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Self-diffusion of water in thermoreversible gels near volume transition
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Chemical Engineering Science, Vol. 53, No. 5, pp. 869—877, 1998 ( 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain S0009–2509(97)00335–7 0009—2509/98 $19.00#0.00
Self-diffusion of water in thermoreversible gels near volume transition: Model development and PFG NMR investigation* S. S. Ray,s P. R. Rajamohanan,s M. V. Badiger,s I. Devotta,s S. Ganapathy,s and R. A. Mashelkartu sNational Chemical Laboratory, Pune 411 008, India; tCouncil of Scientific and Industrial Research, Rafi Marg, New Delhi 110 001, India (Received 21 May 1997; accepted 29 August 1997) Abstract—Pulsed field gradient spin echo (PFG-SE) NMR technique has been used to measure the self-diffusion coefficient (D ) of water in a thermoreversible hydrogel, Poly(N-isopropylac4%-& rylamide). D , was measured as a function of temperature (!5—50°C) and hydration level. 4%-& A theoretical model to predict D was built by using a combination of lattice fluid hydrogen 4%-& bond theory and free volume theory. The fully swollen gel did not show any discontinuous change in D with temperature, Whereas, a partially swollen gel, showing the existence of two 4%-& kinds of water having diffusivities differing by order of magnitude, exhibits a discontinuous change in D . These results were explained within the theoretical framework developed by us. 4%-& The present work thus enables an elucidation of diffusion phenomenon at the volume transition point for the first time. ( 1998 Elsevier Science Ltd. All rights reserved. Keywords: Self-diffusion; Pulse Field Gradient NMR; thermoreversible gel; PNIPAm; LFHB theory; Free volume theory. INTRODUCTION
Hydrogels are becoming increasingly important biomaterials because of their excellent biocompatibility and stimuli responsive characteristics (Dusek, 1993). They have been used in contact lenses (Ratner and Hoffman, 1976), burn wound dressings (Spacek and Kubin, 1973), membranes (De Rossi et al., 1991), bioseparations (Cussler et al., 1984; Badiger et al., 1992), robotics (Osada and Ross Murphy, 1993), and as basic materials for controlled release dosage forms for drugs (Graham and McNeill, 1984). Our school has been involved in investigating diverse innovative applications and microstructure level investigations of such hydrogels (Ganapathy et al., 1989; Badiger et al., 1992; Rajamohanan et al., 1995; Kulkarni et al., 1992). The aspects of thermodynamics of volume transitions in such gels, especially with a view to gain an understanding of the attendant molecular level phenomena, has been one of our key endeavour (Lele et al., 1995). The present report relates to the study of self-diffusion of water in a gel at volume transition. Water plays an
*NCL Communication No: 6395. u Corresponding author. Fax: 91 11 3710618; e-mail: [email protected].
important role in determining the physico-chemical properties of the hydrogels. Water is also known to organise into different states, such as, bound, free and interfacial (Lee et al., 1975). The structure and dynamics of water have been studied by a number of techniques (Pessen and Kumosinski, 1985), nuclear magnetic resonance spectroscopy being one of the techniques. As a continuing effort to study the role, state, structure and dynamics of water in hydrogels, we have undertaken a study on the measurement of self-diffusion coefficient of water in a thermally reversible poly(N-isopropyl acrylamide) (PNIPAm) hydrogel. This hydrogel exhibits a lower critical solution temperature (LCST) phenomenon in the temperature range of 30—32°C, undergoing a sharp discontinuous volume transition at LCST. The swelling—deswelling characteristics of PNIPAm, encompassing the LCST zone, is also of great practical importance (Dong and Hoffman, 1987). PNIPAm has been extensively investigated in recent years for its structure and swelling properties (Schild, 1992). In an earlier study, we have established the correspondence between the macroscopic volume phase transition and microscopic dynamical events taking place at the molecular level using 1H MASS experiments (Badiger et al., 1991; Ganapathy et al., 1995). Dong and Hoffman (1990)
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have reported on the state of water in PNIPAm hydrogel using differential scanning calorimetry. The bound and free water contents in the hydrogel was estimated as a function of temperature. Yasunaga and Ando (1993) have reported a study on the polymer crosslinking and its effect on the molecular motion of water in PNIPAm hydrogel by proton NMR spectroscopy. However, as yet, there are no reports on the self-diffusion coefficient of water just below and above LCST of this polymer hydrated to different extents. We fill this important gap in our paper. In order to predict the self-diffusion coefficients, we employ a two-state model in which the fraction of the bound and free water contents are estimated by using a statistical thermodynamic theory, which has recently been demonstrated to qualitatively predict the thermoreversible volume transition in PNIPAm gel—water system. (Lele et al., 1995). We then use the free volume theory of Vrentas and Duda (1977) to obtain an approximate expression for the self-diffusion coefficient. A qualitative verification of the predictions of our theory is provided by independent pulsed field gradient spin echo (PFG-SE) NMR spectroscopy. More specifically, the self-diffusion coefficient of water in PNIPAm hydrogel is measured by means of PFG-SE NMR technique, through measurements of spin-echo attenuation of water proton signal intensity. The PFG-SE NMR technique enables us to measure directly the translational motion of water held in the polymer matrix. Two representative hydration levels were chosen for our measurements and they typically correspond to small (1.0 g/g) and large (7.4 g/g, equilibrium swollen) swelling ratios. The selfdiffusion coefficient in these hydrogels as well as neat water were measured in the temperature range !5—50°C.
D
i j i 1 # ln o6 #r + + l !+ d2 ln(li /l ) 2 ij i d io r 2 m n m
A B
j v e !+ a2 ln (lj /l )#r j a oj 2 » o n ]v* vN 2
GA B
*k 2"ln (/ /u )#(1!r /r )/ #r oN /2X 2 2 2 1 1 2 1 12 R¹
C
oN PM vN #r ! # 2 #(vN !1) ln(1!o6) 2 ¹M ¹M 2 2
(1)
where a is the number of acceptor groups of j type, j d is the number of donor groups of the i type, l is the i ij fraction of hydrogen bonds formed between i donors and j acceptors. l and l are the fractions of i donors io jo and j acceptors which do not form hydrogen bonds, r and r are the number of lattice sites occupied by 1 2 one molecule of polymer and solvent, respectively, e* and e* are the mer—mer interaction energies for 1 2 polymer and solvent molecules and e*#e*!2f (e*e*)0.5 2 12 1 2 . X "1 12 R¹
(2)
Here, the terms in the first, second, third and fourth line in eq. (1) account for entropy and enthalpy of mixing through physical interaction, equation of state properties of components, hydrogen bonding interactions and elasticity of the entangled network, respectively. Subscripts 1 and 2 correspond to the polymer and solvent, respectively. All the other symbols are explained in detail in our earlier paper(Lele et al., 1995). o6 and l are the reduced density and the numij ber of the hydrogen bonds which are evaluated using
G
L(*G) "o62#PM #¹M ln (1!oN ) Lo6
A C
THEORY
Recently, Lele et al. (1995) have proposed an extended lattice fluid hydrogen bond (LFHB) theory to model the swelling behaviour of PNIPAm gel. The model is obtained by adding the free energy of affinely deformed network to the free energy of mixing given by the LFHB model of Panayiotou and Sanchez (1991). The theory predicts that, at the transition temperature of PNIPAm gel, there is a sharp rearrangement of hydrogen bonds in the mixture. The theory has been successfully used to predict the behaviour of thermoreversible copolymer gels (Lele et al., 1997a, c) and also the reentrant swelling behaviour of PNIPAm gel in a mixture of ethanol and water. We use this theory to predict the total solvent mole fraction in the PNIPAm hydrogel. In this theory, the chemical potential of the solvent in the gel phase is given by
A BH
» 1@3 1 » o o ! » 2 »
#oN 1!
DBH
1 m n !+ + l ij r i j
A B CA B
#
v e ¹M v* » o
A BD
» 1@3 1 » o ! o » 2 »
(3)
and
A B
L(*G) vN l Go ij # ij "ln Ll R¹ l l ij io jo
A B CA B
#
v e »o ij » o
A BD
» 1@3 1 » o o ! » 2 »
(4)
where Go "Eo #P»o !¹So . ij ij ij ij
(5)
Now, by setting the difference between the chemical potential of the solvent in the gel and that of the pure solvent to zero, we get the value of / , which is the 2 volume fraction of the solvent at equilibrium at different temperatures. The total water content in the gel
CES 1962 BRR SAVITHA KESHAV Self-diffusion of water in thermoreversible gels
(per gram of gel) is then given by
A B
/ r M 1 2 . 2 w " (6) 505!- 1!/ r M 2 2 1 Further, the bound water fraction of total water in the gel is calculated by using r M w "/ oJ 1 2 . (7) "06/$ 2 r M 2 1 The measured diffusion coefficient is the population weighted average diffusion coefficient of water in its bound and free states and it is calculated by using the relation D w #D w "06/$ "06/$ . (8) D " &3%% &3%% !7 w 505!Here, D and D are the diffusivities of bound "06/$ &3%% and free water, respectively. We use the free volume theory of Vrentas and Duda (Vrentas and Duda, 1977a,b; Zielinski and Duda, 1992; Vrentas and Vrentas, 1991) to predict the selfdiffusion coefficient of the free water at different temperatures. According to the theory, the self-diffusion coefficient of a small molecule in a cross-linked polymer is given by
C
made negligible by careful shimming of the magnet. Echo attenuation due to ¹ effects are also minimised 2 in the present study since transverse relaxation times in the swollen gels are much longer than the duration (*#d) that we have employed. Thus, the attenuation of the spin echo in our PFG sequence occurs primarily under the influence of experimentally imposed gradient G . By a judicious choice of G , the gradient z z on and off times d and *, a progressive attenuation of the echo is achieved for an accurate estimation of D . The amplitude of the gradient is varied system4%-& atically from experiment to experiment and the attenuation of the spin echo is measured from the Fourier Transformed spectra as a function of the gradient strength. The relationship between the echo amplitude A, strength of the gradient pulse G, the time intervals and the self diffusion coefficient D is given by A"A exp (!c2G2Db) o
A B
d b"d2 *! . 3
EXPERIMENTAL
PFG-SE NMR technique The basic pulsed NMR scheme of PFG measurements of Diffusion coefficient of water is sketched in Fig. 1. The pulse scheme generates a spin echo at 2q when a n pulse is applied at time q after transverse magnetization has been created using a hard n/2 pulse at the begninning of the pulse scheme (Carr and Purcell, 1954; Hahn, 1950). In order to tag the diffusive motion of water, a linear magnetic field gradient (G ) is applied for a fixed duration d. Our choice of z the gradient direction, G is arbitrary since the z measurements are carried out in an isotropic medium. In the absence of G , the spin-echo amplitude is atz tenuated by diffusion dephasing in the residual static B gradients and by transverse relaxation (¹ ). The o 2 echo attenuation due to residual B static gradient is o
(10) (11)
Here, (*!d/3) is called the effective diffusion time, the time interval over which the diffusion is effectively
!(/ »K *#/ m*»K * ) 2 s 1 p D "D exp 4%-& o / (K /c@) (K !¹ #¹)#/ d@(K /c@) (K !¹ #¹) 2 11 21 g,s 1 12 22 g,p where, / and / are the volume fraction of polymer 1 2 and solvent, respectively. ¹ is the glass transition g temperature, »K * is the specific volume at zero degree Kelvin, d@ is the ratio of the specific volumes of the uncross-linked and cross-linked polymer, c@ is the overlap factor, m* is the ratio of critical molar volume of solvent jumping unit to polymer jumping unit and others are the free volume parameters of solvent and polymer which are explained in detail by Vrentas and Duda (1977a).
871
D
(9)
monitored, * is the time interval between two gradient pulses, D is the diffusion coefficient, c is the magnetogyric ratio, G is the applied field gradient strength (calibrated by measurement of D on neat water at 4%-& 25°C), d is the length of gradient pulse. D is estimated by fitting the experimentally measured signal intensities to eq. (10). All the NMR experiments were carried out on a Bruker MSL-300 FT-NMR spectrometer operating at a proton resonance frequency of 300.13 MHz. The spectrometer was equipped with a diffusion accessory. The configured system could achieve maximum gradient of 40 G/cm. The 90° pulse width was 30 ks. The duration d of G was 5 ms while its incremental value ; from experiment to experiment was 1.208 G/cm. Typically, 16—32 experiments were carried out at each temperature. Two transients were co-added with a recycle delay of 10—30 s and the FIDs were apodised using an exponential line broadening of 20—50 Hz before Fourier transformation and data processing in absolute intensity mode. The diffusion coefficients were calculated by fitting the peak intensity/area to eq. (10), using online Bruker utility programe SIMFIT. In our study, the D values spanned in the range 4%-& of 0.6]10~6 and 3.7]10~5 cm2/s and D values in 4%-& this range could be conveniently and accurately measured using PFG-SE sequence without resorting to stimulated echo technique. (Stegskal and Tanner, 1965; Peschier et al., 1993). The temperature variation was
CES 1962 BRR SAVITHA KESHAV S. S. Ray et al.
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Fig. 1. Pulse sequence used for self-diffusion coefficient measurements. The attenuation of spin echo was measured in a series of 16/32 experiments and the data was analysed using eqs (10) and (11).
done by using Bruker BVT-1000 temperature control unit. Temperature at the sample was directly measured using a copper—constanten thermocouple. Synthesis of poly(N-isopropyl acrylamide) hydrogel Poly(N-isopropyl acrylamide) hydrogel was prepared in our laboratory by free radical polymerisation of N-isopropyl acrylamide monomer with a small amount EGDMA as a cross-linking agent. The monomer was synthesised from acryloyl chloride and isopropyl amine and was purified by distillation followed by recrystallisation in heptane—acetone mixture. A total of 3.755 g of N-isopropyl acrylamide and 0.3755 g of ethylene glycol dimethacrylate (EGDMA) were dissolved in 25 ml of pure 1,4 dioxane. The entire solution was bubbled with nitrogen gas for several hours. The polymerisation was carried in a sealed tube at 70°C for 24 h using 2,2-Azobisisobutyronirile (AIBN) as an initiator. After the polymerisation, the gels were taken out of the tube and washed several days with distilled water to remove any unreacted reactants present. Finally, the cylindrical gel pieces were dried in vacuum oven at 40°C. The dried gel was found to have an LCST of 30—32°C and an equilibrium swelling ratio of 7.4 in water at 22°C. For the NMR measurements, PNIPAm gel with two hydration levels, 1.0 and 7.4 g of water per gram of dry gel, were taken. All the samples were prepared, sealed and stored for 3 days for homogenisation. RESULTS AND DISCUSSION
Self-diffusion coefficient of water in PNIPAm gels Figure 2 shows a plot of temperature dependent self-diffusion coefficient (D ) of water in neat 4%-& water(a), equilibrium swollen (b) and 1.0 g/g swollen (c) PNIPAm gels. D of neat water was independent4%-& ly measured to be 2.3]10~5 cm2/s at 25°C and this
value was found to be in good agreement with the literature value (Gillen et al., 1972). The PNIPAm gel at equilibrium takes 7.4 g of water per gram of dry polymer. Since the total bound water fraction is low (0.4—0.7 g water/g of polymer) (Dong and Hoffman, 1990), most of the water present in the gel exists in the free state. The PNIPAm gel, which belongs to the family of LCST polymers, undergoes a reversible discontinuous volume transition at 30—32°C. At and above this temperature, the swollen gel shrinks and expels about 80—90% of the absorbed water. We measured the D of water in the system both below and 4%-& above the LCST. As a function of temperature, D increases mono4%-& tonically from a value of 0.79]10~5 cm2/s (at 0°C) to 3.56]10~5 cm2/s (at 50°C) for equilibrium swollen sample [Fig. 1(b)]. It is important to note that we do not see any discontinuous change in the D of water 4%-& on passing through the LCST zone, whereas the gel undergoes a volume-phase transition at an LCST of 30—32°C. This can be explained as follows. In the hydrated polymer the diffusivity data can be analysed to a first approximation by using a two-site model of water, namely, the bound and free water (Woessner and Snowden, 1970). The diffusion coefficient of bound water (D ) is much smaller due to its strong b association with the polymer compared to the diffusion coefficient of free water (D ). Since there is a rapid f exchange between the bound and free water on the NMR time scale, it is rather difficult to distinguish between the bound and free water. The observed diffusion coefficient (D ) is therefore the population 0"4 weighted average which is given by D "P D #P D . 0"4 b b f f
(12)
Here, P and P refer to the population of water in its b f bound and free states, respectively. In the equilibrium
CES 1962 BRR SAVITHA KESHAV Self-diffusion of water in thermoreversible gels
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Fig. 2. Temperature dependence of water self-diffusion coefficients. Data points denote experimentally determined values and the solid lines depict the observed variation. (a) Neat water (]), (b) equilibrium swollen gel (h), (c) 1 g/g gel (L). For 1 g/g gel, two component behaviour appear at ¹'30°C. Filled circles in (c) indicates the fast diffusing component.
swollen gel, the fraction of free water is large (P AP &20 times) so that measurements at temperf b atures below LCST invariably lead to D values that 4%-& are nearly the same as observed for neat water at the same temperature. At and above LCST, where the gel collapse occurs, there is a large amount of water that is expelled from the polymer matrix. Further, since the resonance positions of water within and outside the gel are not distinguished in the observed spectrum, the signal is dominated by the intensity of the expelled water. The data analysis required a single component fitting to yield D values that tend towards D of 0"4 4%-& neat/free water. Consequently, the discontinuous change in D of water at LCST is not observed in the 4%-& equilibrium swollen PNIPAm gel. It is interesting to note that the measured value of D of water in the equilibrium swollen gel is not 4%-& quite the same as in neat water at any given temperature. For example, the value of D of 1.5]10~5 4%-& cm2/s differs from the value of 2.0]10~5 cm2/s, for neat water, at 14°C. The retardation of water mobility in the equilibrium swollen gel can be understood easily when one takes into account the water held within the polymer network. The decrease of D for 4%-& expelled water in the collapsed gel suggests some association between this water and the polymer at temperatures above LCST.
In order to reduce the dominance of expelled water to the signal intensity, we carried out D measure4%-& ments on a less hydrated (1 g/g) sample as a function of temperature. The results are summarised in Fig. 2(c). The D values decrease roughly by an order of 4%-& magnitude as compared to those for an equilibrium swollen gel. For example, the D of water in 1 g/g gel 0"4 at 23°C is 0.359]10~5 cm2/s as compared to the value of 2.0]10~5 cm2/s for equilibrium swollen gel at the same temperature. We observe that the decay of spin-echo intensity below LCST could be fitted to a single component behaviour. Although the fractions of bound and free water are comparable (P : P &0.6 : 0.4) in this system, the observation of f b a single-component behaviour implies a rapid exchange of water between the bound and free states. In this less hydrated sample, the influence of decreased diffusivity for bound water on the overall D measurement is clearly borne out at temper4%-& atures below LCST. There is a clear microscopic manifestation of an LCST phenomenon on the NMR self-diffusion measurement of PNIPAm gel swollen to 1.0 g/g. The transition temperature of &30°C measured from Fig. 2(c) is also in very good agreement with the swelling data reported earlier (Dong and Hoffman, 1990). Over the temperature range investigated, three different
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S. S. Ray et al.
Fig. 3. Decay of spin echo amplitude as a function of gradient strength in the PFG experiment of PNIPAm gel (1 g/g). at temperatures (a) below and (b) at and above LCST. The symbols denote experimental points and solid lines denote the single/bi component fitting of the data using eqs (10) and (11).
trends for diffusivity data can be seen. As expected, D increases with temperature below LCST (I). At 0"4 and above LCST D requires a bicomponent fit, 0"4 revealing the existence of two kinds of water having two entirely different diffusion coefficients (II), one of which depicts the LCST transition. The two components can be identified as the water interior to the polymer characterised by a self-diffusion coefficient of DI and a water exterior to the polymer with a self4%-& diffusion coefficient of DE . It may be additionally 4%-& noted that, these two kinds of water do not undergo rapid exchange on the NMR time scale. This is conceivable since the water molecules expelled from polymer matrix are incapable of exchanging with the population of water molecules within the polymer. The echo amplitude decay curves at six representative temperatures (three below and three above LCST) are shown in Fig 3. Single-component behaviour below LCST [Fig. 3(a)] and a bicomponent behaviour above LCST [Fig. 3(b)] are readily noticed. For the data above LCST, the major component (+70% of intensity) has a D value of the order of 10~6 cm2/s 0"4 and the minor one (30% of intensity) showed a value which is higher by an order of magnitude [Fig. 2(c), II]. This implies that in 1 g/g gel sample, about 0.7 g water is still associated with the polymer above LCST. This value is likely to correspond to the total bound water present in the collapsed gel, which includes loosely bound as well as strongly bound water. Strongly bound water in this polymer has been shown to be 0.4 g/g (Lele et al., 1997b). Above LCST, D for the expelled water [Fig. 2(c), 0"4 II] increases sharply with an increase in the temperature, as expected, and it approaches the diffusivity value of pure water. However, the water in the gel [Fig. 2(c), III] shows an initial decrease in diffusivity with an increase in temperature and eventually levels off. This can be rationalised as follows. By taking a recourse to eq. (12), the observed diffusivity (DI ) is 4%-&
seem to be population weighted average of water diffusivities in its bound and free states. In the collapsed state, the polymer is hydrated to a level of &0.7 g/g compared to 1.0 g/g below LCST. Hence, one can expect a decrease in D above LCST even 4%-& though there is an increase in temperature. Moreover, as the temperature increases above LCST it is likely that there is a gradual expulsion of water from the polymer matrix. This will lead to further decrease in hydration level and hence a decrease in the self-diffusion coefficient. Similar observations were made by Hoffman and Dong (1990) in a separate study by differential scanning calorimetry. It is also known that above LCST the polymer—polymer interaction predominates over the polymer—water interaction. Consequently, with an increase in temperature, there is a tendency for the polymer to associate strongly by hydrophobic interaction involving the pendent N-isopropyl groups. The water in the gel phase is likely to be associated with the amide functional group. These hydrophobic associations can be a barrier to the translational diffusion of water molecules resulting in decrease of self-diffusion coefficient of water. Therefore, the observed decrease in the D above LCST is most likely due to 4%-& the combination of both the low water content and the hydrophobic association. This is similar to the observation made by Walderhaug et al. (1995) for surfactant polymer systems. Comparison of experimental data with theoretical predictions Figure 4(a) shows the self-diffusion coefficient of water at different temperatures. The value increases with temperature as expected. The free volume parameters of water were estimated as suggested by Vrentas and Duda (1977a) by non-linear regression of the self-diffusion data of pure component. We used Marquart’s non-linear regression technique to estimate
CES 1962 BRR SAVITHA KESHAV Self-diffusion of water in thermoreversible gels
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Fig. 4. Comparison of the experimental and theoretical temperature dependence of the water self-diffusion coefficients. Symbols denote experimental values and solid lines represent model predictions. (a) neat water; (b) equilibrium swollen PNIPAm gel and (c) 1 g/g hydrated PNIPAm gel.
the parameters. It can be seen that the predictions compare well with the experimentally measured selfdiffusion data of neat water. Figure 4(b) shows the self-diffusion coefficient of water in equilibrium swollen poly(N-isopropyl acrylamide) gel. The parameters of the LFHB theory for PNIPAm were not available. Hence, the parameters of Polymethylmethacrylate (PMMA) were used as indicated by Lele et al. (1995). It is interesting to note that the self-diffusion coefficient of water below the LCST of the gel (i.e. below 30°C) increases with temperature although the swelling is decreasing continuously. At around 30°C, the self-diffusion coefficient of water present is sharply decreased. This is attributed to the discontinuous volume-phases transition observed in the PNIPAm gel—water system. As noted earlier the manifestation of LCST phenomenon on NMR self-diffusion data of equilibrium swollen PNIPAm gel was not forthcoming due to the presence of large population of free water. However, theoretical prediction considering only the water associated with the polymer thus shows the expected discontinuity for the self-diffusion coefficient values. Above LCST, the mobility of water is restricted due to the collapse of the polymer network, which in turn reduces the diffusion coefficient of water. While the NMR data for the water associated with the collapsed polymer shows a decrease in diffusion coefficient as a function of temperature after the LCST, the observed plateau in
the model arises due to the assumption of constant water fraction associating with the polymer. Figure 4(c) gives the self-diffusion coefficient of water in the 1.0 g/g PNIPAm gel. As expected, the diffusivity values are very low compared to the equilibrium swollen gel at the same temperature. This is because the water fraction associating with the polymer becomes less than the equilibrium swollen gel. The D value, however, increases with 4%-& temperature upto LCST and then decreases with temperature after LCST. After LCST, this curve merges with the curve for equilibrium swollen gel. This is because the equilibrium solvent content becomes less than 1 g/g of polymer. It can be also seen that the predictions agree reasonably well with our experimental data.
CONCLUSIONS
Pulsed field gradient spin echo (PFG-SE) NMR technique has been used to measure the self-diffusion coefficients (D ) of water in a thermoreversible hy4%-& drogel, Poly(N-isopropylacrylamide). The D meas4%-& ured as a function of temperature on the sample hydrated to equilibrium level (7.4 g/g) indicates the presence of most of the water in the free state and the D values approach towards the D of neat water. 4%-& 4%-& However, they are slightly lower than the values of neat water at any given temperature suggesting,
CES 1962 BRR SAVITHA KESHAV S. S. Ray et al.
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the association of water with the hydrogel. On the otherhand, a considerable decrease in D values 4%-& were observed for polymer hydrated to lesser extent (1.0 g/g) as compared to the equilibrium swollen sample. D was considered as the population 4%-& weighted average of diffusion coefficient of both free and bound water. Although, equilibrium swollen Poly(N-isopropylacrylamide) hydrogel undergoes a discontinuous volume-phase transition at its LCST of 30—32°C, there was no sharp change in D of 4%-& water at any temperature. However, at and above LCST, the less hydrated sample showed the existence of two kinds of water having diffusivities which differ by an order of magnitude. These experimental selfdiffusion coefficient values were explained using a theoretical model which is the combination of lattice fluid hydrogen bond theory and the free volume theory. NOTATION
P E ij Go ij k N N ij r R ¹ »o ij S ij » o »
pressure hydrogen bonding energy standard state free energy change of hydrogen bond formation between i—j pair Boltzmann constant number of molecules number of hydrogen bonds formed between i—j pair segment length gas constant absolute temperature standard state hydrogen-bonding volume change standard state entropy change of H-bonding volume of gel as synthesised volume
Greek letters e mean-field interaction energy per mer / close-packed volume fraction f binary interaction parameter k chemical potential o density l fraction of hydrogen bonds l number of elastically active chains e Subscripts 1 polymer 2 solvent Superscripts — reduced * close packed REFERENCES
Badiger, M. V., Kulkarni, M. G. and Mashelkar, R. A. (1992) Concentration of macromolecules from aqueous solutions: a new swellex process. Chem. Engng Sci. 47, 3—9. Badiger, M. V., Rajamohanan, P. R., Kulkarni, M. G., Ganapathy, S. and Mahselkar, R. A. (1991) Proton MASS-NMR: a new tool to study thermoreversible
transition in hydrogels. Macromolecules 24, 106—111. Blum, F. D. (1989) Self-diffusion of toluene in polystyrene solutions. Macromolecules 22, 3961—3968. Carr, H. Y. and Purcell, E. M. (1954) Effects of diffusion on free precession in nuclear magnetic resonance experiments. Phys. Rev. 94, 630—638. Cussler, E. L., Stokar, M. R. and Vaarberg, J. E. (1984) Gels as size selective extraction solvents. A.I.Ch.E. J. 30, 578—582. De Rossi, D., Kajiwara, K., Osada, Y. and Yamudin, A. (1991) Polymer gels. Fundamentals and Biomedical Applications. Plenum Press, New York. Dong, L. C. and Hoffman, A. S. (1990) Characterisation of water in thermally reversible hydrogels using differential scanning calorimetry. Proc. of Intr. Symp. Control. Rel. Bioact. Mater. 17, 116—118. Dong, L. C. and Hoffman, A. S. (1987) in Reversible Polymeric Gels and Related Systems, ed. P. S. Russo, ACS Symp. Ser. 350, ACS. Washington DC, p. 236. Dusek, K. (Ed) (1993) Responsive gels: volume transition I and II. Advances in Polymer Science, Vol 109, 110. Springer, Berlin. Ganapathy, S., Badiger, M. V., Rajamohanan, P. R. and Mashelkar, R. A. (1989) High resolution solid state proton MASS NMR of superabsorbing polymeric gels. Macromolecules 22, 2023—2025. Ganapathy, S., Ray, S. S., Rajamohanan, P. R. and Mashelkar, R. A. (1995) Hydration in polymer studied through magic angle spinning nuclear magnetic resonance and heteronuclear 13CM11HN overhauser enhancement spectroscopy: cross-relaxation and location of water in poly(acrylamide). J. Chem. Phys. 103, 6783—6794. Gillen, K. T., Douglass, D. C. and Hoch, M. J. R. (1972) Self diffusion in liquid water to !31°C. J. Chem. Phys. 57, 5117—5119. Graham, N. B. and McNeill, M. E. (1984) Hydrogels for controlled drug delivery. Biomaterials 5, 27—36. Hahn, E. L. (1950) Phys. Rev. 80, 580. Hausser, R., Maier, G. and Noack, F. (1966) Kernmagnetische messungen von Selbstdiffusion-koeffiziensten in wasser Und Benzol bis zum kritischen Punkt. Z. Naturforsch 21A, 1410—1415. Halle, B. and Wennerstrom, H. (1981) Interpretation of magnetic resonance data from water nuclei in heterogeneous systems. J. Chem. Phys. 75, 1928—1943. Kulkarni, M. G., Patil, S. S., Premnath, V. and Mashelkar, R. A. (1992) Diffusional transport modulation through reversible bilayer membranes. Proc. Royal. Soc. ¸ondon. 439, 379—384. Lee, H. B., Jhon, M. S. and Andrade, J. D. (1975) Nature of water in synthetic hydrogels 1: dialatometry, specific conductivity and differential scanning calorimetry of poly(hydroxy ethyl methacrylate). J. Colloid. Interface. Sci. 51(2), 225—231. Lele, A. K., Badiger, M. V., Hirve, M. M. and Mashelkar, R. A. (1995) Thermodynamics of hydrogen bonded polymeric gel—solvent mixtures. Chem. Engng Sci. 50, 3535—3545. Lele, A. K., Devotta, I. and Mashelkar, R. A. (1997a) Predictions of thermoreversible volume phase transition in copolymer gels by LFHB theory. J. Chem. Phys. 106, 4768—4772.
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Lele, A. K., Hirve, M. M., Badiger, M. V. and Mashelkar, R. A. (1997b) Predictions of bound water content in poly(N-isopropylacrylamide) gel. Macromolecules 30, 157—159. Lele, A. K., Karode, S. K., Badiger, M. V. and Mashelkar, R. A. (1997c) Predictions of re-entrant swelling behaviour of poly(N-isopropyl acrylamide) gel in a mixture of ethanol water using lattice fluid hydrogen bond theory. J. Chem. Phys. 107, 2142—2148. Osada, Y. and Ross Murphy, S. B. (1993) Intelligent gels. Sci. Am. 268(5), 42—47. Panayiotou, C. and Sanchez, I. C. (1991) Hydrogen bonding in fluids: an equation-of-state approach. J. Phys. Chem. 95, 10,090—10,097. Peschier, L. J. C., Bouwstra, J. A., de Blyser, J., Junginger, H. E. and Leyte, J. C. (1993) Water mobility and structure in poly(2-hydroxy ethyl methacrylate) hydrogel by means of pulsed field gradient NMR technique. Biomaterials. 14, 945—952. Pessen, H., Kumosinski, T. V. (1985) In Methods in Enzymology, eds C. H. W. Hirs and S. N. Timasheff, Vol. 117, p. 219. Academic, New York. Rajamohanan, P. R., Ganapathy, S., Ray, S. S., Badiger, M. V. and Mashelkar, R. A. (1995) Cross relaxation and exchange in poly(acrylamide) hydrogel studied through 1H MASS NMR and 2D nuclear overhauser enhancement spectroscopy. Macromolecules 28, 2533—2536. Ratner, B. D. and Hoffman, A. S. (1976) Synthetic hydrogels for Biomedical Applications, in ‘‘Hydrogels for Medical and Related Applications’’, ed J. D. Andrade, p. 1. ACS, Washington DC. Schild, H. G. (1992) Poly(N-isopropylacrylamide): experiment, theory and application. Prog. Polym. Sci. 17, 163—249.
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Spacek, P and Kubin, M. (1973) Poly(ethylene glycol methacrylate) as a material for hemodialysis. J. Biomed. Mater. Res. 7, 210—216. Stejskal, E. O. and Tanner, J. E. (1965) Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. J. Chem. Phys. 42, 288—292. Vrentas, J. S. and Duda, J. L. (1977a) Diffusion in polymer-solvent systems II: a predictive theory for the dependence of diffusion coefficients as temperature, concentration and molecular weight. J. Polym. Sci. Polym. Phys. Ed. 15, 417—439. Vrentas, J. S. and Duda, J. L. (1977b) Diffusion in polymer—solvent systems I, Reexamination of the free-volume theory. J. Polym. Sci. Polym. Phys. Ed. 15, 403—416. Vrentas, J. S. and Vrentas, C. M. (1991) Solvent diffusivities in cross-linked polymers. J. Appl. Polym. Sci. 42, 1931—1937. Walderhaug, H., Nystrom, B., Hansen, F. K. and Lindman, B. (1995) Interactions of ionic surfactants with a non-ionic Cellulose ether in solution and in gel state, studied by pulsed field gradient NMR. J. Phys. Chem. 99, 4672—4678. Woessner, D. E. and Snowden Jr., B. S. (1970) Pulsed NMR study of water in agar gels. J. Colloid Interface Sci. 34, 290—299. Yasunaga, H. and Ando, I. (1993) Effect of cross-linking on the molecular motion of water in polymer gel as studied by pulse 1H NMR and PGSE 1H NMR. Polymer Gels Network 1, 267—274. Zielinski, J. M. and Duda, J. L. (1992) Predicting polymer/solvent diffusion coefficients using freevolume theory. A.I.Ch.E. J. 38, 405—415.
Chemical Engineering Science, Vol. 53, No. 5, pp. 869—877, 1998 ( 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain S0009–2509(97)00335–7 0009—2509/98 $19.00#0.00
Self-diffusion of water in thermoreversible gels near volume transition: Model development and PFG NMR investigation* S. S. Ray,s P. R. Rajamohanan,s M. V. Badiger,s I. Devotta,s S. Ganapathy,s and R. A. Mashelkartu sNational Chemical Laboratory, Pune 411 008, India; tCouncil of Scientific and Industrial Research, Rafi Marg, New Delhi 110 001, India (Received 21 May 1997; accepted 29 August 1997) Abstract—Pulsed field gradient spin echo (PFG-SE) NMR technique has been used to measure the self-diffusion coefficient (D ) of water in a thermoreversible hydrogel, Poly(N-isopropylac4%-& rylamide). D , was measured as a function of temperature (!5—50°C) and hydration level. 4%-& A theoretical model to predict D was built by using a combination of lattice fluid hydrogen 4%-& bond theory and free volume theory. The fully swollen gel did not show any discontinuous change in D with temperature, Whereas, a partially swollen gel, showing the existence of two 4%-& kinds of water having diffusivities differing by order of magnitude, exhibits a discontinuous change in D . These results were explained within the theoretical framework developed by us. 4%-& The present work thus enables an elucidation of diffusion phenomenon at the volume transition point for the first time. ( 1998 Elsevier Science Ltd. All rights reserved. Keywords: Self-diffusion; Pulse Field Gradient NMR; thermoreversible gel; PNIPAm; LFHB theory; Free volume theory. INTRODUCTION
Hydrogels are becoming increasingly important biomaterials because of their excellent biocompatibility and stimuli responsive characteristics (Dusek, 1993). They have been used in contact lenses (Ratner and Hoffman, 1976), burn wound dressings (Spacek and Kubin, 1973), membranes (De Rossi et al., 1991), bioseparations (Cussler et al., 1984; Badiger et al., 1992), robotics (Osada and Ross Murphy, 1993), and as basic materials for controlled release dosage forms for drugs (Graham and McNeill, 1984). Our school has been involved in investigating diverse innovative applications and microstructure level investigations of such hydrogels (Ganapathy et al., 1989; Badiger et al., 1992; Rajamohanan et al., 1995; Kulkarni et al., 1992). The aspects of thermodynamics of volume transitions in such gels, especially with a view to gain an understanding of the attendant molecular level phenomena, has been one of our key endeavour (Lele et al., 1995). The present report relates to the study of self-diffusion of water in a gel at volume transition. Water plays an
*NCL Communication No: 6395. u Corresponding author. Fax: 91 11 3710618; e-mail: [email protected].
important role in determining the physico-chemical properties of the hydrogels. Water is also known to organise into different states, such as, bound, free and interfacial (Lee et al., 1975). The structure and dynamics of water have been studied by a number of techniques (Pessen and Kumosinski, 1985), nuclear magnetic resonance spectroscopy being one of the techniques. As a continuing effort to study the role, state, structure and dynamics of water in hydrogels, we have undertaken a study on the measurement of self-diffusion coefficient of water in a thermally reversible poly(N-isopropyl acrylamide) (PNIPAm) hydrogel. This hydrogel exhibits a lower critical solution temperature (LCST) phenomenon in the temperature range of 30—32°C, undergoing a sharp discontinuous volume transition at LCST. The swelling—deswelling characteristics of PNIPAm, encompassing the LCST zone, is also of great practical importance (Dong and Hoffman, 1987). PNIPAm has been extensively investigated in recent years for its structure and swelling properties (Schild, 1992). In an earlier study, we have established the correspondence between the macroscopic volume phase transition and microscopic dynamical events taking place at the molecular level using 1H MASS experiments (Badiger et al., 1991; Ganapathy et al., 1995). Dong and Hoffman (1990)
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CES 1962 BRR SAVITHA KESHAV S. S. Ray et al.
870
have reported on the state of water in PNIPAm hydrogel using differential scanning calorimetry. The bound and free water contents in the hydrogel was estimated as a function of temperature. Yasunaga and Ando (1993) have reported a study on the polymer crosslinking and its effect on the molecular motion of water in PNIPAm hydrogel by proton NMR spectroscopy. However, as yet, there are no reports on the self-diffusion coefficient of water just below and above LCST of this polymer hydrated to different extents. We fill this important gap in our paper. In order to predict the self-diffusion coefficients, we employ a two-state model in which the fraction of the bound and free water contents are estimated by using a statistical thermodynamic theory, which has recently been demonstrated to qualitatively predict the thermoreversible volume transition in PNIPAm gel—water system. (Lele et al., 1995). We then use the free volume theory of Vrentas and Duda (1977) to obtain an approximate expression for the self-diffusion coefficient. A qualitative verification of the predictions of our theory is provided by independent pulsed field gradient spin echo (PFG-SE) NMR spectroscopy. More specifically, the self-diffusion coefficient of water in PNIPAm hydrogel is measured by means of PFG-SE NMR technique, through measurements of spin-echo attenuation of water proton signal intensity. The PFG-SE NMR technique enables us to measure directly the translational motion of water held in the polymer matrix. Two representative hydration levels were chosen for our measurements and they typically correspond to small (1.0 g/g) and large (7.4 g/g, equilibrium swollen) swelling ratios. The selfdiffusion coefficient in these hydrogels as well as neat water were measured in the temperature range !5—50°C.
D
i j i 1 # ln o6 #r + + l !+ d2 ln(li /l ) 2 ij i d io r 2 m n m
A B
j v e !+ a2 ln (lj /l )#r j a oj 2 » o n ]v* vN 2
GA B
*k 2"ln (/ /u )#(1!r /r )/ #r oN /2X 2 2 2 1 1 2 1 12 R¹
C
oN PM vN #r ! # 2 #(vN !1) ln(1!o6) 2 ¹M ¹M 2 2
(1)
where a is the number of acceptor groups of j type, j d is the number of donor groups of the i type, l is the i ij fraction of hydrogen bonds formed between i donors and j acceptors. l and l are the fractions of i donors io jo and j acceptors which do not form hydrogen bonds, r and r are the number of lattice sites occupied by 1 2 one molecule of polymer and solvent, respectively, e* and e* are the mer—mer interaction energies for 1 2 polymer and solvent molecules and e*#e*!2f (e*e*)0.5 2 12 1 2 . X "1 12 R¹
(2)
Here, the terms in the first, second, third and fourth line in eq. (1) account for entropy and enthalpy of mixing through physical interaction, equation of state properties of components, hydrogen bonding interactions and elasticity of the entangled network, respectively. Subscripts 1 and 2 correspond to the polymer and solvent, respectively. All the other symbols are explained in detail in our earlier paper(Lele et al., 1995). o6 and l are the reduced density and the numij ber of the hydrogen bonds which are evaluated using
G
L(*G) "o62#PM #¹M ln (1!oN ) Lo6
A C
THEORY
Recently, Lele et al. (1995) have proposed an extended lattice fluid hydrogen bond (LFHB) theory to model the swelling behaviour of PNIPAm gel. The model is obtained by adding the free energy of affinely deformed network to the free energy of mixing given by the LFHB model of Panayiotou and Sanchez (1991). The theory predicts that, at the transition temperature of PNIPAm gel, there is a sharp rearrangement of hydrogen bonds in the mixture. The theory has been successfully used to predict the behaviour of thermoreversible copolymer gels (Lele et al., 1997a, c) and also the reentrant swelling behaviour of PNIPAm gel in a mixture of ethanol and water. We use this theory to predict the total solvent mole fraction in the PNIPAm hydrogel. In this theory, the chemical potential of the solvent in the gel phase is given by
A BH
» 1@3 1 » o o ! » 2 »
#oN 1!
DBH
1 m n !+ + l ij r i j
A B CA B
#
v e ¹M v* » o
A BD
» 1@3 1 » o ! o » 2 »
(3)
and
A B
L(*G) vN l Go ij # ij "ln Ll R¹ l l ij io jo
A B CA B
#
v e »o ij » o
A BD
» 1@3 1 » o o ! » 2 »
(4)
where Go "Eo #P»o !¹So . ij ij ij ij
(5)
Now, by setting the difference between the chemical potential of the solvent in the gel and that of the pure solvent to zero, we get the value of / , which is the 2 volume fraction of the solvent at equilibrium at different temperatures. The total water content in the gel
CES 1962 BRR SAVITHA KESHAV Self-diffusion of water in thermoreversible gels
(per gram of gel) is then given by
A B
/ r M 1 2 . 2 w " (6) 505!- 1!/ r M 2 2 1 Further, the bound water fraction of total water in the gel is calculated by using r M w "/ oJ 1 2 . (7) "06/$ 2 r M 2 1 The measured diffusion coefficient is the population weighted average diffusion coefficient of water in its bound and free states and it is calculated by using the relation D w #D w "06/$ "06/$ . (8) D " &3%% &3%% !7 w 505!Here, D and D are the diffusivities of bound "06/$ &3%% and free water, respectively. We use the free volume theory of Vrentas and Duda (Vrentas and Duda, 1977a,b; Zielinski and Duda, 1992; Vrentas and Vrentas, 1991) to predict the selfdiffusion coefficient of the free water at different temperatures. According to the theory, the self-diffusion coefficient of a small molecule in a cross-linked polymer is given by
C
made negligible by careful shimming of the magnet. Echo attenuation due to ¹ effects are also minimised 2 in the present study since transverse relaxation times in the swollen gels are much longer than the duration (*#d) that we have employed. Thus, the attenuation of the spin echo in our PFG sequence occurs primarily under the influence of experimentally imposed gradient G . By a judicious choice of G , the gradient z z on and off times d and *, a progressive attenuation of the echo is achieved for an accurate estimation of D . The amplitude of the gradient is varied system4%-& atically from experiment to experiment and the attenuation of the spin echo is measured from the Fourier Transformed spectra as a function of the gradient strength. The relationship between the echo amplitude A, strength of the gradient pulse G, the time intervals and the self diffusion coefficient D is given by A"A exp (!c2G2Db) o
A B
d b"d2 *! . 3
EXPERIMENTAL
PFG-SE NMR technique The basic pulsed NMR scheme of PFG measurements of Diffusion coefficient of water is sketched in Fig. 1. The pulse scheme generates a spin echo at 2q when a n pulse is applied at time q after transverse magnetization has been created using a hard n/2 pulse at the begninning of the pulse scheme (Carr and Purcell, 1954; Hahn, 1950). In order to tag the diffusive motion of water, a linear magnetic field gradient (G ) is applied for a fixed duration d. Our choice of z the gradient direction, G is arbitrary since the z measurements are carried out in an isotropic medium. In the absence of G , the spin-echo amplitude is atz tenuated by diffusion dephasing in the residual static B gradients and by transverse relaxation (¹ ). The o 2 echo attenuation due to residual B static gradient is o
(10) (11)
Here, (*!d/3) is called the effective diffusion time, the time interval over which the diffusion is effectively
!(/ »K *#/ m*»K * ) 2 s 1 p D "D exp 4%-& o / (K /c@) (K !¹ #¹)#/ d@(K /c@) (K !¹ #¹) 2 11 21 g,s 1 12 22 g,p where, / and / are the volume fraction of polymer 1 2 and solvent, respectively. ¹ is the glass transition g temperature, »K * is the specific volume at zero degree Kelvin, d@ is the ratio of the specific volumes of the uncross-linked and cross-linked polymer, c@ is the overlap factor, m* is the ratio of critical molar volume of solvent jumping unit to polymer jumping unit and others are the free volume parameters of solvent and polymer which are explained in detail by Vrentas and Duda (1977a).
871
D
(9)
monitored, * is the time interval between two gradient pulses, D is the diffusion coefficient, c is the magnetogyric ratio, G is the applied field gradient strength (calibrated by measurement of D on neat water at 4%-& 25°C), d is the length of gradient pulse. D is estimated by fitting the experimentally measured signal intensities to eq. (10). All the NMR experiments were carried out on a Bruker MSL-300 FT-NMR spectrometer operating at a proton resonance frequency of 300.13 MHz. The spectrometer was equipped with a diffusion accessory. The configured system could achieve maximum gradient of 40 G/cm. The 90° pulse width was 30 ks. The duration d of G was 5 ms while its incremental value ; from experiment to experiment was 1.208 G/cm. Typically, 16—32 experiments were carried out at each temperature. Two transients were co-added with a recycle delay of 10—30 s and the FIDs were apodised using an exponential line broadening of 20—50 Hz before Fourier transformation and data processing in absolute intensity mode. The diffusion coefficients were calculated by fitting the peak intensity/area to eq. (10), using online Bruker utility programe SIMFIT. In our study, the D values spanned in the range 4%-& of 0.6]10~6 and 3.7]10~5 cm2/s and D values in 4%-& this range could be conveniently and accurately measured using PFG-SE sequence without resorting to stimulated echo technique. (Stegskal and Tanner, 1965; Peschier et al., 1993). The temperature variation was
CES 1962 BRR SAVITHA KESHAV S. S. Ray et al.
872
Fig. 1. Pulse sequence used for self-diffusion coefficient measurements. The attenuation of spin echo was measured in a series of 16/32 experiments and the data was analysed using eqs (10) and (11).
done by using Bruker BVT-1000 temperature control unit. Temperature at the sample was directly measured using a copper—constanten thermocouple. Synthesis of poly(N-isopropyl acrylamide) hydrogel Poly(N-isopropyl acrylamide) hydrogel was prepared in our laboratory by free radical polymerisation of N-isopropyl acrylamide monomer with a small amount EGDMA as a cross-linking agent. The monomer was synthesised from acryloyl chloride and isopropyl amine and was purified by distillation followed by recrystallisation in heptane—acetone mixture. A total of 3.755 g of N-isopropyl acrylamide and 0.3755 g of ethylene glycol dimethacrylate (EGDMA) were dissolved in 25 ml of pure 1,4 dioxane. The entire solution was bubbled with nitrogen gas for several hours. The polymerisation was carried in a sealed tube at 70°C for 24 h using 2,2-Azobisisobutyronirile (AIBN) as an initiator. After the polymerisation, the gels were taken out of the tube and washed several days with distilled water to remove any unreacted reactants present. Finally, the cylindrical gel pieces were dried in vacuum oven at 40°C. The dried gel was found to have an LCST of 30—32°C and an equilibrium swelling ratio of 7.4 in water at 22°C. For the NMR measurements, PNIPAm gel with two hydration levels, 1.0 and 7.4 g of water per gram of dry gel, were taken. All the samples were prepared, sealed and stored for 3 days for homogenisation. RESULTS AND DISCUSSION
Self-diffusion coefficient of water in PNIPAm gels Figure 2 shows a plot of temperature dependent self-diffusion coefficient (D ) of water in neat 4%-& water(a), equilibrium swollen (b) and 1.0 g/g swollen (c) PNIPAm gels. D of neat water was independent4%-& ly measured to be 2.3]10~5 cm2/s at 25°C and this
value was found to be in good agreement with the literature value (Gillen et al., 1972). The PNIPAm gel at equilibrium takes 7.4 g of water per gram of dry polymer. Since the total bound water fraction is low (0.4—0.7 g water/g of polymer) (Dong and Hoffman, 1990), most of the water present in the gel exists in the free state. The PNIPAm gel, which belongs to the family of LCST polymers, undergoes a reversible discontinuous volume transition at 30—32°C. At and above this temperature, the swollen gel shrinks and expels about 80—90% of the absorbed water. We measured the D of water in the system both below and 4%-& above the LCST. As a function of temperature, D increases mono4%-& tonically from a value of 0.79]10~5 cm2/s (at 0°C) to 3.56]10~5 cm2/s (at 50°C) for equilibrium swollen sample [Fig. 1(b)]. It is important to note that we do not see any discontinuous change in the D of water 4%-& on passing through the LCST zone, whereas the gel undergoes a volume-phase transition at an LCST of 30—32°C. This can be explained as follows. In the hydrated polymer the diffusivity data can be analysed to a first approximation by using a two-site model of water, namely, the bound and free water (Woessner and Snowden, 1970). The diffusion coefficient of bound water (D ) is much smaller due to its strong b association with the polymer compared to the diffusion coefficient of free water (D ). Since there is a rapid f exchange between the bound and free water on the NMR time scale, it is rather difficult to distinguish between the bound and free water. The observed diffusion coefficient (D ) is therefore the population 0"4 weighted average which is given by D "P D #P D . 0"4 b b f f
(12)
Here, P and P refer to the population of water in its b f bound and free states, respectively. In the equilibrium
CES 1962 BRR SAVITHA KESHAV Self-diffusion of water in thermoreversible gels
873
Fig. 2. Temperature dependence of water self-diffusion coefficients. Data points denote experimentally determined values and the solid lines depict the observed variation. (a) Neat water (]), (b) equilibrium swollen gel (h), (c) 1 g/g gel (L). For 1 g/g gel, two component behaviour appear at ¹'30°C. Filled circles in (c) indicates the fast diffusing component.
swollen gel, the fraction of free water is large (P AP &20 times) so that measurements at temperf b atures below LCST invariably lead to D values that 4%-& are nearly the same as observed for neat water at the same temperature. At and above LCST, where the gel collapse occurs, there is a large amount of water that is expelled from the polymer matrix. Further, since the resonance positions of water within and outside the gel are not distinguished in the observed spectrum, the signal is dominated by the intensity of the expelled water. The data analysis required a single component fitting to yield D values that tend towards D of 0"4 4%-& neat/free water. Consequently, the discontinuous change in D of water at LCST is not observed in the 4%-& equilibrium swollen PNIPAm gel. It is interesting to note that the measured value of D of water in the equilibrium swollen gel is not 4%-& quite the same as in neat water at any given temperature. For example, the value of D of 1.5]10~5 4%-& cm2/s differs from the value of 2.0]10~5 cm2/s, for neat water, at 14°C. The retardation of water mobility in the equilibrium swollen gel can be understood easily when one takes into account the water held within the polymer network. The decrease of D for 4%-& expelled water in the collapsed gel suggests some association between this water and the polymer at temperatures above LCST.
In order to reduce the dominance of expelled water to the signal intensity, we carried out D measure4%-& ments on a less hydrated (1 g/g) sample as a function of temperature. The results are summarised in Fig. 2(c). The D values decrease roughly by an order of 4%-& magnitude as compared to those for an equilibrium swollen gel. For example, the D of water in 1 g/g gel 0"4 at 23°C is 0.359]10~5 cm2/s as compared to the value of 2.0]10~5 cm2/s for equilibrium swollen gel at the same temperature. We observe that the decay of spin-echo intensity below LCST could be fitted to a single component behaviour. Although the fractions of bound and free water are comparable (P : P &0.6 : 0.4) in this system, the observation of f b a single-component behaviour implies a rapid exchange of water between the bound and free states. In this less hydrated sample, the influence of decreased diffusivity for bound water on the overall D measurement is clearly borne out at temper4%-& atures below LCST. There is a clear microscopic manifestation of an LCST phenomenon on the NMR self-diffusion measurement of PNIPAm gel swollen to 1.0 g/g. The transition temperature of &30°C measured from Fig. 2(c) is also in very good agreement with the swelling data reported earlier (Dong and Hoffman, 1990). Over the temperature range investigated, three different
CES 1962 BRR SAVITHA KESHAV 874
S. S. Ray et al.
Fig. 3. Decay of spin echo amplitude as a function of gradient strength in the PFG experiment of PNIPAm gel (1 g/g). at temperatures (a) below and (b) at and above LCST. The symbols denote experimental points and solid lines denote the single/bi component fitting of the data using eqs (10) and (11).
trends for diffusivity data can be seen. As expected, D increases with temperature below LCST (I). At 0"4 and above LCST D requires a bicomponent fit, 0"4 revealing the existence of two kinds of water having two entirely different diffusion coefficients (II), one of which depicts the LCST transition. The two components can be identified as the water interior to the polymer characterised by a self-diffusion coefficient of DI and a water exterior to the polymer with a self4%-& diffusion coefficient of DE . It may be additionally 4%-& noted that, these two kinds of water do not undergo rapid exchange on the NMR time scale. This is conceivable since the water molecules expelled from polymer matrix are incapable of exchanging with the population of water molecules within the polymer. The echo amplitude decay curves at six representative temperatures (three below and three above LCST) are shown in Fig 3. Single-component behaviour below LCST [Fig. 3(a)] and a bicomponent behaviour above LCST [Fig. 3(b)] are readily noticed. For the data above LCST, the major component (+70% of intensity) has a D value of the order of 10~6 cm2/s 0"4 and the minor one (30% of intensity) showed a value which is higher by an order of magnitude [Fig. 2(c), II]. This implies that in 1 g/g gel sample, about 0.7 g water is still associated with the polymer above LCST. This value is likely to correspond to the total bound water present in the collapsed gel, which includes loosely bound as well as strongly bound water. Strongly bound water in this polymer has been shown to be 0.4 g/g (Lele et al., 1997b). Above LCST, D for the expelled water [Fig. 2(c), 0"4 II] increases sharply with an increase in the temperature, as expected, and it approaches the diffusivity value of pure water. However, the water in the gel [Fig. 2(c), III] shows an initial decrease in diffusivity with an increase in temperature and eventually levels off. This can be rationalised as follows. By taking a recourse to eq. (12), the observed diffusivity (DI ) is 4%-&
seem to be population weighted average of water diffusivities in its bound and free states. In the collapsed state, the polymer is hydrated to a level of &0.7 g/g compared to 1.0 g/g below LCST. Hence, one can expect a decrease in D above LCST even 4%-& though there is an increase in temperature. Moreover, as the temperature increases above LCST it is likely that there is a gradual expulsion of water from the polymer matrix. This will lead to further decrease in hydration level and hence a decrease in the self-diffusion coefficient. Similar observations were made by Hoffman and Dong (1990) in a separate study by differential scanning calorimetry. It is also known that above LCST the polymer—polymer interaction predominates over the polymer—water interaction. Consequently, with an increase in temperature, there is a tendency for the polymer to associate strongly by hydrophobic interaction involving the pendent N-isopropyl groups. The water in the gel phase is likely to be associated with the amide functional group. These hydrophobic associations can be a barrier to the translational diffusion of water molecules resulting in decrease of self-diffusion coefficient of water. Therefore, the observed decrease in the D above LCST is most likely due to 4%-& the combination of both the low water content and the hydrophobic association. This is similar to the observation made by Walderhaug et al. (1995) for surfactant polymer systems. Comparison of experimental data with theoretical predictions Figure 4(a) shows the self-diffusion coefficient of water at different temperatures. The value increases with temperature as expected. The free volume parameters of water were estimated as suggested by Vrentas and Duda (1977a) by non-linear regression of the self-diffusion data of pure component. We used Marquart’s non-linear regression technique to estimate
CES 1962 BRR SAVITHA KESHAV Self-diffusion of water in thermoreversible gels
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Fig. 4. Comparison of the experimental and theoretical temperature dependence of the water self-diffusion coefficients. Symbols denote experimental values and solid lines represent model predictions. (a) neat water; (b) equilibrium swollen PNIPAm gel and (c) 1 g/g hydrated PNIPAm gel.
the parameters. It can be seen that the predictions compare well with the experimentally measured selfdiffusion data of neat water. Figure 4(b) shows the self-diffusion coefficient of water in equilibrium swollen poly(N-isopropyl acrylamide) gel. The parameters of the LFHB theory for PNIPAm were not available. Hence, the parameters of Polymethylmethacrylate (PMMA) were used as indicated by Lele et al. (1995). It is interesting to note that the self-diffusion coefficient of water below the LCST of the gel (i.e. below 30°C) increases with temperature although the swelling is decreasing continuously. At around 30°C, the self-diffusion coefficient of water present is sharply decreased. This is attributed to the discontinuous volume-phases transition observed in the PNIPAm gel—water system. As noted earlier the manifestation of LCST phenomenon on NMR self-diffusion data of equilibrium swollen PNIPAm gel was not forthcoming due to the presence of large population of free water. However, theoretical prediction considering only the water associated with the polymer thus shows the expected discontinuity for the self-diffusion coefficient values. Above LCST, the mobility of water is restricted due to the collapse of the polymer network, which in turn reduces the diffusion coefficient of water. While the NMR data for the water associated with the collapsed polymer shows a decrease in diffusion coefficient as a function of temperature after the LCST, the observed plateau in
the model arises due to the assumption of constant water fraction associating with the polymer. Figure 4(c) gives the self-diffusion coefficient of water in the 1.0 g/g PNIPAm gel. As expected, the diffusivity values are very low compared to the equilibrium swollen gel at the same temperature. This is because the water fraction associating with the polymer becomes less than the equilibrium swollen gel. The D value, however, increases with 4%-& temperature upto LCST and then decreases with temperature after LCST. After LCST, this curve merges with the curve for equilibrium swollen gel. This is because the equilibrium solvent content becomes less than 1 g/g of polymer. It can be also seen that the predictions agree reasonably well with our experimental data.
CONCLUSIONS
Pulsed field gradient spin echo (PFG-SE) NMR technique has been used to measure the self-diffusion coefficients (D ) of water in a thermoreversible hy4%-& drogel, Poly(N-isopropylacrylamide). The D meas4%-& ured as a function of temperature on the sample hydrated to equilibrium level (7.4 g/g) indicates the presence of most of the water in the free state and the D values approach towards the D of neat water. 4%-& 4%-& However, they are slightly lower than the values of neat water at any given temperature suggesting,
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the association of water with the hydrogel. On the otherhand, a considerable decrease in D values 4%-& were observed for polymer hydrated to lesser extent (1.0 g/g) as compared to the equilibrium swollen sample. D was considered as the population 4%-& weighted average of diffusion coefficient of both free and bound water. Although, equilibrium swollen Poly(N-isopropylacrylamide) hydrogel undergoes a discontinuous volume-phase transition at its LCST of 30—32°C, there was no sharp change in D of 4%-& water at any temperature. However, at and above LCST, the less hydrated sample showed the existence of two kinds of water having diffusivities which differ by an order of magnitude. These experimental selfdiffusion coefficient values were explained using a theoretical model which is the combination of lattice fluid hydrogen bond theory and the free volume theory. NOTATION
P E ij Go ij k N N ij r R ¹ »o ij S ij » o »
pressure hydrogen bonding energy standard state free energy change of hydrogen bond formation between i—j pair Boltzmann constant number of molecules number of hydrogen bonds formed between i—j pair segment length gas constant absolute temperature standard state hydrogen-bonding volume change standard state entropy change of H-bonding volume of gel as synthesised volume
Greek letters e mean-field interaction energy per mer / close-packed volume fraction f binary interaction parameter k chemical potential o density l fraction of hydrogen bonds l number of elastically active chains e Subscripts 1 polymer 2 solvent Superscripts — reduced * close packed REFERENCES
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