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Langmuir 1999, 15, 4266-4269
Effect of Donnan Osmotic Pressure on the Volume Phase Transition of N-Isopropylacrylamide Gels† Shigeo Sasaki,* Hideya Kawasaki, and Hiroshi Maeda Department of Chemistry, Faculty of Science, Kyushu University 33, Hakozaki, Higashi-ku, Fukuoka 812, Japan Received August 25, 1998. In Final Form: February 17, 1999 The theory for describing the effect of Donnan osmotic pressure on the volume phase transition of NIPA gel is developed. The theory can well explain the experimental result that a continuous volume change behavior of charged NIPA gel in a salt-free solution turns to a discontinuous one in 0.1 M salt solution.
1. Introduction N-Isopropylacrylamide (NIPA) gel is well-known to exhibit1 a volume phase transition, discontinuous volume change with temperature. Before the volume phase transition of NIPA gel was found, it was believed that nonionic polymer gels did not exhibit a transition-like volume change, since the modified Flory-Huggins theory2 had demonstrated that unrealistically high cross-link density in the polymer network is required for the volume phase transition to occur. The first observation of the volume phase transition of gel has been reported3 for the volume change of the copolymer gel of acrylamide and acrylate with change in the acetone content of the wateracetone mixture. The volume phase transition has been considered to be induced by introducing the Donnan osmotic pressure into the gel from the fact that the transition volume of copolymer gel of NIPA and acrylate (NIPA-AA) at the neutral pH increases with increase in an amount of the acrylate.4 However, recently it has been found that the ionic copolymer gels of NIPA-MAPTAC (methacrylamide propyl trimethylammonium chloride)5 and NIPA-SS (styrene sodium sulfonate) shows no volume phase transition.6 This seems inconsistent with the volume phase transition behavior mentioned above. For dissolving this discrepancy, a careful examination of the pH effect on the volume phase transition behavior of NIPA-AA has been carried out.7 We have found that the volume phase transition disappears at pH above 7.5 and appears at pH below 6.3. We conclude that the volume phase transition of NIPA gel disappears when the swelling Donnan osmotic pressure is introduced into the system. The continuous volume change of NIPA-AA or NIPA-SS in the salt-free solution has been found to turn to a discontinuous one in 0.1 or 0.3 M NaCl solution.6 This is considered to be due to the decrease in the Donnan osmotic pressure of counterion in the high salt solution. The transitional volume shrinkage of N-isopropylacrylamide (NIPA) gel in rising temperature is also observed † Presented at Polyelectrolytes ’98, Inuyama, Japan, May 31June 3, 1998.
(1) Hirokawa, Y.; Tanaka, T. J. Chem. Phys. 1984, 81, 6379. (2) Dusˇek, K.; Patterson, D. J. Polym. Sci. A-2 1968, 6, 1209. (3) Tanaka, T. Polymer 1979, 20, 1404. (4) Hirotsu, S.; Hirokawa, Y.; Tanaka, T. J. Chem. Phys. 1987, 87, 1392. (5) Beltran, S.; Hooper, H. H.; Blanch, H. W.; Prausnitz, J. M. J. Chem. Phys. 1990, 92, 2061. (6) Kawasaki, H.; Sasaki, S.; Maeda, H. J. Phys. Chem. 1997, 101, 1B, 4184. (7) Kawasaki, H.; Sasaki, S.; Maeda, H. J. Phys. Chem. 1997, 101, 1B, 5089.
in adding salt8,9 or saccharide10 to the solution outside the gel. The chemical potential of water molecules is a monotonically decreasing function with increase in temperature and/or concentrations of the additives. It should be noted here that the addition of salt to the nonionized NIPA gel results in reducing the chemical potential of water molecule in the gel. This is different from the salt effect on the ionized NIPA gel that the Donnan osmotic pressure in the gel decreases with the salt concentration. We have revealed11 that the chemical potential of water molecule in solutions at the transition is essentially constant in the volume change behavior with temperatures and/or concentrations of additives. It has been also found that the volume change behavior is well described by the difference in the reduced chemical potential (the ratio of the chemical potential to the Boltzmann temperature) from that at the transition.11 It is plausible that water molecules bound to the chain are unbounded and move into the solution with a decrease in the chemical potential of water molecule in the solution. On the basis of these facts we have proposed12 the theory that the coupling effect of the cooperative dehydration of the chain (unbinding of water molecules from the chain) and the entropy force of chains, both of which shrink the gel, induces the volume phase transition. The theory has predicted that introduction of such a small amount of ionized group as 0.002 mol fraction into the NIPA gel makes the volume change continuous.13 The theoretical prediction has been found to be consistent with the volume phase transition behavior 6 of NIPA-AA at high pH in the salt-free solution. The theory should be also consistent with the experimental result that the continuous volume change of ionized NIPA gel in the salt-free solution turns to the discontinuous one in 0.1 or 0.3 M NaCl solution.6 This report describes the developed theory for describing the salt effect on the volume change behavior of the ionized gel. 2. Theory The volume change behavior and the volume phase transition are well described by the chemical potential of water molecules, µW0, in the solution.11,12 The water molecule bound to the chain tends to move into the solution (8) Suzuki, A. Adv. Polym. Sci. 1993, 110, 199. (9) Park; T. G.; Hoffman, A. S. Macromolecules 1993, 26, 50454. (10) Kawasaki, H.; Sasaki, S.; Maeda, H.; Mihara, S.; Tokita, M.; Komai, T. J. Phys. Chem. 1996, 100, 16282. (11) Sasaki, S.; Kawasaki, H.; Maeda, H. Macromolecules 1997, 30, 1847. (12) Sasaki, S.; Maeda, H. Phys. Rev. E 1996, 54, 2761. (13) Sasaki, S.; Maeda, H. J. Chem. Phys. 1997, 107, 1028.
10.1021/la981100+ CCC: $18.00 © 1999 American Chemical Society Published on Web 04/02/1999
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Langmuir, Vol. 15, No. 12, 1999 4267
with decrease in µW0, and the degree of binding of water molecule decreases. The volume decreases with decrease in the degree of binding of water molecules. The volume changes discretely with µW0, if the degree of binding changes discretely with µW0. On assuming the volume change mechanism mentioned above, the theory12 has been developed for explaining the volume phase transition. Details of the theory are described elsewhere.2,13 Here we focus on developing the theory which takes the effect of salt into account. The chain segment takes the hydrating state (h-state) and dehydrating state (d-state). The volume excluded by the h-state segments is much larger than the volume excluded by the d-state segments. The large excluded volume enlarges an end-to-end distance of one chain between the cross-link points R. An alternation of the segment from the d-state to the h-state should be accompanied with the binding of water molecules to the segment. The equilibrium can be obtained as a minimum condition of free energy of the system, which is described in terms of the chemical potentials of water molecules and R. The free energy per one chain of the system is composed of the free energy due to the chain conformation (Gconf), mixing of the hydrated and dehydrated segments on the chain (Gm), the water molecules (GW), and the Donnan osmotic pressure (Gion)
G ) Gconf + Gm + GW + Gion
(1)
Gconf Vhhnh2 + 2Vhdnhnd + Vddnd2 R2 ) + 3 T R n b2
(2)
0
πD ) 2CS{x1 + X2 - 1}T; X)
Rh ) nh/n0
for the gel in the salt solution. Here the ideal Donnan osmotic pressure is assumed. T denotes the Boltzmann temperature. In eq 2, Vhh, Vhd, Vdd, b, n0, nh, and nd are volumes mutually excluded by the h- and h-state segments, the h- and d-state segments, and the d- and d-state segments, unit segment length, number of segments in one chain, and numbers of segments in the h- and the d-states, respectively. In eq 3, h, d, nhh, nhd, ndd, and ζ are intrinsic energies of the h-state segment and the d-state segment, interaction energies between the hand h-state segments, the h- and d-state segments, and the d- and d-state segments which are neighboring along the chain, and cooperativity parameter of the binding. In eq 4, NWt, Nchain, and kh, respectively, are total number of water molecules in the whole system, number of chains in the gel, and number of water molecules bound to the segment in altering from the d-state to the h-state. In eqs 6 and 6′, ne and CS, respectively, are number of charges on the chain and the salt concentration. The minimization conditions of the free energy at equilibrium
)
2hdn - hhn - ddn 2T
(
) )
)
- nhkh µW0
∫∞R πD dR′3 3
3
for the gel in the salt-free solution or
Π(R,CS)
πD R ) 3R2 2 T n0b
(9)
2n0
+ R3 khµW0 qh ξ + 2Rd - 1 )+ ln ln (10) ξ + 2Rh - 1 T qd
(4)
(5)
where
πD ) Tne/R3
R3
R
+2
{-RhVhh + (Rh - Rd)Vhd + RdVdd}
and
Gion ) -
ne
4
and
d + ddn T
Nchain
(8)
πD ) T
h + hhn qh ) exp T
GW )
∂G/∂nd ) 0
n02
(
NWt
(7)
respectively, give
ξ2 ) 1 + 4RhRd(ζ2 - 1)
qd ) exp
∂G/∂R ) 0
-3(Rh2Vhh + 2RhRdVhd + Rd2Vdd)
Rd ) nd/n0
( (
(6′)
2CSR3
and
ξ + 2Rh - 1 ξ + 2Rd - 1 Gm ) nh ln + nd ln + T ξ+1 ξ+1 nh ln qh + nd ln qd (3)
ζ ) exp
ne
(6)
In eq 9, Π(R,CS) ) 1 in the case of salt-free solution, and Π(R,CS) ) (4πne/(κR)22(bλ/R)((1 + X2)1/2 - 1)/X2, κ ) (8πbλCS)1/2, and bλ ) e02/DT in the case of salt solution. Figure 1 schematically demonstrates the Rd-(µW0/T) relation given by eq 10. The curves 1 and 2 in Figure 1 show the Rd-(µW0/T) relation described by eq 10 without the first term in the left-hand side and values of the first term against µW0. Curve 3, which is a sum of the curves 1 and 2, shows the Rd-(µW0/T) relation given by eq 10. The first term can make a Rd-(µW0/T) curve sigmoid, as shown by curve 3. The sigmoid curve indicates the transitionlike binding with change in µW0. The monotonically increasing Rd with decrease in µW0 changes discretely as shown by an upward arrow and the monotonically decreasing Rd with increase in µW0 changes discretely as
4268 Langmuir, Vol. 15, No. 12, 1999
Figure 1. Schematic Rd-µW0/T relation given by eq 10. The curves 1 and 2 show the Rd-µW0/T relation described by eq 10 without the first term in the left-hand side and values of the first term against µW0/T. The curve 3, a sum of the curves 1 and 2 is the Rd-µW0/T relation given by eq 10. The 1R and 3R curves are the R-µW0/T relations corresponding to the curves 1 and 2, respectively. Arrows denote the transitions.
shown by a downward arrow. The µW0 at the former transition, µW01, is always less than that at the latter, µW02. Corresponding to the discrete change in Rd, the volume phase transition occurs as shown by the curve 3R in Figure 1, since no phase separation can be realized in the gel at equilibrium because of the high stress in the phase boundary. The difference between µW01 and µW02 decreases with decrease in the R decrement rate against Rd, since the small rate reduces the magnitude of the first term in eq 10. The phase transition disappears when µW01 ) µW02. The relation between R and Rd is given by eq 9. The decrement rate of the R against Rd increases with a decrease in the ratio of Vdd to both of Vhd and Vhh. When Vdd ) Vhd ) Vhh, the Rd-(µW0/T) relation depicted by curve 1 in Figure 1 and the R-(µW0/T) relation depicted by the curve 1R in Figure 1 are realized. Very small Vdd compared with Vhd and Vhh induces the volume phase transition with change in the (µW0/T). The osmotic pressure term in the right-hand side of eq 9 plays a role to decrease the decrement rate of the R against Rd. The volume phase transition disappears if the R decrement rate against Rd is less than a certain value as the result of application of the osmotic pressure greater than a certain magnitude. 3. Result and Discussion It has been experimentally6 and theoretically13 demonstrated that a critical charge amount, nec, for the alternation from discontinuous volume change to continuous volume change of the NIPA gel (n0 ) 1006) is 0.2. It has been also experimentally demonstrated6 that the continuous volume change behavior of the NIPA gel at ne ) 0.7 in the salt-free condition turns to the discontinuous one in the salt solution at CS ) 0.1 M but not at CS ) 0.01 M as is shown in Figure 2. If the theory gives a valid explanation for the experiment mentioned above, the effective charge amount of chain, neΠ(R,CS) in eq 9 exceeded nec ()0.2) at CS ) 0.01 M but not at CS ) 0.1 M. The calculated values of neΠ(R,CS) at CS ) 0.01 M and CS ) 0.1 M were shown as functions of the gel volume in Figure 3. In Figures 2 and 3, V0 is the gel volume at a synthesis, which has been carried out in the aqueous
Sasaki et al.
Figure 2. Salt concentration dependence of the volume change behavior of the NIPA gel at ne ) 0.7. The continuous volume change in the 0.01 M salt solution turns to the discontinuous one in the 0.1 M salt solution. The broken lines denote the transitions. V0 is the gel volume at the synthesis.
Figure 3. Calculated values of the effective charge amount of chain, neΠ(R,CS) at CS ) 0.01 M (a bold line) and CS ) 0.1 M (a less bold line) as functions of the gel volume. If neΠ(R,CS) exceeds nec ()0.2), the volume change with temperature is continuous, otherwise discontinuous. The dotted lines represent the transition volumes of charged NIPA gel (ne ) 0.7) in the 0.1 M salt solution, which is also shown in Figure 2. V0 is the gel volume at the synthesis.
solution of 0.7 M NIPA monomer.6 In the calculation, it was assumed that R3 ≈ 1024n0/(0.7 × 6.02 × 1023) × (V/V0) ()2.373 × n0 × (V/V0)) nm3 and n0 ) 100 from the molar ratio of the cross-linker to the NIPA monomer at the synthesis.6 As shown in Figure 3, the neΠ(R,CS) at CS ) 0.01 M exceeds nec at the transition volume but the neΠ(R,CS) at CS ) 0.1 M does not. The former and latter lead to the continuous and discontinuous volume changes, respectively. This is consistent with the experimental result mentioned above. Therefore we can say that the present theory describes well the salt concentration dependence of the volume phase transition behavior of ionized NIPA gel.
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Langmuir, Vol. 15, No. 12, 1999 4269
It is to be noted that eq 9 in the case of salt solution is rewritten as
{
-3 (Rh2Vhh + 2RhRdVhd + Rd2Vdd)n02 + 4πbλ x1 + X2 - 1 κ
2
X
2
}
ne2
R 1 +2 ) 0 (11) 4 R n0b2
This equation suggests that the Donnan osmotic pressure can be expressed as the electrostatic excluded volume effect of the charged groups. The excluded volume is given by
4πbλ x1 + X2 - 1 κ2
(12)
X2
The electrostatic excluded volume between the ionized groups in the salt solution is approximately given by the product of the square of Debye length (1/κ) and Bjerrum length (bλ), since the ((1 + X2)1/2 - 1)/X2 value changes only about from 0.5 to 0.1 even when the X value changes from 0.01 to 10. From eq 11 we can say that the Donnan osmotic pressure increase the excluded volumes between the segments by Ve such as
Ve )
()
4πbλ x1 + X2 - 1 ne n0 κ2 X2
2
(13)
The ratio of Ve (X in the swelling condition) + Vhh to Vhh is the ratio of the swelling volume of the charged NIPA gel to that of noncharged NIPA gel. In the case of the 0.001 M salt solution (κ ) 1.04 × 10-1 nm-1), the ratio of the charged NIPA (ne/n0 ) 0.007) to that of noncharged NIPA6 is presumed to be about 1.4 (2.8V0/2V0) from the experimental data shown in Figure 2. The fact that (Vhh + Ve)/ Vhh ) 1.4 indicates that Vhh ()Ve(X ) 0.88)/0.4) ≈
0.043(≈0.353) nm3. If the volume of the noncharged NIPA gel in the swelling condition is presumed to be 2V06 which gives R3 ≈ 475 nm3, then Vhh ()2R5/(3n03b2)) ≈ 0.31(≈0.683) nm3. Here we assume that b ) 0.25 nm. The agreement between these Vhh values is considered to be rather reasonable in taking the ambiguity of the presumed volumes (2V0 and 2.8V0) into account. The value of 1.4 as the ratio of the charged NIPA to noncharged NIPA is judged to be overestimated from the fact that the volume of charged NIPA gel in 0.001 M salt solution seems to increase with decrease in temperature lower than 25 °C as Figure 2 shows. It is worthwhile to mention about the reason the transition temperature of ionized NIPA gel at CS ) 0.1 M is higher than that at CS ) 0.3 M, which is shown in Figure 2. The chemical potential of water molecules µW0 in the salt solution is given by
µW0(CS, T) ) µW0(CS ) 0,T) + T ln RW(CS) (14) where aW(CS) is the activity of water molecule in the presence of salt. The activity is usually a monotonically decreasing function of the salt concentration and is less than 1. The chemical potential of µW0(CS ) 0, T) is a monotonically decreasing function of temperature. Therefore, if µW0(CS1, T1) ) µW0(CS2, T2) the condition that CS1 > CS2 gives the relation that T1 < T2. The chemical potentials of water molecules at the transitions of the gel in the salt solutions considered here are almost same, since the values of the right-hand side of eq 9 in the present case are negligible small. Therefore the transition temperature at CS ) 0.3 M is lower than that at CS ) 0.1 M. Acknowledgment. This work was partially supported by a Grant-in Aid for Scientific Research (C) (No. 10640494) from the Ministry of Education, Science, Sports and Culture of Japan. LA981100+
