel. After complete gelation the tubes were broken, and these freshly prepared gels were dried under vacuum. Care was taken in each case that the gel did not melt during the drying process and the temperature of drying never exceeded 40 °C. The dried gels were then gold coated, and SEM pictures were taken through a SEM (Hitachi, S-415A) instrument. The wide-angle X-ray scattering (WAXS) patterns of the gels were made from the dried gels (dried for 1 month at 40 °C in a vacuum) in a powder diffractometer (Philips, model PW-1710) with Cu KR radiation. For FT-IR study a Nicolet FT-IR instrument [Magna-IR 750 spectrometer (series-II)] was used. The solvent spectra were subtracted from the gel spectra (14) Maitra, B.; Nandi, A. K. Polymer 1993, 34, 2260. (15) Maiti, P.; Chatterjee, J.; Rana, D.; Nandi, A. K. Polymer 1993, 34, 4273.
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Table 1. X-ray Data of PVF2-PMA Blend-DEAZ Gels at Different Blend Compositions [dhkl(calc) for r-Phase PVF2 with a ) 5.02 Å, b ) 9.63 Å, and c ) 4.62 Å; I°hkl ) Observed Intensity] WPVF221 ) 1.0
melt crystal19,20
WPVF2 ) 0.75
dhkl(calc)
I°hkl/I°110
dhkla
I°hkl/I°110
dhkla
I°hkl/I°110
100 020
5.02 4.81
0.52 0.64
110 011
4.45 4.17
1.0 0.17
5.00 4.82 4.67* 4.48 4.27 3.90*
0.41 0.79 1.08 1.00 0.55 0.74
5.05 4.82 4.65* 4.47 4.24 3.89*
0.34 0.55 0.81 1.0 0.34 1.6
3.29 2.76
0.51 0.10
3.28 2.75
0.48 0.12
hkl
021/101 121 130 200 131 002 211/041 230 a
3.33 2.79 2.70 2.51 2.33 2.31 2.15 1.98
0.70 0.41 0.48 0.54 0.52
2.27
0.11
0.51 0.19
2.28 2.05*
0.39 0.18
WPVF2 ) 0.5 dhkla
I°hkl/I°110
4.81 4.67* 4.45
0.61 1.11 1.0
3.91* 3.62* 3.29
1.24 0.31 0.54
2.51
0.07
2.28
0.14
WPVF2 ) 0.25 dhkla
I°hkl/I°110
5.02 4.79
0.24 0.43
4.42
1.0
3.89* 3.62*
0.30 0.20
Asterisks indicate new dhkl values for the gel formation.
to get the PVF2 spectra in the gel form. For the thermodynamic study, the gels were made in Perkin-Elmer large volume capsules (LVCs). Kinetic Study. The kinetics of gelation was studied by the test tube tilting method.5-7,9,10,12,16-19 To prepare the gels at different concentrations, appropriate amounts of PVF2 or its blends (5-60) mg and the solvent DEAZ (0.5 mL; density ) 0.973 g/dL) were taken in glass tubes (8 mm i.d. and 1 mm thick). They were sealed under vacuum (10-3 mmHg) after repeated freezethaw processes. These were then melted at 180 °C in an air oven to make them homogeneous and were quickly transferred to a silicon oil bath. The gelation time (tgel) was counted as the time when no flow occurs after the tube is tilted.5-7,9,10,12,16-20 The accuracy of the gelation time measurement was (5 s by a trial and error procedure of repeated measurements. Measurement of T°gm Values and T°d. The equilibrium melting points [equilibrium gel melting temperature (T°gm) and equilibrium dissolution temperature T°d] are key parameters for analyzing the gelation rate. For their measurement, appropriate amounts of polymer and solvent were taken in LVC pans fitted with Ο-rings and were tightly sealed in a quick press. They were melted at 180 °C for 10 min in a DSC and quenched to the desired isothermal temperature, where they were kept for 3 h. The gels were heated at 10 deg/min in a DSC to obtain the gel melting temperature. The T°gm values were measured by a HoffmanWeeks extrapolation procedure.6 For the measurement of T°d the samples were isothermally crystallized above the gelation temperatures for 12 h and were heated in a DSC to get the Tm. From the Hoffman-Week extrapolation procedure the T°d values were obtained.
Figure 2. WAXS patterns of PVF2-PMA blend gel (dried) in DEAZ: (1) WPVF2 ) 1.0; (2) WPVF2 ) 0.75; (3) WPVF2 ) 0.5; (4) WPVF2 ) 0.25.
Morphology. In Figure 1 the SEM pictures of dried PVF2 gel (4.5 g/dL of PVF2 in DEAZ) and those of its blends containing 4.5 g/dL of PVF2 are presented. From the figure it is clear that the gels have a fibrillar network structure in all cases. With an increase in the PMA concentration in the blend, the fibrils become thinner and curlier, and for the blend composition WPVF2 ) 0.25 (micrograph 1d), the fibrils are intertwinned. So by blending PVF2 with PMA, the fibrillar network is present, but the texture of the fibrils becomes somewhat changed with increasing PMA concentration. Since the gel morphology is determined in the dried state, it is assumed throughout the
work that the gels have similar morphology also in the undried state. Structure. The structures of the PVF2 -PMA blend gels are studied by WAXS. In Figure 2 the WAXS patterns of the dried gels of PVF2-PMA blends of different compositions are shown. From the figure it is clear that R-polymorph PVF2 crystals are produced during gelation.21-24 Therefore, R-PVF2 crystallites may act as crosslinking junctions in the blend gels. In Table 1 the X-ray data of the gels are compared for different blend compositions together with the melt crystal of pure PVF2. It is apparent from the table that some new diffraction peaks (denoted by asterisks) are observed other than those in the melt crystal, and these are almost the same for all the
(16) Tan, H. M.; Hiltner, A.; Moet, A.; Baer, E. Macromolecules 1983, 16, 28. (17) Prasad, A.; Mandelkern, L. Macromolecules 1990, 23, 5041. (18) Domszy, R. C.; Alamo, R.; Edwards, C. O.; Mandelkern, L. Macromolecules 1986, 19, 310. (19) Malik, S.; Jana, T.; Nandi, A. K. Macromolecules 2001, 34, 275. (20) Abdallah, D. J.; Weiss, R. G. Langmuir 2000, 16, 352.
(21) Lando, J. B.; Doll, W. W. J. Macromol. Sci. Phys. 1968, 2 (2), 205. (22) Hasegawa, R.; Takahashi, Y.; Chatani, Y. Polym. J. 1972, 3, 600. (23) Bachmann, M. A.; Lando, J. B. Macromolecules 1981, 14, 40. (24) Saundarayam, P. R.; Tyrer, N. J.; Bluhm, T. L. Macromolecules 1982, 15, 286.
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Figure 3. Solvent-subtracted FTIR spectra of PVF2-DEAZ gel.
blends. This indicates that the cause of the new diffraction peaks is the same, and it may be due to the solvated structure of R-form crystals of PVF2.24 Also the intensity values of different diffraction peaks are compared relative to that of the 110 peak in each sample. In the gels (blend or pure PVF2) the intensity ratios do not match those of the melt crystal. This indicates that in the gels, though the crystal system and d spacing remain the same as those of the melt crystal, the atomic positions of the statistical up and down arrangement of the PVF2 chains may be somewhat changed. So it may be surmised that atomic coordinates in the unit cell are disturbed during gelation of PVF2 and its blends, and it may be due to the polymer solvent complex formation which is evident from the thermodynamic study in pure PVF2 and in its blend gels.8,25 To ensure that there is no change in the polymorphic structure during drying, solvent-subtracted FTIR spectra have been obtained for the pure PVF2-DEAZ gel and are shown in Figure 3. The subtracted spectra have a peak at 532 cm-1 which corresponds to the R-polymorphic structure of PVF2 with the TGTG h conformation.26 So it may be argued that during drying there is no change in the polymorphic structure of the PVF2 and its blend gels. Gelation Mechanism. The gelation rate versus concentration plot is shown in Figure 4 for PVF2 and its blend (wPVF2 ) 0.5), respectively. It first increases with PVF2 concentration and then gradually levels off for all the four systems at each isothermal temperature (Tgel). The gelation rate gradually decreases with an increase in temperature at fixed concentration for both the cases. A comparison of Figure 4 indicates that the isothermal gelation temperatures decrease in the blend, and at a given temperature the gelation rate of pure PVF2 is higher than that of the blend. In Figure 5 a plot of gelation rate with WPMA is shown at different isothermal temperatures. A sharp decrease of gelation rate with increase of WPMA is observed for every gelation temperature. Critical Gelation Concentration. The critical gela/ is the minimum polymer contion concentration Ct)∞ centration required for gelation. It has been measured from the extrapolation of t-1 gel versus concentration plots of Figure 4 to the zero gelation rate. The error limit of / Ct)∞ values obtained by this extrapolation procedure is / values (in terms of total polymer within 2-3%. The Ct)∞ concentration) vary with temperature and increase with (25) Dikshit, A. K.; Nandi, A. K. In preparation. (26) Belke, R. E.; Cabasso, I. Polymer 1988, 29, 1831.
Figure 4. Gelation rate (t-1 gel) versus total polymer concentration plots of PVF2 and PVF2-PMA blend gel in DEAZ at indicated temperatures: (a) WPVF2 ) 1.0; (b) WPVF2 ) 0.5.
Figure 5. Gelation rate (t-1 gel) versus WPMA plot at the total polymer concentration 6 gm/dL: (4) 70 °C; (b) 65 °C; (O) 55 °C; (2) 45 °C.
gelation temperature for all the systems (Figure 6).18 At / values increase with a particular temperature the Ct)∞ an increase in PMA concentration of the blend. This is found to be reasonable because with an increase in PMA concentration the PVF2 concentration becomes diluted and hence formation of PVF2 crystallites is hindered. Since crystallites act as junction points of the gel, to start the network formation, more PVF2 and hence more blend are required. However, a critical analysis of the effect of the PMA concentration of the blend may be done by comparing / Ct)R values (in terms of pure PVF2) at a particular
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/ Figure 6. Plot of Ct)R (in terms of total polymer concentration) with gelation temperature of blend gels in DEAZ: (b) WPVF2 ) 0.25; (O) WPVF2 ) 0.5; (2) WPVF2 ) 0.75; (4) WPVF2 ) 1. /′ Table 2. Ct)r [in Terms of PVF2 Concentration (g/dL)] of the Blends
gelation temp (°C) 80 75 70 65 60 55 50 45
/′ Ct)R for the following compositions of the blend (WPVF2) 1.0 0.75 0.5 0.25
0.75 0.70 0.60 0.45 0.30
2.03 1.88 1.73 1.50 1.28 1.16
1.50 1.40 1.25 1.15 1.0 0.90
0.73 0.68
temperature. This has been calculated by multiplying the / Ct)∞ values of the blend gels with the weight fraction of PVF2 (WPVF2) in the blend. This is shown in Table 2, and it is apparent that a greater amount of PVF2 is required for the starting of network structure in the blends. However, it does not vary much with increasing PMA concentration in the blend. The necessity of a larger amount of PVF2 to start the network structure in the blends may be for the hindrance of crystallite formation due to (I) diffusional difficulty, (II) strong attraction between polymer components, and (III) dilution of the local concentration of PVF2 by PMA. In a PVF2-PMA blend the specific interaction decreases with an increase in PMA concentration in the blend,13,27 so for the blends / . With of higher WPVF2, more PVF2 is required to reach Ct)R / an increase in PMA concentration the Ct)R value does not increase, rather it decreases slightly as interaction decreases. The other parts, for example, diffusion and local concentration of PVF2, appear to be less important here. Macroscopic Mechanism. To elucidate the macroscopic mechanism of gelation, the concentration dependence of the gelation rate of eq 1 is used. At a particular temperature,6-8,12,19
t-1 gel ∝ f(C)
(2)
where f(C) ) φn, φ is the reduced overlapping concentration / / (T)/Ct)R (T). and equals C - Ct)R -1 Plots of log tgel versus log φ are made according to eq 2,7,8 and a representative plot for the PVF2-DEAZ gel is shown in Figure 7. From the figure it is clear that at each gelation temperature the data points fit well in straight (27) Maiti, P.; Nandi, A. K. Macromol. Chem. Phys. 1998, 199, 1479.
Figure 7. Representative plot of log t-1 gel versus log φ for WPVF2 ) 1.0 at indicated temperature. Table 3. n Values for PVF2 and PVF2-PMA Blend Gels in DEAZ Tgel (°C) 90 85 80 75 70 65 60 55 50 45 40 35 30 25 avg st dev
n values for WPVF2 1.0 0.51 0.50 0.47 0.41 0.42 0.43 0.40
0.45 0.04
0.75 0.52 0.54 0.51 0.45 0.42 0.41
0.47 0.05
0.50
0.47 0.46 0.43 0.40 0.35 0.32
0.41 0.06
0.25
0.50 0.47 0.43 0.47 0.41 0.37 0.44 0.05
lines. The least-squares slope values (n) are presented in Table 3. For pure PVF2 the average n value is 0.45. The n value of eq 2 has a close resemblance to the β value of the percolation equation.28,29
G ∝ (P - Pc)β ∝ ∆Pβ
(3)
where G is the gel fraction and P is the conversion factor, Pc is its threshold value, and β is a critical exponent. A comparison of eqs 2 and 3 can be done as follows: when P < Pc, no percolation takes place, and when C < C*, no gelation takes place. So φ of eq 2 and ∆P of eq 3 have a close resemblance to each other. Under the assumption that the rate theory of chemical processes is applicable to the physical gelation process, t-1 gel is proportional to the gel fraction (G). Consequently, n and β must be the same if the gelation process obeys the percolation model.5-7,19 Since the measured n values (Table 3) are close to 0.45 (average ) 0.45) for pure PVF2-DEAZ gel, it may be argued that three-dimensional percolation is a suitable model for gelation of this system. For the gels of the blends, the n values are also close to 0.45, so it may be argued that there is not much deviation from the random percolation for the blend gels. Presently, Liu and Pandey30,31 showed from the finite size scaling theory that for the gels β values (28) Stauffer, D.; Coniglio, A.; Adams, M. In Advances in Polymer Science; Dusek, K., Ed.; Springer-Verlag: Berlin, 1982; Vol. 44, p 108. (29) Zallen, R. The Physics of Amorphous Solids; John Willey & Sons: New York, 1983; p 135. (30) Liu, Y.; Pandey, R. B. J. Chem. Phys. 1996, 105, 825. (31) Liu, Y.; Pandey, R. B. Phys. Rev. 1996, E54, 6609.
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are less sensitive to the quality of the solvent. This is also seen in the PVF2-PMA blend gels, as in the gelling medium both PMA and DEAZ are present and in the PVF2-PMA pair the interaction decreases with increasing PMA concentration.27 So it may be surmised that threedimensional percolation is a universal model for the gelation process of thermoreversible gels. Microscopic Mechanism. The microscopic (molecular) mechanism of gelation may be elucidated from the temperature function of the gelation rate.5-7,19 The gelation rate of this system has a negative temperature coefficient. To analyze the temperature coefficient, we would like to use the scheme6,7 cooled
PVF2 (coil) 98 TGTG h (conformer) f R-crystal (fibrillar gel) The scheme is similar to thermoreversible gelation of syndiotactic poly(methyl methacrylate), where the polymer coil first transforms into a helix which then aggregates to produce the gel.32 But it is somewhat different than the gelation process of gelatin, where three discrete stepss monomer to aggregate formation, random coil to singlehelix transition, and single-helix to triple-helix transitions occur during gelation,33 and is also different from the gelation mechanism of rodlike polymers, where apart from the microphase separation there is rod to rod aggregation prior to gelation.34 Formation of TGTG h Conformers. Flory and Weaver35 propounded a theory for the rate constant (K) of transformation of coil to helix in dilute aqueous collagen solution:
K ) constant exp(-A/kT∆T)
Figure 9. Representative Hoffman-Weeks plot of PVF2DEAZ gel (4.4 g/dL) to obtain T°gm and T°d.
(4)
where A ) 2σ∆F/∆S, σ is the surface energy arising due to the formation of a new surface for the helix formation, ∆F is the free energy of activation to produce the helix, ∆T is the supercooling, T is the temperature of the study, and k is the Boltzmann constant. The above expression may be applied to the formation of any ordered conformer because, like a helix, an ordered conformer also produces a new surface with a loss of entropy for its formation.6,7,19 Since in the gelation process the first step is the formation of an order conformer, t-1 gel may be expressed as
t-1 gel ) constant exp(-A/KT∆Tgel)
Figure 8. Representative DSC thermograms for heating (H.R. 10 deg/min) of the PVF2 gels (4.4 g/dL) prepared at indicated isothermal temperatures for 3 h.
(5)
where ∆Tgel ) T°gm - T and T°gm is the equilibrium gel melting temperature. The T°gm values are determined by the Hoffman-Weeks procedure,36 and representative DSc thermograms for the 4.4% PVF2-DEAZ gels prepared at different isothermal temperatures are shown in Figure 8. It is apparent from the figure that the thermogram aspect changes, and this indicates that some melt recrystallization is taking place in the system.37,38 The melting points (Tm) are plotted against gelation temperature (Tgel), and four different lines are shown in Figure 9. All these four lines are separately extrapolated to the Tm ) Tgel line. However, these extrapolated lines meet at two common points, for example, at 133 and at 155 °C. The T°gm of 4.4% (32) Buyse, K.; Berghmans, H.; Bosco, M.; Paoletti, S. Macromolecules 1998, 31, 9224. (33) Bohidar, H. B.; Jana, S. S. J. Chem. Phys. 1993, 98, 8970. (34) Tipton, D. L.; Russo, P. S. Macromolecules. 1996, 29, 7402. (35) Flory, P. J.; Weaver, E. S. J. Am. Chem. Soc. 1960, 82, 4518. (36) Hoffman, J. D.; Weeks, J. J. J. Res. Natl. Bur. Stand. (U. S.) 1962, 66, 13. (37) Prest, W. M., Jr.; Luca, D. J. J. Appl. Phys. 1975, 46, 4136. (38) Prest, W. M., Jr.; Luca, D. J. Bull. Am. Phys. Soc. 1974, 19, 217.
Figure 10. Representative thermograms of 4.4 g/dL PVF2DEAZ gel: (a) Gelled at 60 °C for 3 h; (1) H.R. 20 deg/min; (2) H.R. 40 deg/min. (b) Crystallized at 100 °C for 12 h; (3) H.R. 20 deg/min; (4) H.R. 40 deg/min.
PVF2 gel is 133 °C. This is because gelation is taking place up to 90 °C (Figure 4) and extrapolation of its Tm yields T°gm. The upper points (closed symbols) arise due to the melt recrystallization; that is, during heating the gel first melts and then recrystallizes. From 60-75 °C the recrystallized samples are capable of further gelation. Consequently, a linear extrapolation of the above points meets the Tm ) Tgel line also at 133 °C. Above 75 °C the melt recrystallization again takes place but no gelation occurs because it does not get sufficient time to produce the gel. The DSC thermograms of the same system isothermally gelled at 60 °C for 3 h and isothermally crystallized at 100 °C are shown in Figure 10 at different heating rates. The thermograms are different from that obtained for a 10 deg/min heating rate (Figure 8), and they gradually change to give a single melting peak with increasing heating rate. This proves that melt recrystallization is taking place both in isothermally produced gels and also in solution crystals. Above 90 °C no gel is produced but solution crystals are produced. These solution crystals show two melting temperatures, and the extrapolations
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Figure 11. Hoffman-Weeks plots of PVF2-PMA (WPVF2 ) 0.5) blend gel in DEAZ (8.8 g/dL). Table 4. T°gm and T°d Values of PVF2 and PVF2-PMA Blend-DEAZ Gel pure PVF2
blend
WPVF2
conc g/dL
T°gm °C
T°d °C
1.0 1.0 1.0
4.4 6.5 9.7
133 134 135.5
155 156 156
WPVF2
conc g/dL
T°gm °C
T°d °C
0.75 0.5 0.25
4.8 8.8 12.6
132 131 130
152 151 150
meet also at a common points155 °Csin the Tm ) Tgel line. Therefore, 155 °C is the T°d for 4.4% PVF2-DEAZ gel. The T°gm and T°d values are presented in Table 4. In the gels of the blends, similar observations as in pure PVF2 gels are observed and a representative HoffmanWeek plot for the PVF2-PMA blend gel is shown in Figure 11. Compared to the case of pure PVF2 (Figure 9), here the data points are represented by three lines. The lower two lines represent the gel melting temperature, whereas the upper one indicates the melting temperature of the solution crystals. The nonoccurrence of melt recrystallization at higher Tc values in the blend is not clear to us, and it may be due to the much slower rate of crystallization in the blend making perfect crystals. However, in the blends also two equilibrium melting temperatures are observed. The occurrence of the two equilibrium melting temperatures (T°gm and T°d) in these systems indicates that there are two different types of PVF2 crystals: (1) strained crystals and (2) strain-free crystals (i.e., normal crystals).7,8,19 During the gelation process the crystals produced may be strained because of making the network, so they melt at lower temperatures compared to those for the normal solution crystals. In small molecular gelators also the molecular packing arrangements in gel strands and in neat crystalline phases have been assumed to be different.39 The T°gm and the T°d values of the blends are also presented in Table 4. From the table it is clear that with an increase in PVF2 concentration both T°gm and T°d increase. For the kinetic study of the blend gels, the concentration is so chosen that the PVF2 concentration remains within 3.2-4.4 g/dL and, therefore, T°gm and T°d should remain constant. However, a small decreasing tendency in both these values is observed with increasing PMA concentration, and it may be attributed to the favorable interaction between PVF2 and PMA.13 In Figure 12 ln t-1 gel is plotted against 1/T∆Tgel for PVF2 and blend gels, respectively. It is apparent from the figures that straight lines are obtained for both systems. This indicates that the transformation of coil to order conformer is the first step in the gelation process of both pure PVF2 (39) Terech, P.; Weiss, R. G. Chem. Rev. 1997, 97, 3133.
Figure 12. Plot of t-1 gel with 1/T∆Tgel (a) for PVF2 [(4) 4.4 g/dL; (b) 6.6 g/dL; (O) 9.7 g/dL] and (b) for PVF2-PMA blend gel [(4) WPVF2 ) 0.25; (b) WPVF2 ) 0.5; (O) WPVF2 ) 0.75] [total PVF2 concentration ) 3.2-4.4 g/dL].
and blend gels. From the least-squares slopes of the lines, A values are calculated and are presented in Table 5. The PVF2-PMA blend gels have higher A values than that of the neat PVF2 gel at 4.4 g/dL concentration, and the A value increases with an increase in PMA concentration. From the A values the ∆F values are calculated using the relation40 ∆S ) ∆H°u/C∝ [∆H°u ) enthalpy of fusion per repeating unit of PVF2 (1.6 kcal /mol), and C∞ is its chain characteristic ratio ()5.5)] and σ ) 1.38 kcal/mol.6,7 The results are presented in Table 5, and with an increase in PVF2 concentration the ∆F value increases. However, in (40) Hoffman, J. D.; Miller, R. L.; Marand, H.; Roitman, D. B. Macromolecules 1992, 25, 2221.
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Dikshit and Nandi
Table 5. Kinetic Parameters of PVF2-DEAZ and PVF2-PMA Blend-DEAZ Gels PVF2-PMA blend gel
PVF2 gel conc (g/dL)
A (kcal/mol)
∆F (kcal/mol)
l (Å)
∆G* (kcal/mol)
WPVF2
conc (g/dL)
A (kcal/mol)
∆F (kcal/mol)
l (Å)
∆G* (kcal/mol)
4.4 6.5 9.7
156.6 162.6 170.5
16.5 17.2 18.0
8.3 9.9 11.1
7.0 7.4 6.8
0.75 0.5 0.25
4.8 8.8 12.6
176.5 179.5 179.5
18.6 18.9 21.0
7.9 7.4 6.6
6.4 5.5 5.8
Figure 13. Plot of free energy (∆F) of activation of conformational ordering against (1) concentration of PVF2 in PVF2DEAZ gel (lower) and (2) WPMA in the blend gel (upper).
the blend gels for the same PVF2 concentration, with an increase in PMA concentration the ∆F value also increases. The increase in the PMA concentration in the blend decreases the favorable interaction,27 and as a result the free energy of activation for conformational ordering should, therefore, decrease. But, we observe an increase in the ∆F value with PMA content. A possible reason may be that with increasing PMA concentration in the solution the viscosity rises, and this may retard the conformational ordering, causing a higher ∆F value. This assertion is also found to be true in the case of pure PVF2 gels, where with an increase in PVF2 concentration the ∆F value increases. In Figure 13 a plot is made for ∆F against PVF2 concentration in the pure PVF2 gel. The plot is linear, and an extrapolation to zero concentration yields a ∆F value of 14.7 kcal/mol. This ∆F value may be considered as the ∆F value for the formation of the TGTG h (R) conformer of an isolated PVF2 chain. Farmer et al.41 showed from the potential energy (PE) calculation that the PE barrier between the highest and lowest energy R-conformers is equal to 9 kcal/mol. Thus, the ∆F value of 14.7 kcal/mol is approximately of the same order as that of the theoretical value. In the figure also a plot of ∆F versus WPMA is made, and this plot is also linear, like earlier, suggesting that the blend composition has a strong influence on conformational ordering. The later plot when extrapolated to WPMA ) 0 meets at 16.6 kcal/mol, which is approximately equal to that of 4.4 g/dL PVF2 gel. Due to the increased ∆F values, the rate of conformational ordering in the blend gel is slower than that of the pure PVF2 gel at a given temperature. Formation of Fibrillar Crystal. We observed a fibrillar network of PVF2 blend gels (Figure 1). So, the TGTG h conformer produced must be stabilized against the chain folding process to form the fibrillar crystals. In most cases polymer-solvent compound formation prevents the chain folding process,42-45 and it has been reported earlier from thermodynamic study that a polymer-solvent (41) Farmer, B. L.; Hopfinger, A.; Lando, J. B. J. Appl. Phys. 1972, 11, 4293. (42) Mal, S.; Nandi, A. K. Langmuir 1998, 14, 2238. (43) Guenet, J. M.; Mckenna, G. B. Macromolecules 1988, 21, 1752.
Figure 14. (a) [ln t-1 gel - (0.0123T° d/∆T) ln ν2] versus T° d/T∆T plot of PVF2 gel in DEAZ: (4) 9.7 g/dL; (b) 6.6 g/dL; (O) 4.4 g/dL. (b) For the blend where (4) WPVF2 ) 0.25, (b) WPVF2 ) 0.5, and (O) WPVF2 ) 0.75 [total PVF2 concentration ) 3.2-4.4 g/dL].
compound with an incongruent melting point is occurring in the PVF2-DEAZ gel.8 The formation of polymersolvent compound in the PVF2-PMA blend gel is also evidenced from WAXS data and thermodynamic study.25 The gelation rate of the system is analyzed with the theory of the growth rate of fibrillar crystals in solution. The growth rate of fibrils in solution can be obtained from the (44) Daniel, Ch.; Deluca, M. D.; Guenet, J. M.; Brulet, A.; Menelle, A. Polymer 1996, 37, 1273. (45) Mal, S.; Nandi, A. K. Macromol. Chem. Phys. 1999, 200, 1074.
Gelation Mechanism of Thermoreversible Gels
Langmuir, Vol. 17, No. 12, 2001 3615
Lauritzen-Hoffman expression.46
growth rate ) G0ν2 exp[-Ga/kT] exp[-∆G*/kT]
(6)
where G0 is the pre-exponential factor, ν2 is the volume fraction of the crystalline polymer, Ga is the free energy of transport, k is the Boltzmann constant, T is the temperature, and ∆G* is the free energy of formation of a critical size nucleus of fibrillar crystals. The Pennings theory for the formation of a fibrillar nucleus in the melt47 has been extended for the formation of fibrillar crystals in solution,48 and the free energy (∆G*) is expressed as
∆G* )
2σskTT°d 4lσ2s T°d ln ν2 ∆H°u∆T b0∆H°u∆T
(7)
where l is the length of the fibril, σs is the surface energy of the fibrillar crystal, T°d is the equilibrium dissolution temperature, ∆H°u is the enthalpy of fusion of a perfect PVF2 crystal, b0 is the molecular width of the crystalline sequence, and ∆T ≈ T°d - T. Now considering the growth rate of eq 6 as the gelation rate (t-1 gel) and putting the value of ∆G* in the growth rate equation and rearranging in logarithmic form
ln
t-1 gel
2σskTT°d 4lσ2s T°d ln ν2 ) A b0∆H°u∆T kT∆H°u∆T
(8)
where A ) ln(G0ν2) - (Ga/kT). Thus, in the plot of the left-hand side of eq 8 versus T°d/T∆T, a straight line is expected, and it is shown in Figure 14 for both pure gel and the blend gels. In both the figures, the straight-line nature of the plots is observed for all the compositions. This proves that fibrillar crystallization is the final step of the gelation process in these systems. From the leastsquares slope of the plots and using the values of σs ) 12.2 erg/cm2 and ∆H°u ) 2.01 × 109 erg/cm,6,7,49 the fibrillar lengths l are calculated and are presented in Table 5. From the table it is clear that the average fibrillar length in PVF2-DEAZ gel is 9.8 Å and it decreases with an (46) Hoffman, J. D.; Thomas Davies, G.; Lauritzen, J. I., Jr. In Treatise on Solid State Chemistry; Hannay, N. B., Ed.; Plenum Press: New York, 1976; Vol. 3, p 497. (47) Pennings, A. J. J. Polym. Sci., Polym. Symp. 1977, 59, 55. (48) Boon, J.; Azcue, J. M. J. Polym. Sci., A-2 1968, 6, 885. (49) Maiti, P.; Nandi, A. K. Polymer 1998, 39, 413.
increase in PMA concentration in the blend. The ∆G* values of these systems are calculated and are also presented in Table 5. The ∆G* values for the pure PVF2DEAZ (4.4 g/dL) are higher than that in the blends, and this indicates that in the blend gel the crystallite nucleus formation is easier. A possible explanation may come from the observation that in the PVF2-PMA blend the PVF2 coil becomes extended due to a specific interaction.49 Consequently, it becomes easier for the PVF2 chain to fit into the lattice to form the nucleus, giving lower ∆G* values. Now, it is interesting to compare the ∆F and ∆G* values of the gelation process. Since the ∆F values are large compared to ∆G* in all cases, the gelation in this system is a two-step process of conformational ordering and crystallization. As soon as the conformational ordering takes place, crystallization occurs, producing the gels. The slower gelation rate of PVF2-PMA blends compared to the pure PVF2 in DEAZ may be explained from the higher ∆F value of the blend, since conformational ordering is the rate-determining step in the gelation process. Conclusion PVF2 and its blends with PMA produce thermoreversible gels in diethyl azelate. SEM study indicates the presence of a fibrillar network in all the gels. The fibrillar morphology becomes thinner and curlier with increasing PMA concentration in the blend. From the WAXS and FT- IR experiments it is concluded that R-crystallites are acting as junction points to form the three-dimensional network for both PVF2 and PVF2-PMA blend gels. Kinetic analysis indicates that the gelation rate becomes slower with an increase in PMA concentration in the blend. Analysis of the gelation rate with concentration function indicates that three-dimensional percolation is obeyed both for pure PVF2 and its blend gels in DEAZ. Temperature coefficient analysis of the gelation rate indicates that the gelations in these systems are two-step processes of conformational ordering and crystallization, the former being the rate-determining step in all the cases. Comparison of kinetic parameters between the pure PVF2 and the blends indicates that with increasing PMA concentration the activation energy of conformational ordering increases, causing a slower gelation rate in the blends. LA001718V
