J. Phys. Chem. B 2001, 105, 3435-3440
3435
Mass Transport in Thermoresponsive Poly(N-isopropylacrylamide-co-acrylic acid) Hydrogels Studied by Electroanalytical Techniques: Swollen Gels Weimin Zhang, ChengSong Ma, and Malgorzata Ciszkowska* Department of Chemistry, Brooklyn College, The City UniVersity of New York, Brooklyn, New York 11210-2889 ReceiVed: NoVember 13, 2000; In Final Form: February 15, 2001
Steady-state voltammetry and chronoamperometry at microelectrodes were used to study mass transport properties of temperature sensitive poly(N-isopropylacrylamide-co-acrylic acid), NIPA-AA, hydrogels. 1,1′Ferrocenedimethylanol, Fc(MeOH)2, and 2,2,6,6-tetramethyl-1-piperidinyloxy, TEMPO, were used as electroactive probe molecules. The activation energy of diffusion of Fc(MeOH)2 in aqueous solutions and in NIPA-AA hydrogels was found to be in the range of 17-19 kJ/mol, which suggests that the local microscopic viscosity does not change significantly because of the gelation process, although the macroscopic viscosity of the gels is extremely large. It was found that the diffusion coefficients of Fc(MeOH)2 and TEMPO in NIPA-AA hydrogels in their swollen state are approximately 20%-50% smaller than those in aqueous solutions, and that the diffusion coefficient of probe molecules in these gels is inversely proportional to the concentration of copolymer in the hydrogels. The “obstruction effect” and “hydration effect” were used to explain this phenomenon, and experimental results were compared with predictions of the model.
Introduction Polymeric gels play a very important role in modern industry. Gels are used to retain water and solutes in the agriculture, food, and cosmetic industries. Gels are also used as control delivery matrixes for drugs and perfumes.1 Polymeric gels have recently come under intense research for more applications, such as batteries, sensors, and artificial muscles. Polymeric gels exist in collapsed and swollen states. A volume phase transition of a gel occurs when it is stimulated by chemical or physical factors, such as temperature, solvent composition, pH, ionic composition, or electromagnetic radiation. Theoretical studies of phase transitions of polymeric gels date back to 1968. Dusek and Patterson2 predicted that when external forces are applied to the gels, the volume of those gels might undergo discontinuous change. Experimentally, discontinuous phase transition of a poly(acrylamide) hydrogel was observed first by Tanaka in 1975.3 The poly(N-isopropylacrylamide-co-acrylic acid), NIPA-AA, hydrogels can discontinuously shrink or swell from a change of temperature. The phase transition of NIPA-AA hydrogel has been studied by several groups.4-8 The phase transition temperature of NIPA-AA hydrogels varies from 33 to 40 °C and depends on the ratio of the two monomers and the ionic strength of the solvent/solution.4,5 The knowledge of transport properties of polymeric gels in their swollen state and during and after phase transition is essential for further understanding and utilization of the polymeric stimuli-responsive gels. The experimental techniques most commonly used for transport studies include electrochemical methods, radioactive tracer methods,9 and pulsed fieldgradient spin-echo NMR.10 Electroanalytical techniques, such as transient generation-collection methods,11 steady-state voltammetry,12 chronoamperometry,13 and scanning electrochemical microscopy,14 can provide fast, relatively inexpensive, and accurate sources of information on transport. Two electroana* To whom correspondence should be addressed. E-mail: malgcisz@ brooklyn.cuny.edu.
lytical methods, steady-state voltammetry and chronoamperometry at microelectrodes, have been used to study mass transport of molecules in solutions and polymeric gels.12,13 The following equation relates the diffusion coefficient of electroactive species with the steady-state current, Iss, at a microdisk electrode:
Iss ) 4nFcDrd
(1)
where n is number of electrons transferred, F is the Faraday constant, c is the concentration of an electroactive probe, D is diffusion coefficient of that probe, and rd is the radius of a microelectrode. Chronoamperometry is often used to determine the diffusion coefficient of probe molecules when their concentration is not known.14,15 When the gels collapse, the aqueous phase and the gel phase separate. The concentration of a probe in the gel phase is then not known. For a microdisk electrode, if the pulse time t satisfies Dt/r2 < 10-4, the normalized current, It/Iss, is given by16
( )
It π1/2 ) 0.7854 + r (Dt)-1/2 Iss 4 d
(2)
where It is the current at the time t, Iss is the steady-state current, rd is the radius of the disk microelectrode, and D is the diffusion coefficient of a probe. In this work, steady-state voltammetry and chronoamperometry at microelectrodes were applied to study the transport properties of NIPA-AA hydrogels in their swollen state. The significance of this project is that the results will lead to a better understanding of the behavior of temperature sensitive polymeric gels and their transport properties. This knowledge is needed for further progress in sensor development and other promising applications of thermosensitive gels, such as power sources materials and drug controlled release matrixes. Experimental Section Reagents. N-isopropylacrylamide (NIPA), N,N′-methylenebisacrylamide (BIS), N,N,N′,N′-tetramethylethylenediamine
10.1021/jp004177r CCC: $20.00 © 2001 American Chemical Society Published on Web 03/28/2001
3436 J. Phys. Chem. B, Vol. 105, No. 17, 2001 (TMED), acrylic acid (AA), potassium iodide, ammonium persulfate, and lithium perchlorate were purchased from Aldrich. 1,1′-Ferrocenedimethanol, Fc(MeOH)2, was purchased from Fluka. 2,2,6,6-Tetramethyl-1-piperidinyloxy, TEMPO, was purchased from Sigma. All chemicals except AA were used as received. The acrylic acid was purified by vacuum distillation (21 mmHg, 52 °C) and was stored in a refrigerator before use. All solutions were prepared using high purity water obtained from Milli-Q (Millipore, Model RG) purification system. Apparatus. Voltammetric measurements were carried out in a jacketed glass cell with a three-electrode system consisting of an Ag/AgCl reference electrode, a Pt wire counter electrode, and Pt microdisk working electrodes (Project Ltd., Warsaw, Poland). A refrigerated circulator (Isotemp model 1016P, Fisher Scientific) controlled the temperature of a cell. Staircase voltammetry and chronoamperometry were applied with a model 283 potentiostat (Perkin-Elmer, PARC) and controlled via a PC computer. Staircase voltammetry parameters were as follows: step height (∆E) 5 mV and frequency (f) 3 Hz. Chronoamperometric experiments were conducted in a Faraday cage. The parameters were as follows: pulse width 5 ms and sample frequency 9090.9 Hz. The working microdisk electrodes were 5.0 and 12.0 µm in radius Pt electrodes. The working electrodes were polished before measurement with Microcloth polishing cloth (Buehler) and 0.1 µm diamond suspension polishing solution (Buehler). Optical inspection of the state of the electrode surface was accomplished with an inverted microscope for reflected light (Nikon, model Epiphot-200). Gel preparation. The synthesis of a NIPA-AA copolymer cross-linked with BIS was modified from a previously reported procedure.7 The polymer gel was synthesized by a conventional radical polymerization method; 0.87 g of NIPA, 0.025 mL of AA, and 0.0156 g of N,N′-methylenebisacrylamide, BIS (crosslinker), were dissolved in 10 mL of distilled water. The pre-gel solution was placed in a water bath and was deoxygenated with argon for 20 min. A total of 5 mg of ammonium persulfate (initiator) was added to the solution followed by 56 µL of N,N,N′,N′-tetramethylethylenediamine, TEMED (accelerator). The polymerization took place at 22 °C for 20 h. Freshly made gels were purified by a spongelike method17 to remove unreacted compounds (mainly monomers) and dried in an oven at 80 °C for several days. A given amount of dry NIPA-AA copolymer was placed into a known volume of a solution with a known concentration of an electroactive probe and supporting electrolyte. To prepare the hydrogels with defined concentration of a probe, a solution with an appropriate concentration of that probe and a copolymer sample were left at room temperature for several days to allow the polymer to swell and produce gel. The discontinuous volume phase transition of these gels occurs at 45 ( 2.5 °C and results in a release of approximately 40% of the solution mass from the gel phase. Result and Discussion The one-electron oxidation processes of Fc(MeOH)2 and TEMPO were studied in aqueous solutions and NIPA-AA gels using Pt microdisk electrodes for a temperature range from 5 to 40 °C. Voltammograms for the oxidation of Fc(MeOH)2 and TEMPO were well defined and reproducible, with a relative standard deviation of the limiting current less than 5% (calculated from 6 voltammograms). Typical steady-state voltammograms of Fc(MeOH)2 oxidation obtained in an aqueous solution and 2.0% (w/w) NIPA-AA gel containing 0.1 M supporting
Zhang et al.
Figure 1. Steady-state voltammograms of the oxidation of 1.8 mM Fc(MeOH)2 in (A) aqueous solution and in (B) 2.0% (w/w) NIPA-AA gel; 0.1 M LiClO4, Pt microdisk electrode, rd ) 5 µm.
TABLE 1: Temperature Dependence of the Diffusion Coefficient of Fe(MeOH)2 in 0.1 M LiClO4 Aqueous Solutions and NIPA-AA Gels D (cm2/s) temp (°C)
aqueous solutiona
25
6.4 × 10-6 ( 3.9 × 10-7 7.2 × 10-6 ( 3.7 × 10-7 8.2 × 10-6 ( 1.4 × 10-7 9.2 × 10-6 ( 1.4 × 10-7 1.0 × 10-5 ( 1.4 × 10-7
30 35 40 45 a
1.2% (w/w) 2.0% (w/w) 4.0% (w/w) NIPA-AA gel NIPA-AA gel NIPA-AA gel 5.1 × 10-6 ( 2.9 × 10-9 5.7 × 10-6 ( 7.7 × 10-9 6.4 × 10-6 ( 1.9 × 10-8 7.3 × 10-6 ( 6.8 × 10-8 8.1 × 10-6 ( 3.3 × 10-9
4.4 × 10-6 ( 5.6 × 10-9 4.9 × 10-6 ( 8.7 × 10-8 5.5 × 10-6 ( 1.6 × 10-7 6.2 × 10-6 ( 1.2 × 10-7 7.1 × 10-6 ( 1.6 × 10-7
3.1 × 10-6 ( 7.8 × 10-9 3.5 × 10-6 ( 1.3 × 10-7 3.9 × 10-6 ( 8.4 × 10-8 4.3 × 10-6 ( 1.5 × 10-7 4.6 × 10-6 ( 4.4 × 10-7
Reported value at 25 °C is 7.3 × 10-6 ( 0.4 cm2/s (ref 12).
electrolyte, LiClO4, are presented in Figure 1. The diffusion coefficients of electroactive probes were determined according to eq 1. Table 1 summarizes the temperature dependence of the diffusion coefficients of Fc(MeOH)2 in aqueous solutions and NIPA-AA gels of various concentrations of the polymer. The values of the diffusion coefficients of Fc(MeOH)2 and TEMPO in aqueous solution at 25 °C were 6.4 × 10-6 ( 0.4 cm2/s and 6.6 × 10-6 ( 0.1 cm2/s, respectively. These values agree well with those reported previously,12 7.3 × 10-6 ( 0.4 cm2/s and 6.6 × 10-6 ( 0.3 cm2/s for Fc(MeOH)2 and TEMPO, respectively. Diffusion coefficients of Fc(MeOH)2 in NIPAAA gels of various compositions are approximately 20%-50% smaller than that in an aqueous solution. Additionally, the diffusion coefficient decreases when the concentration of the copolymer in the gel increases. The diffusion of molecules in an ideal solution should obey the Stokes-Einstein relationship:
D ) kT/6πηr
(3)
where D is the diffusion coefficient of the diffusing species, k is Boltzmann’s constant, T is the temperature, η is the solution viscosity, and r is the hydrodynamic radius of a molecule. It has been reported, however, that the Stokes-Einstein relationship does not apply to diffusion in polymeric gels.12,13,17 The macroscopic viscosity of NIPA-AA gels is always much larger than that of solutions, but the decrease of diffusion coefficient is relatively small. This is always attributed to the comparatively open structure of gels compared to solid materials.
Mass Transport in Thermoresponsive NIPA-AA
J. Phys. Chem. B, Vol. 105, No. 17, 2001 3437
Figure 2. Temperature dependence of the diffusion coefficient of Fc(MeOH)2 in (A) aqueous solution and in (B) 2.0% (w/w) NIPA-AA hydrogel; 0.1 M LiClO4. Figure 4. The diffusion coefficient of Fc(MeOH)2 in 2.0% (w/w) NIPA-AA hydrogel containing 0.1 M LiClO4; (b) measured by steadystate-voltammetry, (1) measured by chronoamperometry.
TABLE 2: Activation Energy of Diffusion of Fc(MeOH)2 in Aqueous Solution and in the NIPA-AA Gels
Figure 3. It/Iss vs 1/t1/2 for the oxidation of 2.0 mM Fc(MeOH)2 in 2.0% (w/w) NIPA-AA gel containing 0.1 M LiClO4; Pt microdisk electrode, rd ) 13 µm. Best fit: It/Iss ) 0.0993t-1/2 + 0.751.
We studied the temperature dependence of diffusivity of Fc(MeOH)2 in NIPA-AA gels and in aqueous solution with supporting electrolyte, LiClO4, for the temperature range 5-40 °C. Note that this temperature range is below the volume phase transition of NIPA-AA gels, and those gels exist in their swollen states. The results are presented in Figure 2. As predicted by the Stokes-Einstein equation, eq 3, the diffusion coefficient of Fc(MeOH)2 should be directly proportional to the temperature of the system. However, because the viscosity of water, and consequently aqueous solutions, is not linearly dependent on temperature, the diffusion coefficient does not increase linearly with the temperature. Although the same concentration of Fc(MeOH)2 was used to prepare solutions and gels, the final concentration of Fc(MeOH)2 in a gel can change because of the volume changes during gel preparation and swelling process. To make sure that the concentration of an electroactive probe does not change during the swelling process, a concentration independent determination of diffusion coefficient of Fc(MeOH)2 was carried out by chronoamperometry. The normalized current, It/Iss, was plotted as a function of t-1/2 (see eq 2) and presented in Figure 3. An average intercept of the It/Iss vs t-1/2 plots was 0.751, the value close to 0.785 predicted by eq 2. The diffusion coefficient values of Fc(MeOH)2 in 2.0% NIPA-AA gel calculated from eq 2 are compared with those from steady-state voltammetric experiments, and they are presented in Figure 4 for the
polymer concentration (w/w) %
D (cm2/s), 25 °C
Ea (kJ/mol)
A
0.0 1.2 2.0 3.1 4.0
6.4 × 10-6 ( 1.9 × 10-7 5.1 × 10-6 ( 2.9 × 10-7 4.4 × 10-6 ( 5.5 × 10-8 3.4 × 10-6 ( 2.8 × 10-8 3.1 × 10-6 ( 7.8 × 10-8
19 19 18 17 17
1.3 × 10-2 1.1 × 10-2 6.4 × 10-3 3.0 × 10-3 2.6 × 10-3
temperature range from 20 to 38 °C. For this temperature range, diffusion coefficients of Fc(MeOH)2 obtained by the two methods are identical within the experimental error. This suggests that the concentration of Fc(MeOH)2 did not change significantly during the gel preparation and swelling process. Note that the concentration of polymer was very small, not greater than 4.0%. The data from Table 2 were analyzed in terms of the Arrhenius-like equation
D ) Ae-Ea/RT
(4)
where Ea is the activation energy of diffusion of the probe of interest in an aqueous solution or in a gel, A is the frequency factor, R is the gas constant, and T is the temperature. Figure 5 shows the data for the aqueous solution and NIPAAA gels of various composition analyzed in the form of ln D vs. 1/T plots, and Table 2 shows values of Ea and A calculated from these data. The value of Ea for the diffusion of Fc(MeOH)2 in aqueous solution and in NIPA-AA gels was in the range of 17-19 kJ/mol. This agrees with the Ea value of 19 ( 1.5 kJ/ mol reported by Jacob et al.18 for diffusion of N,N,N′,N′tetramethylethylenediamine in an aqueous solution. As pointed out by Jacob et al., the activation energy required for diffusion of a species reflects the viscosity of a solvent or solution in which that species diffuses.18 The similarity of the activation energy of diffusion in an aqueous solution and in gels suggests that the microscopic viscosity of a solvent trapped in a NIPAAA gel network is similar to that in aqueous solution, although the macroscopically observed viscosity of gels is significantly larger than that for aqueous solution.17 For example, the macroscopic viscosity of 3.0% (w/w) NIPA-AA hydrogel is 2.3 × 106 cP, which is approximately one million times larger than
3438 J. Phys. Chem. B, Vol. 105, No. 17, 2001
Zhang et al. volume fraction occupied by the hydrated protein molecules, which is defined as φ ) 1 - wg, where w is the weight fraction of water and g is the specific gravity of the solution, and R j is a geometry related coefficient, which is defined as
1 R j ) (Ra + Rb + Rc) 3
(6)
For prolate ellipsoids, if two of their principal axes are identical, that is a ) Fb ) Fc, where F ) a/b and F > 1, Ra and Rb ) Rc can be obtained by the following equations:
Ra )
Figure 5. Arrhenius plots for the temperature dependence of the diffusion coefficient of Fc(MeOH)2 in aqueous solution (A) and in 1.2 (B), 2.0 (C), and (D) 4.0% (w/w) gels. All samples contain 0.1 M LiClO4.
that of an aqueous solution. The smaller diffusion coefficient of Fc(MeOH)2 in the gels can be attributed to a change of the frequency factor A in an aqueous solution and gels. The frequency factors A for the diffusion of Fc(MeOH)2 for various concentrations of gels range from 1.1 × 10-2 to 2.6 × 10-3, compared to 1.3 × 10-2 for an aqueous solution. However, the physical meaning of A is not clear. Several theoretical models have been proposed to describe the self-diffusion of a solvent in colloidal suspensions, microemulsions, and protein solutions. The most appropriate model, however, is still a controversial subject.19-24 We want to extend and apply existing models for colloidal suspensions and protein solutions to thermosensitive polymeric gels. Because the appropriate models to describe diffusion of molecules in polymeric gels are not well developed, we assume that principles describing self-diffusion of solvents in polymeric systems should also be valid to describe diffusivity of any molecule, including electroactive probes. The decrease of the diffusion coefficient of water in colloidal systems and protein solutions was analyzed in terms of two factors.19,20 The first factor is called the “obstruction effect”. The colloidal suspensions, polymer macromolecules, or micellar assemblies act to confine and detour the diffusion of the molecules. The effective diffusion length is increased, and the diffusion coefficient is reduced as compared to the ideal solution. The second possible effect is the “hydration effect”, when some water molecules are bound to the surface of the colloidal objects or polymer molecules, and they form a temporally immobilized structured water layer. The total increased volume of a polymer after hydration can be treated as several times larger than without the hydration layer, and it magnifies the obstruction effect. Wang19 discussed the obstruction effect and its effect on the diffusion of water in protein aqueous solutions. He proposed that the shape of ovalbumin molecules can be approximated by ellipsoids with principal semi-axes a, b, and c, respectively. If only the obstruction effect is considered, the effective diffusion coefficient of water molecules in the protein solution, D′, can be expressed as
D′ ) D° (1 - R j φ)
(5)
where D° and D′ are diffusion coefficients of water in an ideal solution and in a protein solution, respectively, φ is the total
1 F -2 F F + xF2 - 1 ln F2 - 1 2(F2 - 1)3/2 F - xF2 - 1
(7)
2
R b ) Rc )
2 F -2 F F + xr2 - 1 ln F2 - 1 2(F2-1)3/2 F - xF2 - 1
(8)
2
If one axis of prolate ellipsoids, for example a, is significantly longer than the other two axes (b and c), the shape of a molecule is like a cylinder. In this case, according to Wang’s calculations (eqs 6-8),19 the R j value is 1.667. Therefore, with proteins treated as cylinders, the effective diffusion coefficient of water molecules in the protein solution, D′, can be expressed as
D′ ) (-1.667φ + 1) D°
(9)
One should be aware of the limitations of eq 9; it can be used only in very dilute systems, and the polymer fraction must be lower than 0.6. The eqs 5 and 9 were originally used to describe the selfdiffusion of water in ovalbumin aqueous solutions of low ionic strength.19 We assume that the diffusion of electroactive probes obeys the same rules as those for solvent molecules in polymeric gels. In our experiment, NIPA-AA gel is a cross-linked polymer swollen by water or an aqueous solution. To develop an appropriate model, the gel can be simplified and treated as a system consisted of long rods swollen by a solvent. If the obstruction effect described by Wong is valid in a polymeric gel, the diffusion coefficient of water and, consequently, all probe molecules in the gels should satisfy eq 9. The total volume fraction occupied by polymeric units, φ, can be obtained experimentally by measuring the weight fraction of water in the gels and the density of the gels, which implies how much space in the gel is occupied by polymers. In our experiment, because the polymer concentration in gels was very small (e4.0%), the density of a gel was almost the same as that of the aqueous solution. If we assume that polymer chains are not hydrated, the φ value may be treated as the weight concentration of polymer in the gel. Table 3 gives the diffusion coefficient of Fc(MeOH)2 in aqueous solution, D°, and in NIPA-AA gel, D′, for various values of φ, with φ defined as a weight concentration of the polymer in the gel. Experimental data presented in Table 3 are plotted in Figure 6 and can be fitted to the linear eq 10 with a correlation coefficient of 0.997.
D′ ) -14.8φ + 0.99 D°
(10)
The diffusion coefficient of Fc(MeOH)2 in gels is inversely
Mass Transport in Thermoresponsive NIPA-AA
J. Phys. Chem. B, Vol. 105, No. 17, 2001 3439 acrylic acid) in the range 4.25-4.6. Polymeric chains in hydrogels interact with water molecules through a hydrogen bond. Lee et al.24 proposed three states of water in gels in which the “bound” water is attached tightly to the polymer, “nonbound” water is free to diffuse, and “intermediate” state water molecules interact weakly with polymeric chains. Because the bound state water and intermediate state water increase the total volume of the polymer, and consequently it can be treated as a part of the polymer in the hydrogel, we introduce a coefficient H, related to the degree of hydration of the polymers. Now eq 9 can be written as
D′ ) (-1.667Hφ + 1) D°
Figure 6. Dependence of the diffusion coefficient of Fc(MeOH)2 in the NIPA-AA hydrogel on the concentration of the polymer in the gel; best fit D′/D° ) -14.8φ + 0.99, R2 ) 0.997.
TABLE 3: Dependence of the Diffusion Coefficient of Fc(MeOH)2 in NIPA-AA Hydrogels on the Concentration of the Polymer in the Gel polymer concentration (w/w) %
D (cm2/s), 25 °C
D′/Do
Φ
0.0 1.2 2.0 3.1 4.0
6.4 × ( 1.9 × 5.1 × 10-6 ( 2.9 × 10-7 -6 4.4 × 10 ( 5.5 × 10-8 3.4 × 10-6 ( 2.8 × 10-8 3.1 × 10-6 ( 7.8 × 10-8
1.0 0.80 0.69 0.54 0.50
0.00 0.012 0.020 0.031 0.040
10-6
10-7
proportional to the polymer concentration in the gel, as predicated by the obstruction effect.19 As one can see, the concentration dependence of the diffusion coefficient of Fc(MeOH)2 in the NIPA-AA hydrogel system does not agree with the obstruction effect model. If the weight concentration of the polymer in the gel is φ, the slope of the plot in Figure 6 should be -1.667 as predicted by eq 9. However, the experimental value is -14.8, which is 8.87 times larger than the predicted value. If the geometry related coefficient, R j , is correct, it seems that the volume fraction of polymers in the hydrogel is expanded 8.87 times compared to the unhydrated polymer volume fraction. Similar disagreement was reported previously in a colloidal system prepared by dispersing synthetic smectite clay in water.20 The value of the volume fraction of a solid colloid determined experimentally from the self-diffusion of water was 0.12, and it was six times larger than the actual solid volume fraction in the system, 0.02. The experimental value was “unrealistically high” according to the authors,20 because it would be related to a 3 nm thick layer of water on the surface of the clay particles. The reason for this difference is still not clear. Cheever et al.,21 Duval et al.,20 and Von Meerwall et al.22 attributed this difference to the hydration effect, which is related to the water molecules firmly attached to the polymer, forming a temporarily immobilized water film around the polymer chains because of hydration or other hydrodynamic effects. The NIPA-AA copolymer contains many carbonyl and amino functional groups. The pKa of acrylic acid is 4.25 (25 °C), and the pKa of poly(acrylic acid) is 4.6; the more carboxylic groups in a polymeric chain and the shorter distances between them result in an increase in pKa value.23 Because N-isopropylamide is a neutral monomer and carboxylic groups in NIPA-AA copolymer are more separated from each other than in poly(acrylic acid), we expect the pKa of poly(N-isopropylamid-co-
(11)
where -1.667 is a coefficient related to the shape of polymer chains and the obstruction effect. The experimental value of H can be obtained from eqs 9 and 11. The H value for the NIPAAA polymer in a hydrogel is 8.77 according to our experiment. Because the diffusion coefficient of bound water is dramatically smaller than nonbound free to diffuse water, we treated bound water as a part of the polymer chains and made an assumption that the electroactive probes do not diffuse freely in that bound water. The hydration effect coefficient H should be characterized by the following properties. It is related to the properties of polymers and to the strength of interactions between the polymers and solvents. The interactions could result from hydrogen bonding, specific adsorption, and hydrodynamic effects. They are independent of the concentration of a polymer in dilute gels and independent of the concentration of an electroactive probe. If the concentration of a probe in the swollen gel is low, interactions between water and polymer are expected to be much stronger than those between electroactive probes and polymer. Water molecules can form hydrogen bonds with the polymer, and they have a stronger dipole moment than electroactive probes, for example, Fc(MeOH)2. However, after the volume phase transition occurs, the polymer in a gel is dehydrated and the interactions between electroactive probes and polymer could increase. Investigation of such interactions for collapsed gels after the volume phase transition is underway in our laboratory. Equation 11 could be used to describe the self-diffusion of any molecule in any polymeric gel system. If we know the diffusion coefficient of the molecule in an aqueous solution, the hydration effect H of a polymer in its hydrogel, and weight concentration of the polymer in that gel, the diffusion coefficient of that molecule in the gel can be predicted by eq 11. Note that the H value must be determined for a given polymer experimentally using a model probe. To check the above procedure, we performed a series of experiments using TEMPO as the neutral electroactive probe. First, using steady-state voltammetry at a disk microelectrodes and eq 1, we determined diffusion coefficients of TEMPO in an aqueous solution, D°, and in 2.05% NIPA-AA hydrogel, D′, and their dependence on temperature. Then, diffusion coefficients of TEMPO in a 2.05% NIPA-AA hydrogel were calculated based on eq 11, with experimental D° values for various temperatures, the hydration coefficient H ) 8.77 for NIPA-AA in hydrogel, and the volume fraction of polymer in a gel, 0.021. Figure 7 compares calculated diffusion coefficients of TEMPO in 2.05% NIPA-AA gel with experimentally determined values. The difference between calculated and experimental values was less than 7% for the temperature range 5-25 °C. At 35 and 30 °C, the diffusion coefficient of TEMPO
3440 J. Phys. Chem. B, Vol. 105, No. 17, 2001
Zhang et al. we made in the model, where only the dilute polymer gel was considered. We expect that the diffusion of molecules in the polymeric phase in the collapsed gel would decrease dramatically because of the high polymer fraction in the gel.
Figure 7. Temperature dependence of the diffusion coefficient of TEMPO in 2.0% (w/w) NIPA-AA gel; (2) calculated values, (b) experimental values.
obtained from experiments is 14% and 11% off the calculated values, respectively. It might be that the internal structure of the gel changes at higher temperatures when the gel approaches the volume phase transition temperature. Investigations of diffusion in NIPA-AA gels swollen by various organic solvents and in NIPA hydrogels are currently underway in our laboratory. We are also testing our model using variety of electroactive probes, including ionic probes. Equations 9 and 11 could be very useful in many fields. For example, if we are interested in the diffusion coefficient of a specific molecule in a polymeric gel and we know the diffusion coefficient of that molecule in an aqueous solution, we can estimate the diffusivity of that molecule in a polymeric gel on the basis of these equations. The method is that we choose a probe molecule, which can be an electroactive probe, such as Fc(MeOH)2. Its diffusion coefficient in polymeric gels with various concentrations of a polymer can be easily determined using electroanalytical methods. The hydration coefficient, H, for the polymer in the gel can be calculated as describe before, and the diffusion coefficient of that molecule can be estimated by eq 11. As shown before, using the hydration coefficient, H, obtained from diffusivity of Fc(MeOH)2, we successfully predicated the diffusion coefficient of TEMPO in the NIPAAA polymeric gel. This method should work well with small molecules diffusing in polymeric gels. Because only “obstruction effect” and “hydration effect” were considered in the model (eqs 9 and 11), this model is only valid for the description of diffusivity of neutral probes in diluted gel systems. It might possibly be valid to characterize transport of charged probes in noncharged gel systems. However, it is not suitable to describe transport of charged probes in charged polymeric systems. Electrostatic interactions might be stronger than obstruction effect and hydration effect. This model is probably not suitable to describe diffusivity of large diffusing species such as polymeric molecules in gels. In the gel, the crosslinked polymer chains define the passageway through which the molecules diffuse. The passageway constitutes the pores. The molecular weight of diffusing polymeric molecules and the size of pores in a gel affect the diffusivity significantly. If the molecular weight of a diffusing polymer is sufficiently large, it will not penetrate the gel.25 The model we discussed above will not be valid for the gels during and after the volume phase transition. At the collapsed state, the polymer fraction of NIPA-AA polymer phase could reach 0.65-0.70.26 These values are higher than the assumption
Summary Using two electrochemical methods, steady-state voltammetry, and chronoamperometry, we measured the temperature dependence of the diffusion coefficient of Fc(MeOH)2 and TEMPO in aqueous solutions and in NIPA-AA thermosensitive gels in their swollen state. The similar activation energy of diffusion in aqueous solution and in NIPA-AA gels suggests that the local microscopic viscosity of solution trapped in NIPAAA gel networks is similar to that in aqueous solution. We measured the dependence of the diffusion coefficient of Fc(MeOH)2 in NIPA-AA hydrogels on the concentration of the polymer in the gel, and we have shown that in dilute gel systems (w/w % e 4%), the diffusion coefficient of a neutral probe is inversely proportional to the polymer concentration. The obstruction effect and hydration effect were used to explain this phenomenon. A modified equation taking into account both the obstruction effect and hydration effect was proposed, and this equation successfully predicated the diffusion coefficient of TEMPO in the NIPA-AA gel. Acknowledgment. This work was supported in part by the Office of Naval Research under Grant No. N00014-98-1-0244 and by the PSC-CUNY Reach Award number 62385 00 31. References and Notes (1) Tanaka, T. Phase Transition of Gels. In Polyelectrolyte Gels. Properties, Preparation and Application; Harland, R. S., Prud’homme, R. K., Eds.; ACS Symposium Series, Vol. 480; American Chemical Society: Washington, DC, 1992. (2) Dusek, K.; Patterson, D. J. Polym. Sci. 1968, part A-2, 6, 1209. (3) Dagani, R. Chem. Eng. News 1997, 75, 26. (4) Kawasaki, H.; Sasaki, S.; Maeda, H. J. Phys. Chem. B 1997, 101, 5089. (5) Kawasaki, H.; Sasaki, S.; Maeda, H. J. Phys. Chem. B 1997, 101, 4184. (6) Kawasaki, H.; Mitou, T.; Sasaki, S.; Maeda, H. Langmuir 2000, 16, 1444. (7) Kawasaki, H.; Sasaki, S.; Maeda, H. Langmuir 2000, 16, 3159. (8) Hirotsu, S.; Hirokawa, Y.; Tanaka, T. J. Chem. Phys. 1987, 87, 1392. (9) Melnichenko, Y. B.; Klepko, V.V.; Shilov, V. V. Polymer 1993, 34, 1019. (10) Matsukaa, S.; Ando, I. Macromolecules 1996, 29, 7136. (11) Tatistcheff, H. B.; Fritsch-Faules, I.; Wrighton, M. S. J. Phys. Chem. 1993, 97, 2732. (12) Hyk, W.; Ciszkowska, M. J. Phys. Chem. B 1999, 103, 6466. (13) Fan, F.-R. F. J. Phys. Chem. B 1998, 102, 9777. (14) Pyo, M.; Bard, J. A. Electrochim. Acta 1997, 42, 3077. (15) Winlove, C. P.; Parker, K. H.; Oxenhan, R. K. C. J. Electroanal. Chem. 1984, 170, 293. (16) Denuaault, G.; Mirkin, V. M.; Bard, A. J. J. Electroanal. Chem. 1991, 308, 27. (17) Petrovic, S.; Zhang, W.; Ciszkowska, M. Anal. Chem. 2000, 72, 3449. (18) Jacob, S. R.; Hong, Q.; Coles, B. A.; Compton, R. G. J. Phys. Chem. B 1999, 103, 2963. (19) Wang, J. H. J. Am. Chem. Soc. 1954, 76, 4755. (20) Duval, P. F.; Porion, P.; Damme, V. H. J. Phys. Chem. B 1999, 103, 5730. (21) Cheever, E.; Blum, F. D.; Foster, K. R.; Mackay, R. A. J. Colloid Interface Sci. 1985, 104, 121. (22) Von Meerwall, E.; Mahoney, D.; Iannacchione, G.; Skowronski, D. J. Colloid Interface Sci. 1990, 139, 437. (23) Dautzenberg, H.; Jaeger, W.; Kotz, J.; Philipp, B.; Seidel, Ch.; Stscherbina, D. Polyelectrolytes: Formation, Characterization and Application; Hanser/Gardner Publishers: New York, 1994. (24) Lee, H. B.; Jhon, M. S.; Andrade, J. D. J. Colloid Interface Sci. 1975, 51, 255. (25) Refojo, M. F.; Leong, F. L. J. Polym. Sci. Polym. Symp. 1979, 66, 227. (26) Shibayama, M.; Nagai, K. Macromolecules 1999, 32, 7461.
