J. Phys. Chem. B 2002, 106, 5351-5357
5351
Gel Swelling Induced by Organic Vapors; Fast Transient Fluorescence Study O 2 . Pekcan* and M. Erdogˇ an Department of Physics, Istanbul Technical UniVersity, Maslak, Istanbul, 80626, Turkey ReceiVed: May 29, 2001; In Final Form: December 13, 2001
Fast transient fluorescence technique (FTRF) which uses Strobe Master System (SMS) was used to study swelling of disk-shaped poly(methyl methacrylate) (PMMA) gels. Disk-shaped PMMA gels were prepared by free-radical copolymerization of methyl (methacrylate) (MMA) and ethylene glycol dimethacrylate (EGDM). Pyrene (P) was introduced as a fluorescence probe during polymerization, and lifetimes of P were measured during in-situ swelling process. Various organic solvents were used for vapor-induced gel swelling. An equation is derived for low-quenching efficiencies to interpret the behavior of lifetimes, τ during swelling. It was observed that τ values decreased as swelling proceeded. Li-Tanaka equation was used to determine the cooperative diffusion coefficients, Dc, which were around 10-5 cm2 s-1.
Introduction Swelling is directly related to visco elastic properties of a gel. The gel elasticity and the friction between the network and solvent play an important role on the kinetics of the gel swelling.1-3 It has been known that the relaxation time of swelling is proportional to the square of a linear size of the gel1 which has been confirmed experimentally.3 One of the most important features of the gel swelling process is that it is isotropic, that is, when the radius increases 10%, the axial length increases 10% in a long cylindrical gel. The elastic and swelling properties of permanent networks can be understood by considering two opposing effects, the osmotic presure and the restraining force. Usually, the total free energy of a chemically cross-linked network can be separated into two terms: the bulk and the shear energies. In a swollen network, the characteristic quantity of the bulk free energy is the osmotic bulk modulus, K. The other important energy, the shear energy, keeps the gel in shape by minimizing the nonisotropic deformation. The characteristic coefficient of these forces is the shear modulus, µ, which can be most directly evaluated by stress-strain measurements.4,5 Li and Tanaka6 have developed a model where the shear modulus plays an important role that keeps the gel in shape by the coupling of any change in different directions. This model predicts that the geometry of the gel is an important factor, and swelling is not a pure diffusion process. For about the last two decades, the transient fluorescence (TRF) technique for measuring fluorescence decay has been routinely applied to study many polymeric systems.7-11 TRF spectroscopy with a nonradiative direct energy transfer (DET) and quenching has been used to characterize internal morphologies of composite materials.12,13 It has been reported that the local, fractal-like structures of interpenetrating network morphology in blendlike particles can be studied by TRF spectroscopy. Film formation from donor- and acceptor-labeled latex particles has been studied using DET in conjunction with TRF technique.14-16 A single-photon counting method in conjunction with DET was used to study the diffusion of small dye molecules within the interphase domain of dye-labeled poly(methyl methacrylate) (PMMA) particles sterically stabilized * To whom correspondence should be addressed.
by polyisobutylene, where mean lifetimes of fluorescing donor molecules were measured to monitor diffusion17,18 and the Fickian model for diffusion was employed to determine diffusion coefficients. Recently, fast transient fluorescence (FTRF) technique was used in our laboratory to study polymer dissolution,19,20 gel swelling,21,22 and gelation23 processes in solvent. In these studies, Strobe Master System (SMS) was used and a model was employed for low-quenching efficiencies to measure lifetimes of pyrene (P) which was used as a fluorescence probe. In this work, organic vapor-induced swelling of disk-shaped gels formed by FCC of MMA and EGDM was studied using FTRF technique. Lifetimes of P embedded in the gel were monitored during in-situ swelling processes. The Strobe Master system (SMS) was used for lifetime measurements of P in the gel. Lifetime measurements with SMS take much less time than with single-photon counting systems and phase instruments. This advantage of SMS allows one to make at least hundreds of measurements during the swelling process of gels. That is the reason we named this technique fast transient fluorescence (FTRF), which gives us many advantages compared to other lifetime measuring techniques. It is observed that, as gel swells, the lifetime of P decreases, which can be modeled using the low-quenching Stern-Volmer equation. In this work, vaporinduced gel-swelling data was treated using the Li-Tanaka model which has been usually applied for solvent-gel systems. However, here it is assumed that a vapor-gel system combines pure diffusional process with elasticity and can be treated with the Li-Tanaka model. Cooperative Dc and mutual Dm diffusion coefficients were determined by employing the Li-Tanaka equation and were around 10-5 and 10-7 cm2‚s-1, respectively. Swelling of Gels. Swelling experiments of disk-shaped gels in vapor have shown that the relative changes of diameter and thickness are the same, indicating that the gel-swelling processes are not pure diffusional processes, where the equality of the relative changes of diameter and thickness comes from the nonzero shear modulus, µ. The change of total shear energy in response to any small change in shape that maintains constant volume element within the gel should be zero. The high-friction coefficient, f, between the network and the solvent overdamps the motion of the network, resulting in a diffusion-like relaxation. The equation of the motion of a network element
10.1021/jp0120256 CCC: $22.00 © 2002 American Chemical Society Published on Web 05/02/2002
5352 J. Phys. Chem. B, Vol. 106, No. 21, 2002
Pekcan and Erdogˇan
TABLE 1. acetone (AC) chloroform CH) dichloromethane (DM) ethyl acetate (EA) tetrahydrofuran (THF)
a0 (cm)
a∞ (cm)
W(∞) - W(0) (g)
δ (MPa)1/2
V (cm3 mol-1)
τc (s)
R
B1
Dc × 10-5 (cm2 s-1)
0.22 0.22 0.21 0.23 0.22
0.27 0.31 0.30 0.26 0.25
0.0446 0.1705 0.1575 0.0119 0.0331
20.3 19.0 19.8 18.6 18.6
73.53 80.17 64.00 97.89 81.70
3704 2703 1121 4286 6235
2.20 2.20 1.65 2.15 1.55
0.63 0.61 0.81 0.60 0.83
0.31 0.57 2.21 0.27 0.31
series of components; each of them decays exponentially with a time constant, τn. The first terms of the expressions are dominant at large t, that is, at the last stage of swelling. Equation 4 can also be written in terms of vapor uptakes W and W∞ at time t and at equilibrium, respectively, as follows:
W∞ - W
∞
)
W∞ Figure 1. Fluorescence cell in PTI Strobe Master System. I0 is the excitation and I(t) is the emission intensities at 345 and 395 nm, respectively.
(
1-
(1)
where b u is the displacement vector measured from the final equilibrium location after the gel is fully swollen (u ) 0 at t ) ∞). Dc ) (K + 4µ/3)/f is the collective diffusion coefficient. Here, t denotes the time and K is the bulk modulus. Equation 1 has been used with some success to study the swelling of gels.1 However, the studies did not properly treat the shear deformation that occurs within a gel during swelling, and hence, cannot explain, for example, the isotropic swelling of a cylindrical gel. This shortcoming was due to the shear modulus of the network keeping the system in shape by minimizing the nonisotropic deformation. For a disk-shaped gel, any change in diameter is coupled to a change in thickness. The total energy of a gel can be separated into a bulk energy and a shear energy. The bulk energy is related to the volume change, which is controlled by diffusion. The shear energy, Fsh on the other hand, can be minimized instantly by readjusting the shape of the gel.6
δFsh ) 0
)
W ) B1 exp(-ts/τc) W∞
(6)
From eq 5, ΣBn ) 1; therefore, B1 should be less than 1. B1 is related to the ratio of the shear modulus, µ, and longitudinal osmotic modulus, M ) (K + 4µ/3). Hence, once the value of B1 is obtained, one can determine the value of R ) µ/M. Here, eq 6 can also be obtained by using the theoretical results,6 in R f 3/4 (µ/K f ∞), the time constant τc ≈ (3/4 - R)-1 goes to infinity and all Bn’s go to zero except B1, which goes to unity. The dependence of B1 on R for a disk can be found in the literature.6 τc is related to the collective diffusion coefficient Dc at the surface of a gel disk by
Dc )
3a2∞ τcR12
(7)
where R1 is a function of R only and is given in the literature,6 and a∞ stands for the half thickness of the gel in the final equilibrium state. Hence, Dc can be calculated.
(2) Experiments
Each small diffusion process determined by eq 1 must couple to a small shear process given by eq 2 producing the following relation for a disk-shaped gel
ur(r,t) uz(a,t) ) r a
(5)
In the limit of large t, or if τc is much larger than the rest of τn, all higher terms (n g 2) eq 5 can be omitted and the swelling kinetics is given by the following relation:
during the swelling can be given by6
∂u b ) Dc∇ B 2b u ∂t
∑Bn exp(-t/τn)
n)1
(3)
where r is the radius and a is the half thickness of the disk gel. Equation 3 indicates that the relative change in the shape of the gel is isotropic, that is, the swelling rates of a disk in the axial (z) and radial (r) directions are the same. Simultaneous solution of eq 1 and 2 produces the following equations for the swelling of a gel disk in axial and radial directions.6
uz(z,t) ) uz(z,∞)
∑n Bn exp(-t/τn)
(4a)
ur(r,t) ) ur(r,∞)
∑n Bn exp(-t/τn)
(4b)
where the axial and the radial displacements are expressed as
EGDM has been commonly used as cross-linker in the synthesis of polymeric networks. Here, for our use, the monomers MMA (Merck) and EGDM (Merck) were freed from the inhibitor by shaking with a 10% aqueous KOH solution, washing with water, and drying over sodium sulfate. They were then distilled under reduced pressure over copper chloride. The radical copolymerization of MMA and EGDM was performed at 75 °C in the presence of 2,2′-azobisisobutyronitrile (AIBN) (0.26 wt %) as an initiator. P was added as a fluorescence probe during the gelation process. The sample was deoxygenated by bubbling nitrogen for 10 min, and then radical copolymerization of MMA and EGDM was performed at 75 ( 2 °C. Here, EGDM content was kept as 0.025 vol. %, and P concentration was taken as 4 × 10-4 M. After gelation was completed, the gel sample was dried under vacuum for the swelling experiment. Fluorescence decay experiments were performed using the Photon Technology International (PTI) Strobe Master System (SMS). In the strobe, or pulse-sampling technique,24,25 the sample is excited with a pulsed light source. The name comes about because the photo multiplier tube (PMT) is gated or
Gel Swelling Induced by Organic Vapors
Figure 2. Fluorescence decay curve (a) of pyrene in PMMA gel. The incident light pulse (b) is also shown.
Figure 3. Fluorescence decay profiles, I(t) at various swelling steps. The number on each curve represents the swelling time in minutes.
strobed by a voltage pulse that is synchronized with the pulsed light source. The intensity of fluorescence emission is measured in a very narrow time window on each pulse and is saved in a computer. The time window is moved after each pulse. The strobe has the effect of turning on the PMT and measuring the emission intensity over a very short time window. When the data has been sampled over the appropriate range of time, a decay curve of fluorescence intensity versus time can be constructed.
J. Phys. Chem. B, Vol. 106, No. 21, 2002 5353
Figure 4. The single-exponential fit of the data presented in Figure 3.
Since the strobe technique is intensity-dependent, the strobe instrument is much faster than SPC and even faster than a phasemeasuring instrument. The strobe instrument is much simpler to use than SPC, and the data is easier to interpret than the phase system. Because of these advantages, SMS is used to monitor swelling of PMMA gels over a period of several hours. In-situ swelling experiments under vapor were carried out in the SMS of PTI, employing a pulsed lamp source (0.5 atm of N2). Pyrenes in the gel sample were excited at 345 nm and fluorescence decay curves were obtained at 395 nm during insitu swelling experiments, which were performed at room temperature. No shift was observed at the 395 peak during the swelling process. A disk-shaped gel cut from a cylindrical gel sample was placed in the wall of 1 × 1 cm × cm quartz cell and solvent was added at the bottom. The vapor-gel system deoxygenated by bubbling nitrogen for 10 min. The position of the gel, the level of the solvent, and the excitation and emission intensities are shown in Figure 1. Five different solvents, acetone (AC), chloroform (CH), dichloromethane (DM), ethyl acetate (EA), and tetrahydrofuran (THF), were used for five different vapor-induced swelling experiments. The characteristics of solvents are given in Table 1. The fluorescence decay data were collected over more than two decades of decay and fitted by linear least squares using a deconvolution method, with a dry gel as a scatterer standard. The uniqueness of the fit of the data to the model is determined by χ2 (χ2 e 1.10), the distribution of the weighted residuals, and the autocorrelation of the residuals. Results and Discussions A typical decay curve of P and the lamp pulse obtained from SMS are shown in Figure 2. To probe the swelling process during vapor-induced swelling, the fluorescence decay curves were measured and were fitted to the monoexponential functions
I(t) ) A exp(-t/τ)
(8)
5354 J. Phys. Chem. B, Vol. 106, No. 21, 2002
Pekcan and Erdogˇan
Figure 6. Fit of the 〈I〉 data to eq 12. Linear regression of the curve provides the B1 value.
between vapor uptake W and P intensities 〈I〉 from the gel during the swelling process is given by the following relation:22
〈I0〉 - 〈I〉 W ) W∞ 〈I0〉 - 〈I∞〉
(10)
where 〈I0〉 and 〈I∞〉 are the P intensities from the gel before and at the equilibrium state of swelling, respectively. W∞ is the vapor uptake of the fully swollen gel. Since I0 > I∞, eq 10 becomes
〈I〉 W )1W∞ 〈I0〉
(11)
This relation predicts that as W increases, 〈I〉 decreases. Combining eq 11 with eq 6 the following relation can be obtained:
ln Figure 5. The plot of the measured τ values versus swelling time, ts, for (a) chloroform and (b) ethyl acetate. These values were obtained by fitting the data in Figure 3 to eq 8.
where τ and A are the pyrene lifetime and the corresponding amplitude of the decay curves. Figures 3 and 4 present the fluorescence decay profiles and their fit to eq 8 for chloroform at various swelling steps (0, 48, 78, and 183 min). As the swelling time ts is increased, excited pyrenes decay faster and faster which indicates that as chloroform vapor uptake is increased, quenching of excited pyrenes increases. The measured τ values for the gel samples exposed to CH and EA vapor are plotted versus swelling time ts in Figure 5a and 5b, respectively. τ values decrease as vapor uptake is increased. To quantify the above observations, the area under the fluorescence decay curve is calculated using eq 8 according to following relation:
〈I〉 )
∫t
[ ]
ts 〈I〉 ) lnB1 τ 〈I0〉 c
As an example, 〈I〉 data for CH sample are plotted in Figure 6 according to eq 12 where a linear relation is obtained. Linear regression of the curve in Figure 6 provides us with the B1 value from eq 12. B1 values for all solvents are listed in Table 1. In Figure 5, exponential decrease in τ is observed as the swelling time, ts is increased. To quantify these results, the collisional type of quenching mechanism may be proposed for the fluorescence decay of P in the gel sample during the vaporinduced swelling process, where the following relations are given:26 excitation of ground-state pyrene, P to excited state of pyrene, P*
P + hν f P* collisional quenching of P* to P by Q k1
t2
Idt ) τA
(9)
z (P*Q) f P + Q P* + Q y\ k -1
1
where the integral is taking from the peak (t1) to the end point (t2) of the decay curve as shown in Figure 2. The relation
(12)
the decay of P*,
P* f P + hν′
Gel Swelling Induced by Organic Vapors
J. Phys. Chem. B, Vol. 106, No. 21, 2002 5355
Figure 8. The plot of the relation between solubility parameters, δ, and (a) Dc and (b) τc.
The rate equation for P* with delta excitation can be written as
d[P*] ) -(τ0-1 + kq[Q])[P*] + δ(t - t0)[P] dt
(15)
Here [ ] represents the concentration of P* and Q molecules and δ(t - t0) is the light pulse of SMS. Solution of eq 15 produces eq 8, where
τ-1 ) τ0-1 + kq[Q]
(16)
Figure 7. The fit of the normalized data in Figure 5 to eq 18. The produced τc and kq values are listed in Table 1.
For low-quenching efficiency, where τ0kq[W] , 1, eq 16 becomes
where Q represents the quencher molecules, k1 and k-1 are the diffusional rate constants, and k2 is the rate for internal quenching via electron transfer or spin exchange.27 Here, quenching efficiency is given by
τ ≈ τ0(1 - τ0kq[Q])
γ)
k2 k-1 + k2 + τ0-1 + k1[Q]
(13)
where τ0 is the lifetime of P in dry gel in which no quenching has taken place. If k2 . (k-1 + τ0-1 + k1[Q]) then eq 13 result γ ≈ 1 and k1 becomes the quenching rate constant, kq, given by Smoluchowski equation as26
4πNADmR kq ) 1000
If one integrates eq 17 over the differential volume (dυ) in the gel from the initial a0 to final a∞ thickness, the following relation is obtained.
τ ) 1 - C + CB1 exp(-ts/τc) τ0
where Dm ) Dp + Ds is the sum of the mutual diffusion coefficients of P and solvent molecules, R ) Rp + Rs is the sum of their interaction radii, and NA is the Avogadro’s number.
(18)
where C ) τ0kqW∞/υ and υ is the swollen volume of the gel. Here the vapor uptake, W, is calculated over differential volume by replacing Q with W as
W) (14)
(17)
∫aa
∞
[W]dυ
(19)
0
eq 18 can be fitted to the normalized lifetimes of P in Figure 7a and b for CH and EA, respectively. τc is measured from the fit of the curve in Figure 7. Using known B1 values from the previous calculations, the Dc and kq values are obtained for all
5356 J. Phys. Chem. B, Vol. 106, No. 21, 2002
Pekcan and Erdogˇan
Figure 9. The plot of the relation between molar volume, V, and (a) Dc and (b) τc.
samples. Here τ0 ) 500 ns was used for calculating the quenching rate constant. Experimentally obtained parameters, τc and Dc, together with the solubility parameter, δ, and molar volume, V, are listed in Table 1, where a0, a∞, and W(∞) W(0) values are also presented for AC, CH, DM, EA, and THF experiments. Here, measured τc and Dc values are strongly correlated on the molar volume, V, and the solubility parameter, δ, of the organic vapor molecules. Penetration of organic molecules into gel substantially depends on the hydrocarbon employed. Here, it is convenient to test whether the solvent quality, that is, polymer-solvent interaction, is responsible from the swelling processes or not. Solution theory predicts that the polymer-solvent interaction parameter, χ, is related to solubility parameter (δ) and molar volume (V) via the following relation28
χ)
V (δ - δp)2 RT
(20)
where R is the gas constant, T is the temperature, and δp is the solubility parameter of the polymer. It is seen in Table 1 that there are strong correlations between solubility parameter, δ, and Dc and τc values. Figure 8a and b presents Dc and τc versus δ plots, respectively, where it is seen that DM molecules penetrate into gel faster than the others. As a result, Dc of DM is larger than the others. This behavior of DM indicates that both the solubility parameter and the molar volume are responsible from gel swelling. Solubility parameter, δ, of PMMA, 19 (MPa)1/2, is more close to CH than DM; however, the small volume of DM plays an important role during penetration of the solvent molecule into the gel. As a result, Dc is much higher for DM molecule than CH. In Figure 9, Dc and
Figure 10. The plot of (a) (W(∞) - W(0)) vapor uptake and (b) (a∞ - a0) gel thickness versus solubility parameters, δ.
τc are plotted versus V, where a strong correlation is seen between these parameters. In other words, small molecules penetrate faster than large molecules into the gel. This behavior of organic vapor molecules can be summarized as follows. As the network is swollen by absorption of vapor molecules, the chains between the network junction are required to assume elongated configurations, a force akin to the swelling process. As swelling proceeds, this force increases and the dilution force decreases. Dc is the measure of the force of retraction in a stretched network structure. Here, as the gel swells faster (small τc), higher force of retraction is applied; as a result, the Dc value presents a larger value as in DM. However, slow penetration of vapor molecules into the gel present a smaller Dc value as in EA and AC. In Figure 10a and b, the variation in the final and initial disk thickness (a∞ - a0) and vapor uptake W(∞) - W(0) is plotted versus the solubility parameter, δ, of solvents. There is strong correlation between these parameters, that is, as (δ ∠ δp) approaches zero, (a∞ - a0) and W(∞) - W(0) values present larger numbers. From here, one can conclude that vapor uptake is strongly correlated to the polymer-solvent-interaction parameter, χ. In other words, for the best vapors (CH and DM), the degree of swelling of the gel is highest. The sum of the mutual diffusion coefficients were calculated from eq 14 by using the kq values and were around Dm = 10-7 cm2 s-1, where R is taken as 8 A°. The observed mutual diffusion coefficient, Dm, is typical for a small molecule diffusing in a swollen rubbery environment7 and is much smaller than the cooperative diffusion coefficient, Dc. This result is expected because an element of swollen network moves much faster, because of the restraining forces, than the P and solvent molecules in the swollen, viscous environment.
Gel Swelling Induced by Organic Vapors In summary, in this paper we have shown that the FTRF technique can be used to measure cooperative and mutual diffusion coefficients during vapor-induced swelling of a polymeric gel. Here, one can argue that measuring single lifetime by using FTRF in vapor-induced swelling gel provides simple data. However, data obtained by using τ1 and τ2 when the gel embedded in solvent are more complicated to interpret. In conclusion, we introduced a novel FTRF method to study gel swelling under vapor, which can produce more reliable results than other techniques. References and Notes (1) Tanaka, T.; Filmore, D. J. Chem. Phys. 1979, 70, 1214. (2) Peters, A.; Candau, S. J. Macromolecules 1986, 19, 1952. (3) Chiarelli, P.; De Rossi, D. Prog. Colloid Polym. Sci. 1988, 78, 4. (4) Dusek, K.; Prins, W. AdV. Polym. Sci. 1969, 6, 1. (5) Candau, S.; Baltide, J.; Delsanti, M. AdV. Polym. Sci. 1982, 7, 44. (6) Li, Y.; Tanaka, T. J. Chem. Phys. 1990, 92 (2), 1365. (7) Pekcan, O ¨ .; Winnik, M. A.; Egan, L. S.; Croucher, M. D. Macromolecules 1983, 16, 669. (8) Pekcan, O ¨ .; Winnik, M. A.; Croucher, M. D. Phys. ReV. Lett. 1988, 61, 641. (9) Pekcan, O ¨ .; Egan, L. S.; Winnik, M. A.; Croucher, M. D. Macromolecules 1990, 23, 2210. (10) Pekcan, O ¨ . Chem. Phys. Lett. 1992, 20, 198.
J. Phys. Chem. B, Vol. 106, No. 21, 2002 5357 (11) Pekcan, O ¨ . Trends Polym. Sci. 1994, 2, 236. (12) Pekcan, O ¨ .; Winnik, M. A.; Egan, L. S.; Croucher, M. D. Chem. Phys. 1990, 146, 283. (13) Pekcan, O ¨ . Chem. Phys. 1993, 177, 619. (14) Pekcan, O ¨ .; Winnik, M. A.; Croucher, M. D. Macromolecules 1990, 23, 2673. (15) Wang, Y.; Zhao, C. L.; Winnik, M. A. J. Chem. Phys. 1991, 95, 2143. (16) Wang, Y.; Zhao, C. L.; Winnik, M. A. Macromolecules 1993, 26, 3147. (17) Pekcan, O ¨ . J. Appl. Polym. Sci. 1993 49, 151. (18) Pekcan, O ¨ . J. Appl. Polym. Sci. 1996, 59, 521. (19) Pekcan, O ¨ .; Ugˇur, S. J. Appl. Polym. Sci. 1999, 74, 948. (20) Ugˇur, S¸ .; Pekcan, O ¨ . Polymer 2000, 41, 1571. (21) Pekcan, O ¨ .; Kaya, D.; Erdogˇan, M. Polymer 2000, 41, 4915. (22) Erdogˇan, M.; Pekcan, O ¨ . J. Polym. Sci., Part B: Polym. Phys. 2000, 38, 739. (23) Pekcan, O ¨ .; Kaya, D.; Erdogˇan, M. Polymer 2001, 42, 645. (24) Lakowicz, J. R. Principles of Fluorescence Spectroscopy; Plenum Press: New York, 1983. (25) Ware, W. R.; James, D. R.; Siemiarczuk, A. ReV. Sci. Instrum. 1992, 63, 1710. (26) Birks, J. B. Photophysics of Aromatic Molecule; Wiley-Interscience: New York, 1971. (27) Birks, J. B.; Lumb, M. D.; Munro, I. H. Proc. R. Soc., Ser. A 1964, 277, 289. (28) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953.
