Molecular Approach To Understand the Tacticity Effects on the

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Molecular Approach To Understand the Tacticity Effects on the Hydrophilicity of Poly(N-isopropylacrylamide): Solubility of Dimer Model Compounds in Water Yukiteru Katsumoto,*,† Noriyuki Kubosaki,† and Tatsuhiko Miyata‡ Graduate School of Science, Hiroshima UniVersity, Kagamiyama 1-3-1, Higashi-Hiroshima 739-8526, Japan and Department of Physics, Ehime UniVersity, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan ReceiVed: August 7, 2010

Although it has been suggested that the tacticity affects the hydrophilicity of poly(N-isopropylacrylamide) (PNiPA), little is known about the physical background of this phenomenon. In this study, we investigated the solubility of the dimer model compounds (DNiPA). The partition coefficient of DNiPA in the two phases of a water/chloroform mixture has indicated that DNiPA with the racemo configuration (r-DNiPA) is more soluble in water than DNiPA with the meso configuration (m-DNiPA). The difference of the hydration free energy between m- and r-DNiPA is estimated to be 1.2 kJ mol-1. The molecular mechanics (MM) calculations with the GB/SA model have revealed that r-DNiPA in water is more stable by ca. 1 kJ mol-1 than m-DNiPA, which is in excellent agreement with the experimental result. The MM calculations have also indicated that the intramolecular interaction of m-DNiPA is stronger than that of r-DNiPA, while r-DNiPA is advantageous in terms of the hydration free energy and conformational entropy. Introduction An aqueous solution of poly(N-isopropylacrylamide) (PNiPA) undergoes a lower critical solution temperature (LCST) type phase separation.1-5 The phenomenon has attracted the attention of scientists and engineers because it is the fundamental aspect of the stimuli responsiveness of PNiPA.1,2 Recently, several research groups have revealed that the stereoregularity of PNiPA significantly affects the phase separation temperature (Tps) of the aqueous solution.6-8 Suito et al.6 found that the Tps of stereocontrolled PNiPAs with a high meso (m) diad content (socalled “isotactic-rich PNiPA”) in water is lower than that of an atactic PNiPA. Ray et al.7 revealed that the Tps of PNiPA in water decreases with increasing m content of the polymer; for example, PNiPAs with m ) 45% and 66% exhibit the phase separation at Tps ) 31.1 and 17.0 °C, respectively. Hirano et al.8 found that the Tps of a syndiotactic-rich PNiPA (m < 45) in water is higher than that of an atactic PNiPA. In the previous papers,9 we investigated the tacticity effects on the phase boundary of PNiPA in water. By preparing a set of well-defined PNiPA samples that have similar Mn and Mw/Mn but different m contents, it was revealed that the phase boundary curve of PNiPA in water with high m contents appears in a lower temperature region. The tacticity also has an influence on the shape of the phase boundary curves of PNiPA in water. Interestingly, an isotactic-rich PNiPA undergoes an upper critical solution temperature (UCST) type phase separation in bis(2-methoxyethyl) ether (diglyme).10 The IR study combined with quantum chemical calculations clarified that isotactic partial chains of PNiPA in diglyme form a helical structure with the aid of an intramolecular CdO · · · H-N hydrogen bond. Temperature- and concentration-dependent IR spectra suggested that the folding and * To whom correspondence should be addressed. Fax: +81-82-424-7408. E-mail: [email protected]. † Hiroshima University. ‡ Ehime University.

unfolding of isotactic PNiPA chains are correlated with the thermal changes in the solubility of the polymer in diglyme. These observations imply that the interaction between a solvent and PNiPA is significantly influenced by the stereoregularity of the polymer chain. It is likely that the solvation of the polymer chain competes with the interactions among the neighboring side chains as we suggested in previous papers.10-12 The purpose of the present paper is to clarify the molecular origin of the tacticity effects on the hydrophilicity of PNiPA. First, we prepared a dimer model compound, N,N′-diisopropyl-2,4-dimethylglutarylamide (DNiPA), to examine the effects of stereoregularity on the solubility of DNiPA in water. Second, the molecular mechanics (MM) calculations were performed to reveal how the hydration and intramolecular interaction are affected by the stereoregularity of DNiPA. Computational Method Searching the Conformational Space. The conformation search for DNiPAs was carried out by the MM calculation with the MMFF94s force field using the CONFLEX program.13-15 The definition of the configuration, chirality, and diad tacticity of the dimer model are summarized in Table 1. 2R(2S),4S(4R)-DNiPA is corresponding to the m configuration, whereas the two enantiomers of 2R,4R- and 2S,4SDNiPAs are the racemo (r) configuration. The calculation results concerned with the stable conformers and their energy were compatible for two enantiomers of r-DNiPA, r-RR and r-SS. Each conformer found for r-SS is one of the mirror images of the conformers obtained for r-RR, and their energies are the same. In this paper, therefore, we show only the molecular structure of r-SS as the calculation results for r-DNiPA unless otherwise stated. The search limit (SEL) of 10 kcal mol-1 (ca. 42 kJ mol-1) was used. The number of the atropisomer was estimated by the symmetry of each conformer. The GB/SA model was used to estimate the solvation effect on the optimized conformers.

10.1021/jp107442h  2010 American Chemical Society Published on Web 10/04/2010

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TABLE 1: Definition of the Chirality and Diad Tacticity of DNiPAs

Calculation of Ensemble Average Energies. The difference in the free energy between m- and r-DNiPA, ∆Frfm, is evaluated through the partition function (Z) of each dimer model as follows

( ) { }

∆Frfm ) -kBT ln

Z≈

∑ exp i

-

Zm Zr

Ei kBT

(1)

∑

Ei exp(-Ei /kBT) Z

(3)

∑

Eist exp(-Ei /kBT) Z

(4)

∑

µiGB/SA

i

〈Est〉 )

i

〈µGB/SA〉 )

i

exp(-Ei /kBT) Z

(6)

The difference in the conformational entropy between m and r-DNiPA, ∆Srfm, is estimated by using eq 7

T∆Srfm ) ∆〈E〉rfm - ∆Frfm

(7)

3D-RISM Theory. The hydration structure around the DNiPA molecules is examined by the 3D reference interaction site model (3D-RISM) theory. The 3D-RISM theory is the 3D statistical mechanical theory of molecular liquids based on the integral equation theory. 3D-RISM theory describes the 3D distribution function (3D-DF) of the solvent around the solute,

∑ ci,VuV(r)*(wVγVV(r) + FVVhVγVV(r))

(8)

V

uV uV where hi,γ (r) and ci,γ (r) are the total correlation function and the direct correlation function of the solvent site γ around the VV VV (r), hVγ (r), and FVV are solute conformer i, respectively, and wVγ the site-site intramolecular correlation function of the solvent, the site-site total correlation function of the solvent, and the number density of the solvent site ν, respectively. r and r denote the 3D position vector relative to the center of a solute molecule and the 1D intermolecular separation between the solvent sites, respectively. “u” and “V” stand for solute and solvent, respectively. The asterisk, *, represents the convolution integral. wVV Vγ(r) VV (r) is the reflects the molecular shape of the solvent. hVγ correlation function of the bulk solvent and is obtained from the dielectrically consistent RISM (DRISM) theory17,18 prior to uV (r) and application of eq 8. Equation 8 is to be solved for hi,γ uV ci,γ(r). To this end, we employ another relationship between uV uV (r) and ci,γ (r) to couple with eq 8, which is referred to as hi,γ 3D-KH closure of the form

uV 1 + hi,γ (r) )

(5)

The difference in quantity A between m- and r-DNiPA, ∆〈A〉rfm, is defined as

∆〈Α〉rfm ) 〈Α〉m - 〈Α〉r

uV hi,γ (r) )

(2)

where kB is the Boltzmann constant, T is the temperature, and Ei is the steric energy or the potential of mean force of conformer i obtained from the optimization process of MM calculations. When the optimization is carried out in the gas phase, Ei is equal to the steric energy of each conformer Eist. In the case that the optimization is performed with the GB/SA model, Ei ) Eist + µiGB/SA is assumed, where µiGB/SA is the solvation (GB/ SA) free energy of the i conformer. The ensemble average of Ei 〈E〉, the steric energy 〈Est〉, and the solvation free energy 〈µGB/SA〉 are calculated by eqs 3, 4, and 5, respectively.

〈E〉 )

which can be related to thermodynamic quantities such as the solvation free energy by a spatial integration of the relevant correlation functions with a proper form of the integrands. The details of 3D-RISM theory have been described elsewhere.16 Here, we shall present a brief outline of the theory. The 3D-RISM equation reads

{

uV uV exp(di,γ (r)) for di,γ (r) e 0 uV uV 1 + di,γ (r) for di,γ (r) > 0

(9)

where uV uV uV uV di,γ (r) ) -βui,γ (r) + hi,γ (r) - ci,γ (r)

(10)

uV (r) is the interaction potential energy. β is defined as Here, ui,γ β ) 1/kBT, where kB and T are the Boltzmann constant and temperature, respectively. The simultaneous solution of eqs 8 uV (r) through the following relation and 9 gives the 3D-DF gi,γ

uv uv gi,γ (r) ) 1 + hi,γ (r)

(11)

It has been shown that under eqs 8 and 9 the solvation free for the solute conformer i is expressed by the energy µRISM i following analytical formula16,19

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µiRISM ) -kBT

Katsumoto et al.

∑ FγV ∫ dr[ci,γuV (r) - 21 Θ(-hi,γuV (r))hi,γuV (r)2 + γ

1 uV uV (r) h (r)ci,γ 2 i,γ

]

(12)

where Θ(x) is the Heaviside step function. Equation 12 indicates that the solvation free energy can be calculated by spatially integrating the correlation functions within the framework of the 3D-RISM theory. The program code for the 3D-RISM developed to date by one of the authors (T. M.) and his co-workers16,20,21 has assumed an interaction modeled by the Lennard-Jones 12-6 and the Coulomb potentials. The DNiPA molecule is modeled by the OPLS/AA parameter.22,23 The SPC/E model24 was employed for water with a correction upon the Lennard-Jones parameters of the hydrogen atom (σ ) 0.4 Å and
) 0.05 kcal mol-1, where σ and
have the standard meanings concerning the Lennard-Jones potential). The Lorentz-Berthelot mixing rule was applied to the water-DNiPA Lennard-Jones parameters. In the 3D-RISM calculation, the temperature, number density of water, and dielectric constant of water were chosen as 298.15 K, 0.033329 Å-3, and 78.4, respectively. Further, the number of spatial grid points and size of the cubic cell for solving eqs 8 and 9 were set as 192 × 192 × 192 and 48 × 48 × 48 Å3, respectively. Experimental Section Materials. Chemicals were from WACO and TCI. N,N′DNiPA prepared according to the literature.25 In brief, ptoluenesulfonyl chloride (31.6 g), 2,4-pentanediol (8.4 g), and triethylamine (60 mL) were stirred overnight at room temperature. The reaction was stopped by adding an aqueous solution of sodium hydrogen carbonate. A yellow powder (1) was obtained by filtration. NaCN (16.0 g) was added to a dimethylsulfoxide solution of 1 (23 g/20 mL) at 60 °C with stirring. After stirring the solution for 4 days, 200 mL of CH2Cl2 was added. The organic layer was washed with 500 mL of water. The organic layer was evaporated, and then the crude product was subjected to column chromatography with silica gel as a stationary phase and ethyl acetate/n-hexane (1/1, v/v) as an eluent to yield 2,4-dimethyl gultaronitrile (2) as a light yellow solid. A 100 mL amount of concentrated HCl was added to 2.3 g of 2, and then the mixture was refluxed for 5 h. Diethyl ether was added, and the organic layer was collected. After evaporating, a yellow liquid containing 2,4-dimethyl glutaric acid (3) was obtained. 1,4-Dimethylglutaroyl chloride (4) was obtained by stirring the mixture of 3 (2.5 g) and an equivalent amount of thionyl chloride for 4 h at room temperature. By adding dropwise a diethyl ether solution of isopropylamine (1.3 g/100 mL) to 4, DNiPA was obtained. 1 H NMR. The measurement of 1H NMR spectra was made using a JEOL JNM-LAMBDA spectrometer (500 MHz) at the Natural Science Center for Basic Research and Development (N-BARD), Hiroshima University. The ratio of m- and r-DNiPA in a solution was determined from the integral intensity of the methylene proton peaks.26 Results and Discussion Partition Coefficient of DNiPA in the Two Phases of a Water/Chloroform Mixture. The dimer model compounds prepared in this study are a racemic mixture of m- and r-DNiPAs. The diad configuration of DNiPA can be identified by 1H NMR. The methylene proton signals due to the m

Figure 1. 1H NMR spectra of DNiPA (a) as prepared, (b) distributed in the CDCl3 phase, and (c) distributed in the D2O phase.

TABLE 2: Mole Fraction of DNiPAs Distributed in the D2O or CDCl3 Phase of the Mixture total m r a

xw

xcl

RT ln(xcl/xw)a/kJ mol-1

4.8 × 10-4 1.8 × 10-4 3.0 × 10-4

7.7 × 10-3 3.8 × 10-3 3.8 × 10-3

6.9 7.5 6.3

R ) 8.31 J mol-1 K-1, T ) 298 K.

configuration appear at around 1.3 and 1.9 ppm, but that arising from the r configuration is located at 1.6 ppm.26 Figure 1(a) shows the 1H NMR spectrum of DNiPA as prepared. The integral intensity of the bands due to m-DNiPA is equal to that arising from r-DNiPA, indicating that the population of r and m in the prepared DNiPA is the same. To investigate the difference in the hydrophilicity of r- and m-DNiPAs, 80 mg of the racemic DNiPA was placed in 4 mL of a D2O/CDCl3 (1/1, v/v) mixture. After stirring the mixture for 12 h, it was kept at 298 K for 24 h. The weight of DNiPA dissolved in each phase was measured after removing the solvent. The mole fraction of DNiPA distributed in CDCl3 (xcl) is 7.7 × 10-3, while that in D2O (xw) is 4.8 × 10-4. Figure 1(b) and 1(c) represent the 1H NMR spectra of DNiPA partitioned into CDCl3 and D2O, respectively. Interestingly, the relative intensity of the bands due to m-DNiPA in D2O is smaller than that due to r-DNiPA. By calculating the integral intensity of the bands, we concluded that the m:r of DNiPA in D2O is 38:62. Note that the m:r of DNiPA in CDCl3 is almost 50:50. According to the NMR result, we estimated the mole fraction of m- and r-DNiPA in each phase. The results are compiled in Table 2. The quantity of RT ln(xcl/xw) is assumed to be concerned with the difference in the solvation free energy, ∆Gclfw

∆Gclfw ) RT ln(xcl /xw)

(13)

∆Gclfw for m-DNiPA is estimated to be 7.5 kJ mol-1, while ∆Gclfw for r-DNiPA is 6.3 kJ mol-1. Therefore, the difference in the hydration free energy between m- and r-DNiPA, ∆∆Grfm ) ∆Gclfw (r) - ∆Gclfw (m), is 1.2 kJ mol-1, indicating that m-DNiPA is less hydrophilic than r-DNiPA. This result is in good agreement with the experimental observation for the tacticity effects on the hydrophilicity of stereocontrolled PNiPA reported previously: a m-rich PNiPA is more hydrophobic than a r-rich PNiPA.7-9 Molecular Mechanics (MM) Calculations for DNiPAs. As a result of the conformation search, 728(1456) conformers for m-DNiPA in the gas phase were found. The number of conformers including atropisomers is written in parentheses (an

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TABLE 4: Ensemble Average Energies for DNiPA Calculated for the Aqueous Phase

c

Figure 2. Most stable conformers for m-DNiPA and r-DNiPA in the gas phase (mv001 and rv001) and those in water (mw001 and rw001).

TABLE 3: Ensemble Average Energies for DNiPA Calculated for the Gas Phase

c

configuration

meso

chirality

RS, SR a

no. of conformers population ratio Z Fb 〈Est〉b

728(1456 ) 1.0 1.16668 × 1031 -177.3315 -170.5773

difference ∆Frfmb ∆〈Est〉rfmb T∆Srfmb, c ∆Srfmd

-0.5624 -2.789 -2.227 -0.007468

racemo RR

SS

707 0.5 9.29884 × 1030 -176.7691 -167.7884

707 0.5 9.29884 × 1030

a Number of conformers including the atropisomers. T ) 298 K. d kJ T-1 mol-1.

b

kJ mol-1.

example of atropisomers can be found in the Supporting Information). On the other hand, 707 conformers were identified for both r-RR and r-SS. The geometries of the most stable conformers obtained for r- and m-DNiPAs are depicted in Figure 2. Both conformers (mv001 and rv001), in the gas phase, form an intramolecular hydrogen bond between two amide groups. The rotational isomers concerned with the pentane backbone, which corresponds to the main chain of polymer, are identified by the rotation of two CC bonds (for example, C2C1 and C1C9 for mv001). The main chain conformation of mv001 is trans-gauche (TG), whereas that of rv001 is TT. It is generally considered for vinyl polymers that a TG conformer is predominant for a partial chain with the m configuration.27 Indeed, the main chain of the stable conformers calculated for m-DNiPA tends to be TG as seen in Table S1, Supporting Information. This may be due to the steric hindrance of the amide groups. Table 3 compiles the ensemble average energies for the dimers in the gas phase calculated by eqs 1-7. ∆Frfm ) -0.56 kJ mol-1 is obtained, indicating that m-DNiPA in the gas phase is slightly more stable than r-DNiPA. The stability of m-DNiPA in the gas phase arises from the intramolecular interaction because 〈Est〉 of m-DNiPA is smaller by 2.8 kJ mol-1 than that of r-DNiPA. On the other hand, 2.2 kJ mol-1 of T∆Srfm was obtained at 298 K, suggesting that r-DNiPA is more favorable

configuration

meso

chirality

2R,4S-, 2S,4R-

2R,4R-

racemo 2S,4S-

no. of conformers Z Fb 〈Est + µGB/SA〉b 〈Est〉b 〈µGB/SA〉b

a

443(886 ) 6.70493 × 1029 -170.2503 -161.9739 -147.5465 -14.4274

360 9.75853 × 1029 -171.1807 -162.4930 -145.3752 -17.1178

360 9.75853 × 1029

difference ∆Frfmb ∆〈Etotal〉rfmb ∆〈Est〉rfmb ∆〈µGB/SA〉rfmb T∆Srfmb, c ∆Srfmd

0.9304 0.5191 -2.1713 2.6904 -0.4112 -0.001379

a Number of conformers including the atropisomers. T ) 298 K. d kJ T-1 mol-1.

b

kJ mol-1.

than m-DNiPA in terms of the conformational entropy. As a result, the absolute value of ∆Frfm in the gas phase becomes small. The most stable conformers of r- and m-DNiPA in aqueous media evaluated by the MM calculations with the GB/SA model are different from those in the gas phase as shown in Figure 2. The conformations of the main chain of mw001 and rw001 are TG and TT, respectively. This indicates that the stable conformation of the main chain in water is similar to that in the gas phase. However, the orientations of the amide groups in mw001 and rw001 are different from those in the gas phase. Their amide groups seem not to form an intramolecular hydrogen bond. It is inferred that DNiPA in water is stabilized by hydration of the amide groups. The ensemble average energies estimated for DNiPA in water are listed in Table 4. ∆Frfm is calculated to be 0.93 kJ mol-1, indicating that r-DNiPA in water is more stable than m-DNiPA. This result is in good agreement with the experimental results for the partition coefficient of DNiPA in D2O-CDCl3 described in the previous section. The ∆〈Est〉rfm value indicates that the intramolecular interaction of m-DNiPA in water is stronger than that of r-DNiPA. This tendency is similar to the result obtained for the gas phase. However, ∆〈µGB/SA〉rfm suggests that the hydration free energy of r-DNiPA is lower by 2.7 kJ mol-1 than that of m-DNiPA. The stability of r-DNiPA in water is also gained by the advantage in the conformational entropy, although the absolute value of T∆Srfm in water is smaller than that in the gas phase. Competition between Hydration and Intramolecular Interaction. To discuss the relationship between the conformation and the hydration of the dimers, a detailed analysis on µiGB/SA and Eist is carried out. In Figure 3, the values of Ei, µiGB/SA, and Eist are plotted against the ID number for the conformers of DNiPAs in the range from 1 to 32. Note that the ID of each conformer is arranged according to Ei. In this range, Ei of each conformer for r-DNiPA is smaller than that for m-DNiPA. As seen in Figure 3, the µiGB/SA and Eist values are not correlated with the ID number, i.e., the relative importance of µiGB/SA to Eist, both of which contribute to stabilize either r-DNiPA or m-DNiPA, is strongly dependent on the conformations. Thus, the contribution of µiGB/SA and Eist to the total energy can be reversed in some cases. For example, rw001 is advantageous in Eist but disadvantageous in µiGB/SA compared with mw001. On the other hand, rw002 is less stable than mw002 in terms of Eist but more stable in terms of µiGB/SA. Figure 4 depicts the conformers that have the lowest value for µiGB/SA or Eist. The

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Figure 3. Plot of Ei, µiGB/SA, and Eist versus the ID number of m- and r-DNiPA conformers obtained by MM calculations with the GB/SA method.

Figure 4. Conformers that are most advantageous for solvation (µiGB/SA) and intermolecular interaction (Eist) in an aqueous solution.

mw014 and rw002 conformers are the most preferable geometry for the hydration, whereas the mw005 and rw077 conformers give rise to the lowest energy for the intramolecular interaction. However, these conformers do not give the lowest energy in Ei. These results strongly suggest that the balance between µiGB/SA and Eist is very important for the stability of DNiPAs in an aqueous solution. For the mw005 and rw077, the neighboring amide groups seem to form an intramolecular hydrogen bond. The intramolecular hydrogen bonding in rw077 is not advantageous in terms of the hydration free energy. On the other hand, the geometry of mw005 is similar to that of mv001, although the CdO · · · H-N distance of the former is larger than that of the latter. Since Ei of mw005 is relatively low, it is inferred that m-DNiPA can

Katsumoto et al. form an intramolecular CdO · · · H-N interaction even in water. As discussed in the previous section, -2.2 kJ mol-1 of ∆〈Est〉rfm indicates that the intramolecular interaction of m-DNiPA in water is stronger than that of r-DNiPA. 3D-DF of Water Molecules Around DNiPAs. Since the GB/ SA model is one of the continuum medium models, it is not possible to depict the 3D-DF of water molecules around DNiPAs. In order to visualize their hydration structure, we employed the 3D-RISM calculation, which is a statistical mechanical theory based on a molecular picture for the solvent as well as for the solute.16 It should be of note that the force field used in the 3D-RISM calculation is different from that in the MM calculations with the GB/SA model. Although in principle the MMFF94s force field, which is used for the conformational search and energy evaluation mentioned in the previous two subsections, can also be applied to the 3D-RISM framework, we adopt another force field in performing the present 3D-RISM calculation so that we could employ the 3DRISM code without a rather tremendous modification for the interaction function form. The difference in force fields surely results in a quantitative deviation in energies, but we do not focus on this point in the present paper. The main objective of employing the 3D-RISM in this study is an observation of the 3D picture for the hydration structure around the DNiPA molecule, which is never obtained from the GB/SA calculation. The conformation search with the 3D-RISM calculation is now in progress. Figure 5 shows the isosurface representation for 3D-DF of oxygen (O) and hydrogen (H) atoms of water around DNiPAs obtained by the 3D-RISM calculation. It is clearly depicted that water molecules are not uniformly distributed around the solute. In the first hydration layer, H atoms of water come close to OdC groups while O atoms of water are located near H-N groups as shown in Figure 5b, 5d, 5f, and 5h. The isopropyl groups, however, seem not to be strongly hydrated. When the amide groups form an intramolecular hydrogen bond, formation of the first hydration layer is blocked as described in the previous section. Note that it is difficult to judge the hydrophilicity of the conformer by looking at the isosurface representation for 3D-DF. µiRISM of several conformers for m- and r-DNiPA is calculated by the 3D-RISM theory. The obtained relative solvation free energy of r-DNiPA to m-DNiPA (∆µiRISM) is compiled in Table 5, together with that estimated by the GB/SA model (∆µiGB/SA). The ∆µiRISM values show a similar tendency to ∆µiGB/SA, although the absolute values of the solvation free energy are different from each other. This indicates that the differences both in the force fields and in the methods employed in this study affect the quantity of the energy, but the qualitative tendency is not changed. It has been pointed out that the GB/ SA model suffers from inaccuracy in energetics for some systems; for example, it overestimates the binding free energy between a very large cellulose and a protein molecule by more than 150 kcal mol-1.28 For another example, the GB model is known to overestimate the stability of the salt-bridging structure of a polypeptide.29 On the contrary, 3D-RISM theory is found to be quite accurate in describing the thermodynamics or energetics of solutions including a solvation free energy.28,30 DNiPA, the solute molecule under consideration, is not so large and is nonionic. Therefore, the system treated in this study is expected to be one of such systems that the GB/SA model works relatively well for the description of the energies. The qualitative agreement between the two methods seen in Table 5 may partly reflect this aspect.

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Figure 5. Isosurface representation of the three-dimensional distribution function (3D-DF) of water oxygen (right-hand side, pink) and hydrogen (left-hand side, light blue) around m- and r-DNiPA. In each figure, the surfaces show the areas where the 3D-DF is greater than the threshold written under the picture.

TABLE 5: ∆µi Obtained by the 3D-RISM Theory and MM Calculations with the GB/SA Model ∆µi/kJ mol-1 ID mw001 mw002 mw005

rw001 rw002 rw005

GB/SA

RISM

10.98 -12.74 -1.499

7.377 -7.899 -1.290

Why are Meso-Rich PNiPAs Hydrophobic. This is because partial chains of PNiPA with the m configuration are more hydrophobic than those with the r one. The experimental and simulation results suggest that the balance between the intramolecular interaction and hydration determines the hydrophilicity of r- and m-DNiPA. In the polymer, it is presumed that the intramolecular interaction between the neighboring side chains with the m configuration is stronger than that with the r one. On the other hand, the r configuration is advantageous in terms of the hydration free energy and conformational entropy. This

can reasonably explain the effect of the diad tacticity on Tps of PNiPA in water previously reported.6-9 When the m content is smaller than 55%, Tps is almost linearly proportional to the m content.7 This observation is similar to the decrease in Tps by copolymerization of a hydrophobic monomer with NiPA. For example, Tps of poly(NiPA-co-N-secbutylacrylamide(NsBA)) linearly goes down with increasing NsBA content.31 When m < 55%, one can expect that two monomer units with the m configuration behave as one hydrophobic unit. In the range of m > 55%, however, the descent of Tps is not linearly proportional to the m ratio.7 This implies that the solubility of PNiPA in water is also influenced by the stereoregularity of three or more adjacent monomer units. It is not likely that the hydrophobicity of isotactic multimers (mm trimer or mmm tetramer, for example) can be expressed by a linear combination of that of m-DNiPA. A study on the solubility of stereocontrolled trimers or tetramers is necessary to reveal the tacticity dependence of Tps for PNiPA with m > 55% in water.

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Acknowledgment. This work was supported by the Grantin-Aid for Scientific Research (No. 21750126). Supporting Information Available: Example of atropisomers of m-DNiPA; molecular geometries of all conformers of m- and r-DNiPA obtained by the conformation search. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Shild, H. G. Prog. Polym. Sci. 1992, 17, 163. (2) Gil, E. S.; Hudson, S. M. Prog. Polym. Sci. 2004, 29, 1173. (3) Heskins, M.; Guillet, J. E. J. Macromol. Sci., Chem. 1968, A2, 1441. (4) Fujishige, S.; Kubota, K.; Ando, I. J. Phys. Chem. 1989, 93, 3311. (5) Tong, Z.; Zeng, F.; Zheng, X.; Sato, T. Macromolecules 1999, 32, 4488. (6) Suito, Y.; Isobe, Y.; Habaue, S.; Okamoto, Y. J. Polym. Sci., Part A: Polym. Chem. 2002, 40, 2496. (7) Ray, B.; Okamoto, Y.; Kamigaito, M.; Sawamoto, M.; Seno, K.; Kanaoka, S.; Aoshima, S. Polym. J. 2005, 37, 234. (8) Hirano, T.; Okumura, Y.; Kitajima, H.; Seno, M.; Sato, T. J. Polym. Sci., Part A: Polym. Chem. 2006, 44, 4450. (9) Katsumoto, Y.; Kubosaki. Macromolecules 2008, 41, 5955. (10) Koyama, M.; Hirano, T.; Ohno, K.; Katsumoto, Y. J. Phys. Chem. B 2008, 112, 10854. (11) Katsumoto, Y.; Tanaka, T.; Sato, H.; Ozaki, Y. J. Phys. Chem. A. 2002, 106, 3429. (12) Katsumoto, Y.; Tanaka, T.; Ihara, K.; Koyama, M.; Ozaki, Y. J. Phys. Chem. B 2007, 111, 12730.

Katsumoto et al. (13) Goto, H.; Osawa, E. J. Am. Chem. Soc. 1989, 111, 8950. (14) Goto, H.; Osawa, E. J. Chem. Soc., Perkin Trans. 2 1993, 187. (15) Goto, H.; Ohta, K.; Kamakura, T.; Obata, S.; Nakayama, N.; Matsumoto, T.; Osawa, T. CONFLEX; Conflex Corp.: Tokyo, Japan, 2004. (16) Hirata, F. Molecular Theory of SolVation; Kluwer: Dordrecht, 2003. (17) Perkyns, J. S.; Pettitt, B. M. Chem. Phys. Lett. 1992, 190, 626. (18) Perkyns, J.; Pettitt, B. M. J. Chem. Phys. 1992, 97, 7656. (19) Kovalenko, A.; Hirata, F. J. Chem. Phys. 1999, 110, 10095. (20) Miyata, T.; Hirata, F. J. Comput. Chem. 2008, 29, 871. (21) Miyata, T.; Ikuta, Y.; Hirata, F. J. Chem. Phys. 2010, 133, 044114. (22) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. J. Am. Chem. Soc. 1996, 118, 11225. (23) Some OPLS/AA parameters can be found in the TINKER software, see: http://dasher.wustl.edu/tinker/. (24) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269. (25) Kobayashi, M. Doctoral Thesis (in Japanese), Tokyo Institute of Technology, 2000. (26) Bulai, A.; Jimeno, M. L.; de Queiroz, A-A.A.; Gallardo, A.; Roma´n, J. S. Macromolecules 1996, 29, 3240. (27) Flory, P. J. Statistical Mechanics of Chain Molecules; Wiley: New York, 1969. (28) Yui, T.; Shiiba, H.; Tsutsumi, Y.; Hayashi, S.; Miyata, T.; Hirata, F. J. Phys. Chem. B 2010, 114, 49. (29) Zhou, R. Proteins 2003, 53, 148. (30) Imai, T.; Kovalenko, A.; Hirata, F. Chem. Phys. Lett. 2004, 395, 1. (31) Li, P.; Wang, W.; Xui, R.; Yang, M.; Ju, X.; Chu, L. Polym. Int. 2009, 58, 202.

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