J. Phys. Chem. B 2010, 114, 14995–15002
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Thermodynamic Properties of N-Isopropylacrylamide in Water: Solubility Transition, Phase Separation of Supersaturated Solution, and Glass Formation Shigeo Sasaki* and Satoshi Okabe Yuji Miyahara Department of Chemistry, Faculty of Sciences, Kyushu UniVersity, 33 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan ReceiVed: June 17, 2010; ReVised Manuscript ReceiVed: September 29, 2010 嘷 w This paper contains enhanced objects available on the Internet at http://pubs.acs.org/JPCB.
The solubility of N-isopropylacrylamide (NIPA) in water was found to discretely change at 25 °C. The highly concentrated NIPA solution separated into two solutions, the concentrations of which were higher than the solubility below 25 °C and lower than the solubility above 25 °C. The X-ray crystallographic analysis indicated that a NIPA crystal formed in the aqueous solution was H2O free. When the aqueous NIPA phase-separated solutions were cooled down to -90 °C at a rate faster than 35 °C/min, the glassy structure formed. On the other hand, the crystalline solid formation of NIPA and H2O were observed when the solutions were cooled to -50 °C at a slower rate than 3 °C/min. The DSC measurements of the phase-separated solutions revealed that the energy levels of NIPA were +15.2, +11.5, and -0.08 kJ/mol (regarding the crystalline solid state at 25 °C as the ground state) for the liquid state, the H2O-poor solution and the H2O-rich solution in the phaseseparated state, respectively. The experimental results are explained in terms of the molecular assemblies of NIPA and H2O molecules in the solutions. 1. Introduction Volume phase transition of poly(N-isopropylacrylamide) gel in water1,2 has aroused much interest not only because of its applicability3 but also the transitionally changing physical properties such as dielectric constant4 and elasticity5 at 34 °C, which is near the physiological temperature. The swollen poly(N-isopropylacrylamide) gel shrinks and then collapses along with the dehydration of the hydrated hydrophobic isopropyl groups on increasing the temperature.6-8 The hydration shell around the isopropyl group has a cagelike network structure stabilized by the hydrogen bonding primarily among the water molecules and partly between the water molecule and the amide group of NIPA. For stabilizing the hydrophobic hydration, the distinct entropy loss of the hydrated water molecules, ∆Sh, in forming the hydrophobic hydration structure should be compensated by the reduction in energy due to the hydrogen bonding, ∆Eh.9 When the contribution of the entropy term to the free energy increases with an increase in temperature and overcomes the contribution of the enthalpy term, the water molecules in the hydration shell are released into the bulk water phase.10 Thus, the dehydration-hydration transition of the hydrophobic entities in the aqueous solution is expected to occur at a temperature given by ∆Eh/∆Sh. Hydration-dehydration transition of the hydrophobic entity located nearby the amide groups of biomaterials often plays a key role in association-dissociation of biomacromolecules in the biological cells.11 In order to gain insight into the thermodynamic mechanism12 of the hydration-dehydration in the system having hydrophobic residues with nearby amide groups, we investigated the interaction of monomeric N-isopropylacry* To whom correspondence should be addressed. Tel./Fax: +81-92-6422609. E-mail:
[email protected],
[email protected].
lamide (NIPA) with water and found several unique features such as solubility transition, liquid-liquid phase separation, and glass formation. In the present experiments, we obtained a phase diagram exhibiting the phase separation of the aqueous NIPA solution and the discretely changing solubility at 25 °C. The phase diagram reveals that the NIPA concentrations of the phaseseparated solutions are higher than the solubility below 25 °C and that the reverse is true above 25 °C. Furthermore, the NIPA concentrations of the phase-separated solutions at 25 °C are coincident with the solubility values discretely changing at 25 °C. The X-ray crystallographic analysis of the crystal formed in the aqueous NIPA solution revealed that it was H2O free. The measurements of differential scanning calorimetry (DSC) gave the energy levels of +15.2, +11.5, and -0.08 kJ/mol for the NIPA molecules in the melting state, the H2O-poor solution and the H2O-rich solution, respectively, when the crystalline solid state was regarded as the ground state. From the solubility, the energy levels of +5.6 kJ/mol below 17 °C and +20 kJ/mol above 17 °C were found for the NIPA molecules in the aqueous solution equilibrated with the crystalline solid. Cooling the H2Opoor part of the phase-separated solutions to -90 °C at a faster rate than 3 °C/min induced the formation of solid glass of NIPA-H2O mixture, while cooling at a rate slower than 3 °C/ min crystallized out NIPA and H2O from the solution separately. Glass formation was also observed for the phase-separated solutions in cooling to -90 °C at a rate of 35 °C/min. 2. Experimental Methods The NIPA monomer (Kohjin Co. Tokyo) was recrystallized from toluene/hexane and water was double distilled. The DSC measurement of the NIPA aqueous solution was carried out at a given temperature-changing rate using a DSC
10.1021/jp1055792 2010 American Chemical Society Published on Web 10/25/2010
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calorimeter (DSC120 Seiko inc. Japan). A mixture of NIPA and H2O with a given mole ratio of H2O to NIPA, rH2O, was encapsulated in an aluminum cell for DSC, sealed at a room temperature, heated to 60 °C, and incubated for 30 min at the temperature before measurement. The DSC measurement was made with cooling at first and then heating. The experiments of phase separation were carried out as follows. When the needle-like NIPA crystals were mixed with 10-fold mole excess of H2O in a glass tube at 30 °C, stoppered and shaken, the liquid was initially turbid, but separated into two phases of transparent solutions on standing. The temperature of the solution was controlled within 0.1 °C using a thermoregulator system (Thermoregulator NCB-1200, Eyela lnc., Japan). After equilibration of the phases for a period longer than 12 h, the solutions of the upper and the lower parts were carefully withdrawn separately and their H2O/NIPA mole ratios, FH2O, were evaluated from the area ratios of the 1H NMR peak for the H2O protons (ca. 4.5 ppm) and the methine proton of NIPA (ca. 4 ppm). The 1H NMR spectra, shown in Figure S1 in the Supporting Information, were obtained on a Bruker DRX600 NMR spectrometer. The phase boundary of the H2O-rich solution at a temperature below 10 °C in the phase diagram was determined by the cloud point measurements on a series of solutions with different concentrations, because withdrawing the supersaturated solutions induced crystal formation. The cloud points were determined by monitoring the turbidity of the solutions contained in glass tubes with a laser light (λ ) 532 nm) while the temperature of the solutions was raised or reduced step by step (0.5 °C step). The temperatures at which the solutions became turbid on heating and transparent on cooling coincided with each other. The H2O/NIPA mole ratio rH2O of the prepared solution in the cloud point experiment is regarded as FH2O at the cloud point. The solubility of NIPA in H2O, FHS 2O, at a temperature below 25 °C was evaluated by means of 1H NMR spectroscopy for the saturated solution by using the procedure described above. On the other hand, the solubility of NIPA in H2O at T above 25 °C was obtained from the dissolution experiment as follows. A mixture of NIPA-H2O with a given rH2O ( 0. The entity melting at THm is the crystalline solid of NIPA, judging from the fact that an amount of the NIPA crystalline solid dissolved into H2O is transitionally increased at about 25 °C as described in the previous section concerning with the solubility which is shown in Figure 1. The endothermic L , ∆HH2O, which is peak area per mole of H2O observed at Tm defined as ∆HH2O ≡ ∆HL/(rH2OnT), is estimated as 6.1 ( 0.6 kJ mol-1 as shown in Table S1 of the Supporting Information. Here ∆HL is an observed enthalpy change with the endothermic L and nT a total mole amount of NIPA in the transition at Tm sample. The value of 6.1 ( 0.6 kJ mol-1 is compatible with the fusion enthalpy of H2O crystalline solid, 6.0 kJ mol-1. This L is the H2O crystalline indicates that the entity melting at Tm solid. In the cooling processes, two exothermic peaks are observed for the samples with rH2O ) 2.7-11 and rH2O ) 0.2-0.6, but only one peak for the sample with rH2O ) 1. For the samples with rH2O ) 2.7-11, the two peaks, a sharp peak at a higher temperature and a broad peak at a lower temperature as shown in Figure 2, are observed. It should be mentioned that, because the supercooling of the solution occurs, the exothermic peaks were observed at slightly different temperatures in measurements on the same sample. The sharp peak at the higher temperature and the broad peak at the lower temperature are attributed to the crystallization of H2O and the crystallization of NIPA, respectively. This assignment is confirmed by the DSC curves shown in Figure 4 where one endothermic peak is observed at L H ∼-2 °C but not at Tm ∼25 °C in heating the sample which Tm gives only one exothermic peak at T around -21 °C in cooling. Thus, it can be said that the H2O in the sample with rH2O ) 2.7-11 solidifies at a higher temperature than NIPA in spite of a lower melting temperature of the H2O crystalline solid than that of NIPA crystalline solid. On the other hand, the temperature at which H2O solidifies on cooling the sample with rH2O < 1 is lower than that of NIPA as shown in Figure 3. It should be mentioned that H2O and NIPA in the sample with rH2O ) 1 are solidified at the same temperature as shown by one exothermic peak at -25.5 °C in Figure 2. The endothermic peak area per mole of NIPA in the mixture at about 25 °C, ∆HN decreases with an increase in rH2O as shown in Figure 5, where an enthalpy change per mole of NIPA in the H is defined as ∆HN ≡ ∆HH/nT. Here ∆HH is an transition at Tm observed endothermic enthalpy change with the transition at THm. A part of the NIPA crystalline solid dissolves into the liquid
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Figure 4. Cooling process dependent DSC curves obtained for the NIPA-H2O mixtures. The lower two curves show no endothermic peaks at 25 °C on heating the sample just after detecting one exothermic peak with cooling.
Figure 6. Dependence of the endothermic enthalpy change at 25 °C shown in Figure 4.
is an enthalpy change in transferring 1 mol of NIPA in the L-phase solution to the H-phase solution. The derivation of eq 1 is described in Appendix II. A linear relation between ∆HN and rH2O is obtained as shown by the dotted line in Figure 5, from which (∆HNfL + [rL/(rL - rH)]∆HLfH) ) 12.27 kJ/mol can be evaluated. In the case of rH g rH2O, a part of NIPA in H is transferred to the H-phase the saturated solution below Tm solution and the NIPA crystalline solid that remained below H H melts to dissolve at Tm . The rH2O dependence of ∆HN in the Tm case of rH g rH2O is given by
∆HN )
rH2O rH
∆HNfH -
rH2O rL
(
∆HNfL + 1 ∆HMH
Figure 5. rH2O dependence of the endothermic enthalpy change at 25 °C shown in Figure 3.
H2O to form the saturated aqueous NIPA solution at a L H and Tm . It should be mentioned that temperature between Tm the L-phase and H-phase solutions coexisted with the NIPA H . The concentrations of the L-phase and crystalline solid at Tm H are identified as the discretely changed H-phase solutions at Tm H is caused by the solubilities. The enthalpy change at Tm transitional dissolution and redistribution of NIPA as follows. H melts to The NIPA remained as crystalline solid at T below Tm H dissolve into the L-phase and H-phase solutions at Tm, and the NIPA in the solution is redistributed into the L-phase and H-phase solutions in the case of rL g rH2O g rH, where rL ()22.5) and rH ()1.3), respectively, are FH2O values of the H L-phase and H-phase solutions at Tm . The rH2O dependence of ∆HN in the case of rL g rH2O g rH is given by
∆HN ≡
(
)(
)
rH2O rL ∆HH ) ∆HNfL + ∆HLfH 1 nT rL - rH rL (1)
where ∆HNfL is an enthalpy change in melting 1 mol of NIPA crystalline solid and forming the L-phase solution, and ∆HLfH
rH2O rH
(
rH2O rH
1-
)
∆HM +
rH2O rH
)
(2)
where ∆HM is the melting enthalpy of 1 mol of NIPA crystalline solid (15.2 kJ/mol), and ∆HMH is a mixing enthalpy of 1 mol of liquid NIPA and the NIPA-H2O assemblies consisting of 1 mol of NIPA in the H-phase solution. The values of ∆HMH ) -3.2 kJ/mol, ∆HLfH ) 11.6 kJ/mol, and ∆HNfL ) -0.08 kJ/ mol can be estimated from the dotted line shown in Figure 6, which is approximately fitted to ∆HN ≈ 15.2 - 5.32rH2O + 1.92rH2O2. Therefore, we can say ∆HNfH ) 11.5 kJ/mol. It should be mentioned here that a positive endothermic enthalpy change corresponds to an increase in the state energy of NIPA molecule with the transition. Structure of NIPA Crystals. The melting enthalpy of NIPA crystalline solid, ∆HM ) 15.2 kJ/mol, is much larger than the hydrogen-bonding energy of 6.3 kJ/mol reported for CdO · · · HN between amide groups.13 Therefore, the presence of interactions other than the hydrogen bonding may be inferred for NIPA molecule in crystals. The structure of NIPA in crystals formed in the phase-separated solution at T below 25 °C is determined by the X-ray crystallography and is shown in Figure 7 and Table S4 in the Supporting Information. The fact that no H2O molecule is present in the crystal indicates stronger attraction between the like molecules than that between the different molecules of NIPA and H2O. The possible hydrogen bonding and van der Waals interactions judging from the interatomic distances are shown in Figure 7. The strong attraction of both the hydrogen bonding of CdO---HN and the van der Waals force between
Thermodynamics of Aqueous NIPA Solution
Figure 7. Ball-stick model of NIPA crystal structure. Molecules are linearly connected by hydrogen bonds between CO and HN groups and arrayed to form two planes, which are perpendicular to each other. The van der Waals attractions, a part of which is shown, connect the planes to stabilize the crystal structure. Broken lines and double green lines, respectively, represent the hydrogen bond (H-bond) and the van der Waals attraction (vW-att). Gray, white, green, and red balls represent carbon, hydrogen, nitrogen, and oxygen atoms, respectively.
CdO and the apolar groups surrounding CdO group are responsible for segregation of NIPA from H2O in solidifying NIPA molecules in the H-phase solution as their thermal motions are reduced on cooling. The hydrogen-bonding energy between H2O themselves, H2O · · · HOH, is reported to be about 6.3-15.3 kJ/mol in the literature14,15 and exceeds that between H2O and the amide group. This is considered to induce the segregation and separation of H2O from NIPA as supported by the fact shown in Figure 4 that H2O is frozen prior to the appearance of NIPA crystalline solid in the supercooled liquid of the phaseseparated solutions. Glassy Solid Formation of the Supersaturated Solutions with Rapid Cooling. The glassy solid is formed when the molecular motion in the supercooled liquid is frozen on cooling rapidly.16 The transparent appearance of the H-phase liquid was kept with losing the fluidity when the solution was cooled down to -90 °C at a rate faster than 10 °C/min. However, on cooling more slowly, the H-phase liquid became opaque because of formation of microscopically segregated crystalline solids of NIPA and H2O. As shown in Figure 8, exothermic transitions are observed at about -50 °C in heating the sample of the H-phase solution (rH2O ) 1) which was cooled once down to -90 °C at a cooling rate faster than 3 °C/min. These observations suggest the glass formation in the H-phase solution with the rapid cooling. The exothermicity can be observed on heating the glassy solid because the crystalline solid with lower state energy than the glassy solid was formed. The DSC curves shown in Figure 8 demonstrate that the structures formed are crystalline solids of H2O and NIPA, which are identified from the fact that the endothermic peaks are observed at TLm and THm in the heating L process. In contrast, none of the two endothermic peaks at Tm H and Tm was observed on heating the samples, which were specially prepared by cooling down rapidly to -50 °C without showing an exothermic peak. The formation of glassy solid was also observed for the phase-separating sample (rH2O > 2) in cooling to -90 °C at a rate of 35 °C/min. The results described above demonstrate that the rapid cooling can sustain the L . amorphous structure of liquid even at T much lower than Tm
J. Phys. Chem. B, Vol. 114, No. 46, 2010 14999
Figure 8. DSC curves of the NIPA solutions at rH2O ) 1 prepared with different cooling rates. The samples are prepared by cooling down the NIPA solutions at rH2O ) 1 to about -100 °C at rates 0.5 (red), 1.0 (purple), 3.0 (green), 6.0 (pink), and 25 (orange) °C/min and are heated at a rate of 0.5 °C/min. Sharp exothermic peaks observed in the region between -35 and -25 °C in the cooling processes at rates 0.5 and 1.0 °C/min are not observed in the case of cooling rates 3.0, 6.0, and 25 °C/min (not shown). The exothermic peaks of DSC curves (green, pink, and orange) in the regions between -55 and -40 °C are due to the crystallizations of NIPA and H2O from the glassy NIPA-H2O complex.
It should be noted that the low critical cooling rate for forming the glassy solids from the phase-separated solutions, 35 °C/ min, compared with that for forming the glassy solid of water,17 108 °C/min, can be explained by one-molecule-like NIPA-H2O assembly structures which are formed in the phase-separated solutions by the strong attraction between NIPA and H2O molecules. For forming NIPA and H2O crystalline solids, the liquids of NIPA and H2O should be segregated from the NIPA-H2O assembly. Because of the time-consuming processes of the segregation, the mechanism of which is not well understood at present, the amorphous structure of the assembly is frozen during the rapid cooling. 4. Discussion Thermodynamic data obtained by the present experiments are tabulated in Table 1 and shown in Figure S2 of the Supporting Information. The enthalpy changes in transforming the liquid NIPA to the L-phase solution, ∆HDL, and the H-phase solution, ∆HDH, are negative as shown in Table 1. These negative enthalpies are mainly brought about by the formation of hydrogen bonding between NIPA and H2O molecules. The enthalpy change in transforming the liquid NIPA to the L-phase solution (∆HDL ) -15.3 kJ/mol) is significantly lower than the enthalpy change in transforming the liquid NIPA to the saturated aqueous NIPA solution (-9.6 kJ/mol below 17 °C and +4.8 kJ/mol above 17 °C), suggesting that more hydrogen bonds are formed in the liquid structure of NIPA and H2O at the L-phase boundary than those in the saturated aqueous NIPA solution. The cagelike hydrogen-bonded network structure of H2O molecules surrounding NIPA molecules formed at the L-phase boundary has more hydrogen bonds near to one NIPA molecule than the liquid structure of saturated aqueous NIPA solution. The enthalpy change in transforming the liquid NIPA to the H-phase solution (∆HDH ) -3.7 kJ/mol) is smaller than the enthalpy for transforming the liquid NIPA to the aqueous
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TABLE 1: Thermodynamic Data of NIPA at the Various Transitions symbol
initial state
final state
Tm or T (K)
∆H (kJ mol-1)
∆S (J K-1 mol-1)
∆HM ∆HLfH ∆HNfL ∆HNfH ∆HDH ∆HDL -
NIPA crystals L-phase NIPA crystals NIPA crystals NIPA liquid NIPA liquid NIPA crystals NIPA crystals NIPA liquid NIPA liquid
NIPA liquid H-phase L-phase H-phase H-phase L-phase NIPA solution NIPA solution NIPA solution NIPA solution
338.5 298.2 298.2 298.2 298.2 298.2 T < 290.2 T > 290.2 T < 290.2 T > 290.2
+15.2 +11.6 -0.08 +11.5 -3.7 -15.3 +5.6 +20 -9.6 +4.8
+45 +39 -0.3 +39 -
solution (+4.8 kJ/mol), suggesting that the hydrogen bonds among NIPA and H2O molecules more than those in the saturated solution stabilize the H-phase solution. The energy needed for transferring one H2O molecule from the H-phase solution to the L-phase solution can be estimated as 3.4/NA kJ because it is the sum of the exchanging energy of one NIPA molecule in the L-phase solution with one H2O molecule in the H-phase solution, 15/NA kJ, and the energy level of one NIPA molecule in the L-phase solution relative to that of the H-phase solution, -11.6/NA. The former energy is derived from ∆HH(N)TW(L) described in the Results section and the latter is from ∆HLfH shown in Table 1. We can say from the energy mentioned above that number of hydrogen bonds for one H2O molecule in the H-phase solution is larger than that in the L-phase solution by 0.2-0.5, assuming one hydrogen bonding energy between H2O molecules as 6.3-15.3/NA kJ.14,15 It is worthwhile to mention that the solubility lines at T above 25 °C and below 25 °C, respectively, intersect the H-phase boundary and the L-phase boundary as shown in Figure 1. The FHS 2O value changes transitionally from FH2O ) 22.5 of the L-phase boundary to FH2O ) 1.3 of the H-phase boundary at 25 °C; that is, the solubility transition occurs there. The solubility transition is generally induced by the structural change of the solid and/or the liquid. No observation of an enthalpy change at 25 °C in the DSC measurements for the sample at rH2O ) 0 indicates that the solubility transition is primarily caused by a change in the liquid structure of NIPA solution. A hydrophobic hydration shell can form around an isopropyl group of NIPA in the saturated solution at FHS 2O greater than 22.5 but not in the saturated solution with FHS 2O less than 1.3. Therefore, it can be said that the crystalline solid dissolves into the solution phase with forming the hydrophobic hydration at T below 25 °C and without it at T above 25 °C. The experimental result that the energy level of one NIPA molecule in the saturated solution at T above 25 °C is higher than that in the liquid state by 4.8/NA kJ as shown in Table 1 suggests that H2O molecules in the solution at FHS 2O less than 1.3 reduce the attractive interaction energy among NIPA molecules such as hydrogen bonding and van der Waals interaction. The estimation that the number of hydrogen bonds per one molecule of H2O in the solution at FH2O ) 1.3 is larger by 0.2-0.5 than that in the solution at FH2O ) 22.5 provides us a picture that an assembly of the H2O molecules connected by the hydrogen bonding is enclosed with NIPA molecules in the solution at FH2O ) 1.3. The structure of the solution mentioned above reduces the NIPA-NIPA contact area compared with that of the NIPA liquid and decreases the energy of van der Waals interaction among NIPA molecules. It is important to point out that the hydrogen bonds of the network are continuously formed and broken in the aqueous solutions. The lifetime of the hydrogen bonds in the hydrophobic hydration shell in the solution phase has been reported to be an
order of 1 ps, which is about twice of that in the bulk water.18,19 Femtosecond 2D IR spectroscopy20 has revealed that defects in the hydrogen-bonded network, broken hydrogen bonds in the shell re-form within 200 fs. It has been also reported21 that relaxation times of the reorientation of HOD molecules in the hydrophobic shell and in the bulk, respectively, are much longer than 10 ps and shorter than 2.5 ps. It can be inferred, therefore, that the hydrogen-bonded network consisting of many H2O molecules surrounding the NIPA assembly in the L-phase solution or surrounded by the NIPA assembly in the H-phase solution has a longer life than that in the bulk water and is reinforced because of a lower breaking ratio of hydrogen bonds (approximately a ratio of the re-forming time of defect to the lifetime of hydrogen bond) in hydrophobic hydration shell than that of hydrogen bonds in the bulk. Two successive exothermic peaks as shown in Figure 8 were observed in the heating process of the glassy solid that was obtained by rapid cooling of the H-phase solution. Similar two successive exothermic peaks were also observed at about -50 °C in heating the samples at rH2O ) 0.4-11.4, which were cooled down to -90 °C at the rate of 35 °C/min. The observed exothermic enthalpies are tabulated and shown in Table S3 in the Supporting Information. The result that the exothermic enthalpies divided by total amounts of NIPA in the system are much more consistent than those divided by total amounts of H2O as shown in Table S3 in the Supporting Information suggests that the exothermic transition observed is related to the crystallization of NIPA. If the cooling procedure to -90 °C strengthens the hydrogen bonds among the H2O molecules in the hydration shell surrounding the nonpolar groups of NIPA and weakens the hydrogen bonds between the amide group and the hydration shells, then the number of the hydrogen bonds that re-formed among H2O molecules for crystallizing H2O is very small while most of the hydrogen bonds among NIPA molecules should be re-formed for crystallizing NIPA. This is suggested by the result shown in Figure 4 that the crystallization of H2O occurs faster than that of NIPA at a temperature lower L H and Tm . The endothermic enthalpy due to the breaking than Tm hydrogen bond between NIPA and H2O in the midway of the hydrogen bond formation among NIPA molecules might make one exothermic peak split into two as shown by the exothermic peaks in the heating curves in Figure 8. It is worthwhile to mention that the glassy solid is also formed in the L-phase solution at FH2O ) 11.4 with rapid cooling. This indicates that the L-phase solution consists of molecule-like NIPA-H2O assemblies as the H-phase solution does. The present experimental results suggest the possibility that the L-phase and the H-phase solutions are occupied with H2O assemblies surrounding NIPA molecules and NIPA assemblies surrounding H2O molecules, respectively. The low critical cooling rate, 35 °C/min, for forming the glassy solid from the L-phase solution which is much lower than that for forming
Thermodynamics of Aqueous NIPA Solution the glass formation of H2O,17 108 °C/min, indicates that the freezing rate of the thermal motion of the NIPA assembly is much higher than the dissociating rate of H2O molecules or NIPA molecules from the assembly. Other than the very low disintegration rate of the assembled structure, we could not explain the critical cooling rate of the glass formation from the L-phase solution mentioned above. The low disintegration rate could be induced by a longer lifetime of hydrogen bonded network of H2O molecules in the assemblies. We can say that there exists a great activation barrier for disintegrating the hydrophobic hydration surrounding the NIPA assemblies in the L-phase and the H-phase solutions.
J. Phys. Chem. B, Vol. 114, No. 46, 2010 15001 The total numbers of NIPA and H2O molecules of the whole system are given by NN ) ∑A)L,HnN(A)C(A) and NW ) ∑A)L,HnW(A)C(A). The entropy of total system can be given by
S ) k ln{
∏
NA!(nA(L) !)-C (nA(H) !)-C } (H)
(L)
A)N,W
or
S/k )
∑
[NA(ln NA - 1) -
A)N,W
∑
nA(B)C(B){ln nA(B) -
B)L,H
1}] (I-1)
5. Conclusions It is found that the NIPA crystalline solid solubility in water changes discretely at 25 °C and that the aqueous NIPA solutions at the concentrations of the solubilities can coexist as the phaseseparated solutions equilibrating with the crystalline solid at 25 °C. The phase separation is observed for the NIPA solution. The NIPA concentrations in the phase-separated solutions are higher than the solubility at T below 25 °C and lower than the solubility at T above 25 °C. This indicates that the phaseseparated solutions are supersaturated or metastable at T below 25 °C. The NIPA content of the phase-separated H2O-rich solution decreases with the temperature T, although the NIPA contents in the H2O-poor solution and the solubility increase with T. The structure of H2O-free NIPA crystal, which is formed in the aqueous solution, is revealed by the X-ray crystallography. The phase-separating H2O-rich and -poor NIPA solutions cooled down at a rate 35 °C/min become glassy solids. It is found from the DSC measurements of the mixtures of the phase-separated solutions that the energy levels of NIPA in the liquid state, the H2O-poor solution, and the H2O-rich solution in the phaseseparated state are +15.2, +11.5, and -0.08 kJ/mol, respectively. Here the crystalline solid state is regarded as the ground state. The energy levels of NIPA in the aqueous solutions are given as +5.6 kJ/mol at a temperature below 17 °C and +20 kJ/mol at a temperature above 17 °C from the solubility measurements. The experimental results described above suggest the existence of two types of assembled structures of NIPA molecules and H2O molecules in the solution: the NIPA assembly surrounded by the hydrophobic hydration shell and the H2O assembly surrounded by NIPA molecules.
From the free energy given as G ) E(L) + E(H) - TBS/k, E(L) ) C(L)ε(L), and E(H) ) C(H)ε(H) for the assembling energies ε(L) and ε(H), the chemical potentials are given as
Supporting Information Available: Proton NMR spectra of H-phase NIPA solution (Figure S1); energy map of NIPA molecules in the various states at 25 °C (Figure S2); transition temperatures, TC and enthalpy changes with transitions, ∆H (Table S1); transition temperatures, TC and enthalpy changes with transitions, ∆H (Table S2); exothermic enthalpy change in crystallizing with heating the glass (Table S3); crystallographic data for NIPA (Table S4); and an X-ray crystallographic file (CIF in the HTML version of the paper). This material is available free of charge via the Internet at http:// pubs.acs.org.
The right-hand side of eq I-4 is interpreted as a change in the energy with exchanging one H2O molecule in the H-phase for one NIPA molecule in the L-phase.
Appendix I: Thermodynamics of Assemblies in the Phase Separation It is assumed here that the L-phase and the H-phase, respectively, are packed with the C(L) assemblies of nN(L) NIPA (H) assemblies molecules surrounded by n(L) W H2O molecules and C (H) (H) of nW H2O molecules surrounded by nN NIPA molecules. The superscripts (L) and (H) and the subscripts N and W will represent the L- and H-phases, and NIPA and H2O molecules.
µA(B) ≡
∂G dE(B) ) - TB(ln NA - ln nA(B)); ∂NA(B) dNA(B) C(B)nA(B),
NA(B) )
(A ) N, W;B ) H, L) (I-2)
Then the equilibrium between L- and H-phases can be described by
dE(H) dE(H) dE(L) dE(L) (H) + T ln F ) + TB ln FH(L)2O B H O (H) (H) (L) (L) 2 dNW dNN dNW dNN (I-3) (H) (H) (L) (L) In deriving the equation above, F(H) H2O ) nW /nN and FH2O ) nW / (L) nN are used. On the assumption that the assembling energy is independent of TB, eq I-3 is rewritten as
∂ ln FH(H)2O /∂(1/TB) - ∂ ln FH(L)2O /∂(1/TB) ) (H)
} {
{
(H)
dE(L) dN(L) W
dE dE dE(L) + dN(H) dNN(H) dNN(L) W
}
(I-4)
Appendix II: Equations for Describing the Enthalpy Changes with the Transitions The following notations are used in deriving the equations for describing the enthalpy changes with the transitions: nT, a total molecular amount of NIPA in the system; nL, a molecular amount of NIPA in the L-phase; nH, a molecular amount of NIPA in the H-phase; ∆HH, an observed enthalpy change with the endothermic transition at a melting temperature of crystalline H ∼ 25 °C; ∆HL, an observed enthalpy solid NIPA in water, Tm change with the endothermic transition at a melting temperature L ∼ -2 °C; ∆HM, a mole enthalpy of H2O crystalline solid, Tm change with melting the NIPA crystalline solid; ∆HDH, an enthalpy change of 1 mol of liquid NIPA in forming the H-phase H ; ∆HDL, an enthalpy change of 1 mol of NIPA solution at Tm H . The relations liquid with forming the L-phase solution at Tm ∆HNfL ) ∆HM + ∆HDL and ∆HLfH ) ∆HDH - ∆HDL can be
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J. Phys. Chem. B, Vol. 114, No. 46, 2010
derived. We define ∆HN ≡ ∆HH/nT as an enthalpy change for H and ∆HH2O ≡ ∆HL/ 1 mole of NIPA with the transition at Tm (rH2OnT) as an enthalpy change for 1 mole of H2O with the L . transition at Tm We will derive ∆HN in the case rL g rH2O g rH, where rL ()22.5), rH ()1.3), and rH2O are respectively the mole ratio of H , the mole ratio of H2O to NIPA in the L-phase solution at Tm H , and the mole ratio H2O to NIPA in the H-phase solution at Tm of H2O to NIPA in the total system. The relations nT ) nL + nH and rH2OnT ) rHnH + rLnL derived from the mass conservations of NIPA and H2O give another relation, (rH2O - rH)nH ) (rL - rH2O)nL. The relations described above can be rewritten as follows: nH ) nL(rL - rH2O)/(rH2O - rH), nL ) nT(rH2O - rH)/ (rL - rH), and nH ) nT(rL - rH2O)/(rL - rH). For estimating ∆HN, the fact that nL* ) nTrH2O/rL moles of NIPA dissolve into H should be taken into account. H2O before the transition at Tm H In the transition at Tm, nL* - nL ) (rH(rL - rH2O))/((rL - rH)rL)nT moles of NIPA are transferred from the L-phase solution to the H-phase solution and nH* ) nT - nL* ) nT(rL - rH2O)/rL moles of NIPA melt to form the H-phase solution. Therefore, the H is given as ∆HH ) nH*∆HNfH + (nL* transition enthalpy at Tm - nL)∆HLfH. Substituting the relations described above into the relation mentioned above, we could obtain a relation
∆HN ≡
(
∆HH ) nT
∆HNfL +
)(
rH2O rL ∆HLfH 1 rL - rH rL
)
(II-1 or (1))
The following are taken into account for deriving ∆HH in the case of rH g rH2O. The L-phase solution forms with nT(rH2O)/ H H . At Tm , (rL) moles of NIPA dissolved into H2O at T below Tm the L-phase solution is transferred to the H-phase solution and nT((rH2O)/(rH) - (rH2O)/(rL)) moles of NIPA melt to form the H-phase solution. Above THm, nT(1 - (rH2O)/(rH)) moles of NIPA melt to dissolve into the H-phase solution to form the saturated solution with inducing an additional enthalpy change, which ∆HH includes because of the apparent continuity of the H as shown in Figure 3. Then endothermic DSC peak around Tm a relation
Sasaki et al.
∆HN )
(
1-
rH2O
∆HNfH -
rH rH2O rH
)
rH2O rL
∆HNfL +
∆HM + ∆HMH
rH2O rH
(
1-
rH2O rH
)
(II-2 or (2))
can be obtained, where ∆HMH is a mixing enthalpy of NIPA liquid molecules and NIPA-H2O assemblies constituting the H . saturated solution at T above Tm References and Notes (1) Dusˇek, K., Ed.; Responsive Gels: Volume Transitions I. In AdVances in Polymer Science; Springer: New York, 1993; Vol. 109. (2) Dusˇek, K., Ed.; Responsive Gels: Volume Transitions II. In AdVances in Polymer Science; Springer: New York, 1993; Vol. 110. (3) Fukumori, K.; Akiyama, Y.; Yamamoto, M.; Kobayashi, J.; Sakai, K.; Okano, T. Acta Biomater. 2009, 5, 470–476. (4) Sasaki, S.; Koga, S.; Maeda, H. Macromolecules 1999, 32, 4619– 4624. (5) Sasaki, S.; Koga, S. Macromolecules 2002, 35, 857–860. (6) Koga, S.; Sasaki, S.; Maeda, H. J. Phys. Chem. 2001, 105, 4105– 4110. (7) Afroze, F.; Nies, E.; Berghmans, H. J. Mol. Struct. 2000, 554, 55– 68. (8) Geukens, B.; Meersman, F.; Nies, E. J. Phys. Chem. B 2008, 112, 4474–4477. (9) Blokzijl, W.; Engberts, J. B. F. N. Angew. Chem. Int. Ed. Engl. 1993, 32, 1545–1579. (10) Smith, D. E.; Zhang, L.; Haymet, A. D. J. J. Am. Chem. Soc. 1992, 114, 5875–5876. (11) Gill, S. J.; Dec, S. F.; Olofsson, G.; Wadso˜, I. J. Phys. Chem. 1985, 89, 3578–3761. (12) Paschek, D. J. Chem. Phys. 2004, 120, 10605–10617. (13) Gellman, S. H.; Dado, G. P.; Liang, G.; Adams, B. R. J. Am. Chem. Soc. 1991, 113, 1164–1173. (14) Sˇasˇic´, S.; Segtnan, V. H.; Ozaki, Y. J. Phys. Chem. A 2002, 106, 760–766. (15) Smith, J. D.; Cappa, C. D.; Wilson, K. R.; Messer, B. M.; Cohen, R. C.; Saykally, R. J. Science 2004, 306, 851–853. (16) Sarjeant, P. T.; Roy, R. Mater. Res. Bull. 1968, 3, 265–280. (17) Strnad, Z. Glass-Ceramic Materials; Elsevier: Amsterdam, 1986; p 9. (18) Ball, P. Chem. ReV. 2008, 108, 74–108. (19) Qvist, J.; Halle, B J. Am. Chem. Soc. 2008, 130, 10345–10353. (20) Eaves, J. D.; Loparo, J. J.; Fecko, C. J.; Roberts, S. T.; Tokmakoff, A.; Geissler, P. L. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 13019–13022. (21) Rezus, Y. L. A.; Bakker, H. J. Phys. ReV. Lett. 2007, 99, 148301.
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