J . Phys. Chem. 1990, 94, 2706-2113
2706
Structural and Dynamical Properties of the Sol-Gel Transition R. Winter,+ D. W. Hua, X. Song, W. Mantulin,l and J. Jonas* School of Chemical Sciences, University of Illinois, Urbana, Illinois 61801 (Received: August 3, 1989)
A variety of experimental techniques (multinuclear NMR, Raman, fluorescence polarization, small-angle neutron scattering, viscosity, turbidity, static and dynamic light scattering experiments) have been employed to investigate the nature of the sol-gel transition of tetramethoxysilicate,Si(OCH,), (TMOS). These experiments probe changes in structural and dynamical properties at the macroscopic and microscopic levels in the course of the sol-gel transition. The experimental results are compared with recent theories for the gelation process. The experiments show that no drastic change in structure occurs at the gelation threshold of TMOS. The formed silica network exhibits a self-similar structure, and the gross features of the sol-gel transition of TMOS can be described within the framework of percolation theory. The underlying growth process might be classified as reaction-limited cluster-cluster growth. However, the detailed chemical structure and reactivity of the reactants, e.g., the time-dependent functionality of the monomers during the hydrolysis step, also play an important role and have to be taken into account for a more quantitative theoretical description of this gelation process.
1. Introduction It has been established that the sol-gel process has a promising future as a unique process for preparing glasses, films, and fibers.'J In the silica-based sol-gel process, gelation occurs in two stages, the hydrolysis stage and the condensation stage, which can be schematically represented by the reactions Si(OCH3)4+ nHzO Si(OCH,),-,(OH), nCH,OH (hydrolysis) (1)
-
+
and >Si-OH or >Si-OH
+ HO-Si
+ RO-Si
-
-
-Si-0-Si-
-Si-0-Si-
+ H20
+ ROH (condensation) (2)
where n varies from 1 to 4. At our experimental conditions of neutral pH, the hydrolysis step is rather slow so that condensation already occurs from partially hydrolyzed monomers. The gel is subsequently dried and heat treated to yield the desired glass. The potential applications of these materials are expected to be substantial.1$2 A variety of physical and chemical factors (e.g., temperature, pressure, pH value, concentration of reactants, and catalysts) influence the polymerization process and thus the properties of the final glass. In order to understand and control the structure of the product, a detailed understanding of the sol-gel transition and the underlying polymer growth process is essential. The subsequent stages of the glass-making procedure depend strongly on the initial structure of the wet gel formed in the course of the gelation reaction. The process of gelation and aggregation is also of fundamental importance in the description and understanding of many other physicochemical and biological processes, like, e.g., catalysis, electrostatic precipitation, aggregation of blood coagulation, denaturation processes, aggregation of antibody and antigen, etc. Also, from a theoretical point of view, the nature of the sol-gel transition is a subject of extensive d i s c u s ~ i o n .A ~ ~gelling solution represents a unique state of matter because it is neither liquid nor solid but is in between these two states. The gelation process can be viewed as the growth process of randomly multiconnected polymer clusters starting from multifunctional monomer units, which can link together by, e.g., chemical reaction. At the gel point, a giant cluster appears, having a macroscopic size. The sol-gel transition can generally be characterized by a divergence of the connectivity correlation length, not of a spatial correlation 'Present address: Institute of Physical Chemistry, Philipps-University of Marburg, D-3550 Marburg, FRG, 'Department of Physics, University of Illinois, Laboratory for Fluorescence Dynamics Urbana, IL 61801
0022-3654/90/2094-2706$02.50/0
length like that of usual second-order phase transition^.^^^ In our studies, we report on recent viscosity, small-angle neutron scattering (SANS), Raman, multinuclear NMR, fluorescence polarization, turbidity, static light scattering (SLS), and dynamic light scattering (DLS) experiments on the polycondensation of TMOS. These various experiments lead to a detailed understanding of the nature of the gelation process by elucidating how macroscopic and microscopic structural and dynamical properties change in the course of the sol-gel transition. The experimental results are compared with growth models for the polymerization process and with recent theories for the gelation process. 2. Experimental Section The samples were prepared by dropwise addition of a H20/ C H 3 0 H mixture to the silicon alkoxide TMOS (supplied by Aldrich Co.), which is diluted in CH,OH, under vigorous stirring.6 The concentrations of the reagents were adjusted to yield a final mole ratio TMOS:H,0:CH30H = 1:4:4. The experiments have been conducted at neutral pH without any addition of catalyst. The sol gelIed at tgel = 32.45 f 0.1 h at T = 23 OC. In the following, we define the gelation time by the absence of flow in the solution-containing flask, which is accurate to within 0.1 h. The viscosity measurements have been performed with a falling-ball viscosimeter from Gilmont Co. The SANS experiments have been performed with the SAD instrument at the Intense Pulsed Neutron Source at Argonne National Laboratory. The measurements were carried out in closed quartz cells. The neutron-beam diameter at the sample position was 1 cm and the integrated neutron flux 4 X lo4 neutrons cm-* s-I. The scattered neutrons were detected by a 64 X 64 array area sensitive proportional counter, while the wavelengths of the neutrons are determined by their time of flight. The Q range [Q = (4.rr/X) sin (0 2); 8, scattering angle] covered by the instrument is 0.005-0.35 For more details, see ref 7. The NMR experiments were performed on a 300-MHz pulsed N M R spectrometer (Model GN300 from General Electric). Spin-lattice relaxation times TI were measured by the inversion
1
(1) Hench, L. L.; Ulrich, D. R. Science of Ceramic Chemical Processing, Wiley: New York, 1986. (2) Ulrich, D. R. J . Non-Cryst. Solids 1988, 100, 174. (3) Meakin, P. In Time Dependent Effects in Disordered Materials; Pynn, R., Riste, T., Eds.; Plenum Press: New York, 1987. (4) Stauffer, D.; Coniglio, A,; Adam, M. Adu. Polym. Sci. 1982, 44, 103. (5) Stanley, E., Ostrowsky, N., Eds. On Growth and Form-Fractal and Non-Fractal Patterns in Physics; Nato AS1 E No. 100; Nijhoff Dordrecht, The Netherlands, 1986. (6) Winter, R.; Chan, J.-B.; Frattini, R.; Jonas, J. J . Non-Cryst. Solids 1988. 105. 214. (7) Winter, R.; Hua, D.-W.; Thiyagarajan, P.; Jonas, J. J . Non-Crysi. Solids 1988, 108, 137.
0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 6, I990 2707
Sol-Gel Transition Structural and Dynamical Properties recovery method; the line widths (Avl12) were measured by a Lorentzian fit to the peaks. The Raman experiments were done using an argon-ion laser operating at 488 nm at a power of 600 mW. A Spex Model 1403 double monochromator interfaced to a computer for data acquisition and instrument control was used. A 1.3-cm-’ slit was used, and the spectra were recorded every 4 cm-I. The samples were placed in glass tubes and sealed, and spectra were successively recorded from the preparation time up to times well after gelation. The turbidity measurements were carried out in the absorbance mode at 340 nm with a Perkin-Elmer Lambda V spectrophotometer. The wavelength of 340 nm was chosen because the reactants are transparent at this wavelength and a measurable large turbidity (apparent absorbance) change parallels the reaction. The fluorescence polarization studies were performed on a photon-counting fluorometer (ISS Instruments, Inc., GREG PC) with Glan-Thompson polarizers and either filters or a monochromator in the emission path. Background counts from an unlabeled blank, even after gelation, were less than 1% of the fluorescence signal. At each time point, the measured fluorescence polarization P was corrected for the transmission of horizontally (H) polarized excitation light (g = I,v/IHH) = (IVV - IVHg)/(IVV
+ IVHg)
(3)
where I corresponds to the fluorescence intensity and the subscript V refers to the vertically polarized component of the light.*v9 The first subscript relates to the orientation of the excitation polarizer and the second to the emission polarizer. The fluorescence probes were obtained from Molecular Probes (Eugene, OR) or Aldrich Chemical Co. (Milwaukee, WI) and were used as received. The probes were introduced at micromolar concentrations into the reaction mixture during sample preparation. The light scattering experiments were performed with an argon-ion laser and a B1-2030 correlator from Brookhaven Instrument Co. The wavelength of the incident light was 488 nm, and the laser power used was 50 mW. The solutions were filtered with a 0.2-pm PTFE filter and capped in quartz cells. For the SLS, the data collection time was 5 s. For each sample, intensities at different angles were measured, and the intensities were normalized by measurements of the solvent C H 3 0 H under the same conditions.I0 For the measurements at different times, a small portion of the sample was taken out of a thermostated bath and diluted into methanol to the desired concentration c. In order to obtain the weight-average molecular weight, extrapolations were made to zero angle and zero concentration by running 50:1, 125:1, 250: 1, and 500:l dilutions at five different scattering angles, and the refractive index increment dn/dc had to be measured as a function of the extent of reaction. The intensity scattered from a polymer solution can be related to the average molecular weight M , and the average radius of gyration RG by the following equation: lim Kc/ARe = (l/M,)(l
+ 16r2RG2sin2 (0/2)/3h2)
(4)
where A& is the measured excess Rayleigh ratio, which is related to the scattered intensity and can be expressed as
with
K = (2~~n,,~(dn/dc)~)/N,X~
(6)
where no is the refractive index of the solvent, NAis Avogadro’s constant, dn/dc is the change of the refractive index with concentration c of the solute, and 0 is the scattering angle of light. (8) Chen, L.A.; Dale, R. E.; Roth, S.; Brand, L. J . Biol. Chem. 1977,252, 216. (9) Shinitzky, M.; Dianoux, A.-C.; Gitler, C.; Weber, G. Biochemistry 1971, IO, 2106. (IO) Kaye, W.; Havlik, A. J . Appl. Opt. 1973, 12, 541. (11) Zimm, B. H. J . Chem. Phys. 1948, 26, 1099.
tltgel
Figure 1. Time evolution (in t / t g s l ) of monomeric (M), dimeric and trimeric (D,T), and higher branched (P) silicon groups as obtained from N M R and Raman spectroscopy (maximum error: 10% in percent Si). 30 25 20
2
15
I
5
10 05
00 -051
-LO
,
,
-3 5
-30
-
5
In c1
Figure 2. Time dependence (in t/t,,) of the SANS profile In I ( Q ) vs In Q of T M O S sols.
From the Zimm plot of c/ARe vs sin2 (0/2) and by extrapolation to zero angle and infinite dilution, M , can be obtained. For the DLS, the scattered light was detected at 90° with a 2-ps sampling time and analyzed by a BI-2030 autocorrelator. The light intensity autocorrelation functions G ( t ) recorded from the correlator were transfered to a VAX-11 computer for data processing. In all experiments, the temperature of T = 23 OC was held constant with a water-thermostated bath to within 0.1 O C . 3. Results and Discussion a. Structural Properties. In order to follow the time dependence of the structural evolution of the silica polymer network, Raman and high-resolution N M R experiments, capable of detecting individual species or groups of molecules during the polymerization process? have been performed. As an example of the combined results from the ?Si NMR and Raman experiments, we present Figure 1, which shows the relative concentrations of monomers M, dimeric D and trimeric T silica species, and the concentration of all the higher branched silica polymers P as a function of time, normalized to the gelation time tgcl. As can be clearly seen, about 5 1 0 % of monomers are still present at the gelation point and the amount of higher polymeric species P increases considerably even after the gelation (t/tgel = 1). Due to the large complexity and overlap of the Raman signals and the dipolar broadening of the NMR resonances of the higher branched polymer particles, the detailed structure of the developing polymer network cannot be obtained by these spectroscopic methods. Therefore, we had to resort to an established technique, such as SANS, which can provide more information about the structure of complex systems. In describing complex disordered structures, the concept of fractal geometry provides a valuable means of quantitatively describing the average structure of these obj e c t ~ . ~ , ~We ~ - ’applied ~ the SANS technique to measure the (12) Schaefer, D. W.; Keefer, K. D. Phys. Rev. Leu. 1984, 53, 1383. (13) Martin, J. E.; Wilcoxon, J.; Adolf, D. Phys. Rev. A 1987, 36, 1803.
2708
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990
Winter et al.
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Figure 4. Time dependence of the SANS intensity I ( 0 ) for TMOS sols.
By computer simulation, a variety of growth processes have been proposed for the silicon oxide systems. Our final value of D = fractal dimension D of the polymeric structure and to yield in2.2 is close to that of the reaction-limited cluster-cluster growth formation about the underlying growth process. The intensity model (D = 2.1).3~'8-20 The increasing slope of the scattering Z(Q) of the scattered neutrons in the region l / R G < Q < I/a, curve Z(Q) during the gelation process might be explained by the where RG is the radius of gyration and a is the monomer size, polycondensation of incompletely hydrolyzed monomer species,'J9 depends on the geometric structure of the scattering entities and which leads to an internal reconstruction of the clusters with time, can be analyzed in terms of a power law giving more compact objects. Figure 4 shows the increase of scattering intensity I ( 0 ) at Q I(Q) = Qp (7) = 0 as a function of time, which reflects the increase in volume The exponent ~c is related to the fractal dimension D of the sample, Vor molecular weight of the growing polymer as Z(0) a N p . 2 1 which relates the size R of the object to its mass, M = RD. For Around t / t g e l = 0.8, ;.e., rather close to the gelation point, I ( 0 ) mass fractals of dimension 1 < D < 3, D = -p.15 starts to increase rapidly, continuing even after gelation. Figure 2 shows a selection of scattering curves (plot of In Z(Q) A similar result has been obtained by turbidity measurements that also relate the growth of large particles, large relative to the vs In Q ) as a function of relative time, t / t g e l . The scattering intensity Z(Q) and the slope of the curves progressively increase wavelength of light employed in this study, to the time course of the reaction. Figure 5 shows the time course of the turbidity with time. Figure 3 depicts the time evolution of the fractal dimension D , which has been obtained from the slope of the (absorbance at 340 nm) of the TMOS gelation reaction, also scattering curves according to eq 7. No significant change in the normalized to the gelation time tge,. Over all, the turbidity inscattering profile or D value is observed at the crossover from the creases about 6-fold with the major increase occurring after gesol to the gel. The D value even increases with time after the gel lation. Since light scattering measurements preferentially detect point and reaches a final value of D = 2.2 f 0.1 not before t/tgel the population of large particles, the results in Figure 5 are = 3. consistent with the accumulation of larger polymer networks in Taking into account the polydispersity of the p ~ l y m e r , ' a~ , ~ ~ the postgelation phase, which then terminates at approximately fractal dimension of 2 is obtained at f/tge,= 1. This value is only t/tgeI = 2.5. close to the value D = 2.5 as observed for three-dimensional percolation at the gel p ~ i n t . ~ * I ~ (17) Stanley, H. E. J. Stat. Phys. 1984, 36, 843. (14) Meakin, P. Ado. Colloid Inferface Sci. 1988, 28, 249. (15) Pietronero, L., Tosatti, E., Eds. Fracfals in Physics; Elsevier: Am-
sterdam, 1986. (16) Martin, J. E.; Ackerson, B. J. Phys. Reu. 1985, A31, 1180.
(18) Brown, W. B.; Ball, R. C . J . Phys. 1985, A18, L517. (19) Brinker, C. J. J . Non-Cyst. Solids 1988, 100, 31. (20) Schaefer, D. W.; Keefer, K. D. Mar. Res. SOC.Symp. Proc. 1986, 73,
277. (21) Bouchaud, E.; Delsanti, M.; Adam, M.; Daoud, M.; Durand, D. J . Phys. (Les U h , Fr.) 1986, 47, 1273.
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990 2709
Sol-Gel Transition Structural and Dynamical Properties
2.5
0
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-
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--
1.0
0.5
4 -
3
-1.5
-1.2
0.0 -0.8
log [ 1 - t / t
-0.3
gel
- t/tgelfor TMOS
(1 -
t/fgeP
Figure 8. Viscosity 7 of TMOS sols as a function of relative time t / t g c l . 2.0
The time dependence of D, I(O), and the turbidity thus clearly demonstrates that the polymer network still changes a long time after gelation. Even simple measurements like turbidity can provide useful information about the polymer growth process and its temporal development. In order to obtain a more quantitative picture about the evolution of the average cluster mass during gelation, we performed static light scattering (SLS) experiments, which allow extraction of the weight average cluster mass Mw as a function of time. The time evolution of M , is shown in Figure 6. The average cluster mass increases markedly around t/tgel.= 0.85 and then seems to diverge when approaching the gelation point. This behavior suggests a power law behavior. M w a
I .e
0.8
0.0
]
Figure 7. log-log plot of the molecular weight M, vs 1 sols.
0.6
0.3
0.0
-0.8
(8)
In the classical Flory-Stockmayer (FS) approach22-26to gelation, y = l . These authors formulated a mean field theory for the polycondensation of bi- and polyfunctional monomers. In light of percolation theory, however, M , is supposed to diverge near the gelation point with y = 1.76.3,4,26-28 The log-log plot of M , vs 1 - t/tgel is shown in Figure 7. It exhibits a slope of -2.6 f 0.1, assuming a reel value as obtained by the tilt method. Obviously, in our case M , diverges stronger than the predictions of FS or percolation theory. The value of -2.6 is similar to that found for acid/base-catalyzed TMOS systems.I3 The discrepancy between theory and experiment suggests that a more refined theoretical model might be needed for describing the gelation process of TMOS, where the detailed mechanisms of the chemical reactions are taken into account. For example, the structure of the monomer is in reality already more complicated than the often used mathematical point model with constant functionality of chemical bonding sites. b. Dynamical Properties. The dynamical properties of the sol-gel transition can be described phenomenologically by changes in the viscoelastic properties, like, e.g., the v i s ~ o s i t y . ~As ~~~ depicted in Figure 8, we measured the bulk viscosity 9 of the sol up to the gel in situ, Le., in the reaction bath. In the first stage of the polymerization reaction, 9 does not change significantly with time, but it increases rapidly after t/tge,= 0.8. Here, the (22) Flory, P. J. J . Am. Chem. SOC.1941, 63, 3083. (23) Flory, P. J. J . Phys. Chem. 1942, 46, 132. (24) Stockmayer, W. H. J . Chem. Phys. 1943, 11,45. (25) Flory, P. J. Principles of Polymer Chemistry; Comell: London, 1953. (26) de Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University: Ithaca, NY, 1979. (27) Stauffer, D.J . Chem. Soc., Faraday Trans. 2 1976, 7 2 , 1354. (28) Stauffer, D. Phys. Rep. 1979, 54, 1. (29) Gauthier-Manuel, B. In Physics of Finely Divided Matter, Boccara, N., Daoud, M., Eds.;Springer Proceedings in Physics, Vol. 5; Springer: Berlin, 1985.
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log ( 1 - t / t gel) Figure 9. log-log plot of the viscosity 7 of TMOS sol vs 1
~
~
0.0
- t/rgel.
aggregates seem to be large enough so that their clustering results in the formation of a silicon skeleton that fills the sample cell in a rather short time. The viscosity seems to diverge near tgcl, thus suggesting a power law behavior of the form 9 = (1 - t/tgcl)-S
(9)
As can be seen in Figure 9, a straight line is observed in the log-log plot for tgcl = 32.3 h-which is within the experimental error of the value of the gelation time, as determined by the tilt method, leading to an exponent of s = 0.75 f 0.05. This s value is similar to that reported for the copolymerization of styrenedi~inylbenzene.~~ The result is also in agreement with the percolation prediction of s = 0.7, which, however, is only based on an analogy between the viscosity divergence and the divergence of the conductivity in a superconductor-resistor netw~rk!,~~-~~ In percolation theory, it is assumed4 that the viscosity near the gelation point takes the form 9 = (1 - p/p,)", where p is the conversion factor, Le., the number of bonds on an N-site lattice, which takes the value p = pc at the percolation point. For systems that are governed by a chemical reaction, the conversion factor might be replaced by the time of the reaction near the percolation threshold, thus leading to eq 9. Although no exact value from percolation theory was known for s until now, our results suggest that our gelation process can, at least qualitatively, be described by the critical theory of percolation. In this approach, the gel point is the statistical event that indicates the first appearance of a cluster that spans the whole sample region. In the following section, we describe how the (30) Adam, M.; Delsanti, M.; Okasha, R.; Hild, G. J . Phys. Letr. 1979,
40, L539.
(31) de Gennes, P.-G. C. R. Sceances Acad. Sci., Ser. B 1978, 131, 2886. (32) de Gennes, P.-G. J . Phys. (Les Ulis, Fr.) 1979, 40, L197.
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2710
The Journal of Physical Chemistry, Vol. 94, No. 6 , 1990
Winter et ai. I - -0 - 20 - -
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Figure 12. 2H spin-lattice relaxation time TI of the solvent species as a function of relative time t / t g e l .
00
1.50
1.20
1'1 gel
Figure 10. IH spin-lattice relaxation time T , of the CH3 group of methanol as a function of t / t g c l .
t
l2
A 10 *t 1 32 1 03
0 94
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0 75 0 40
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1
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Figure 11. Representative *H spectra of TMOS/MeOH/D,O sols as a function of relative time t / t g c l .
microscopic motional state of the solvent, probe molecules, and the polymer clusters is affected by the formation of the silica network and the sol-gel transition. In order to study the motional state of the solvent molecules in the course of the gelation reaction, we performed a series of multinuclear N M R relaxation time measurements. As a first example, Figure 10 shows the 'H spin-lattice relaxation time T, of the CH3 group of the cosolvent methanol as a function of relative time tit,,,. T I decreases up to nearly t / t g e l= 1, where the curve levels off, thus indicating the transition from the sol to the gel state. Spin-lattice relaxation times of other groups of 'H and nuclei show similar changes when passing the sol-gel transition. Corresponding measurements of the line widths (Avllz or T2* = 1/nAvIj2)exhibit only very small changes in passing the gelation point. As complicated inter- and intramolecular and spin-rotational relaxation mechanisms can contribute to the observed value of the measured relaxation times, the evaluation of a motional correlation time cannot be performed unambiguously. For obtaining the time evolution of the reorientational correlation time, we therefore performed deuterium NMR- TI measurements, because the quadrupolar relaxation mechanism represents the dominant contribution to T I . Figure 11 shows 2H NMR spectra of the system TMOS/ C H 3 0 H / D 2 0for a few selected relative times t/tgel.The higher peak arises from the combination of all "OD" species ( D 2 0 ,
Figure 13. Time dependence of the rotational correlation time iC for the solvent molecules as obtained from 2H NMR-TI measurements.
CH,OD, ...). The chemical shifts 6 are assigned to that of pure D20, which is set to zero. The small shoulder is due to the silicon family Si(OD),(OR),. Its peak intensity decreases with time and finally merges with the OD peak, which shifts to higher 6 values with increasing time. In replacing H 2 0 by D 2 0 in the sol, the deuteron spin-lattice relaxation time T Ican be measured, which is directly correlated with the reorientational correlation time 7, of the molecule. Figure 12 shows the temporal change of T I of deuterons, which reflects the motional state of the solvent molecules (D20, CH30D, ...) during the polymerization reaction. As can be clearly seen, T , decreases continuously up to about t* = t/tgel= 0.8, and then it levels off and becomes nearly constant. For *H N M R under the extreme narrowing condition, the molecular reorientational correlation time T, can be calculated by the following e q ~ a t i o n : ~ ~ . ) ~ 1/T, = (3r2/10)(2Z + 3)/(12(2I- 1))(1 + ~ ~ / 3 ) ( e ~ Q q / h(10) )~~, where $Qq/h = 230 kHz is the quadrupole coupling constant for 2H, the asymmetry parameter x for the electric field gradient q can be neglected, and I is the nuclear spin quantum number ( I = 1 for 2H). Thus, from measuring T I ,one can calculate the molecular reorientational correlation time 7, (see Figure 13). It increases slowly from about 7 to 10 ps around t*, i.e., the overall change in motion of the solvent molecules is relatively small. The increasing correlation time T, before t* can be attributed t o the continuously increasing restriction of motion during the developing connectivity of the silica network. Around T,, the molecular mobility reaches its minimum probably due to the confinement (33) Farrar, T. C.; Becker, E. D.Pulse and Fourier Transform NMR; Academic Press: New York, 197 1. (34) Jonas, J.; DeFries, T.; Wilbur, D. J.; J . Chem. Phys. 1976, 65, 582.
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990 2711
Sol-Gel Transition Structural and Dynamical Properties
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