Monomer Hydrophobicity as a Mechanism for the LCST Behavior of

Jens-Uwe Sommer. The Journal of Physical Chemistry B 2018 122 (1), 392-397 .... Macromolecules 0 (proofing), .... PEG-based hydrogel membrane coat...
0 downloads 0 Views 81KB Size
Download PDF
Ind. Eng. Chem. Res. 2006, 45, 5531-5537

5531

Monomer Hydrophobicity as a Mechanism for the LCST Behavior of Poly(ethylene oxide) in Water Henry S. Ashbaugh† and Michael E. Paulaitis*

Downloaded via UNIV OF TOLEDO on June 21, 2018 at 06:20:22 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

Department of Chemical and Biomolecular Engineering, Tulane UniVersity, New Orleans, Louisiana 70118, and Department of Chemical and Biomolecular Engineering, Ohio State UniVersity, Columbus, Ohio 43210

Poly(ethylene oxide) (PEO) has unlimited solubility in water at physiological temperatures over a wide range of polymer molecular weights but phase separates from aqueous solution with increasing temperature at a lower critical solution temperature (LCST). We examine the potential origins of this LCST behavior by applying recent advances in information theory modeling of hydrophobic hydration, supported by molecular simulation, and the Flory-Huggins theory of polymer solutions. We find that attractive interactions between PEO monomers and water provide the driving force for the unlimited mutual solubility at ambient temperatures. However, it is the intrinsic hydrophobicity of the PEO monomer that drives phase separation with increasing temperature. We also calculate the local densities of water oxygens and hydrogens around the ether oxygen and the carbon groups of the PEO monomer. Water structure around the carbons is found to be essentially equivalent to that for methane in water, while water structure around the ether oxygen resembles the structural features of water-water hydrogen bonding in pure liquid water. Although the latter points to water hydrogen bonding to the ether oxygen, our calculations show that attractive electrostatic interactions make a lesssubstantial contribution to the free energy of hydration of PEO compared to attractive dispersion interactions. Introduction Poly(ethylene oxide) (PEO), (-CH2CH2O-)m, is used extensively in applications requiring the biocompatibility of foreign materials in biological environments.1 Foremost among the properties that make this polymer suitable for such applications is its unlimited mutual solubility in water at physiological temperatures over a wide range of molecular weights.2 The solubility of PEO in water is striking in light of the observation that polyethers with monomers differing by only a single methylene groupsi.e., poly(methylene oxide) (PMO) and poly(propylene oxide) (PPO)sare water insoluble.2,3 The concomitant water solubility of PEO and water and the insolubility of PPO can be attributed to the greater hydrophobicity of the PPO monomer, suggesting that hydrophobic interactions play an important role in the aqueous solution behavior of these polyethers. The insolubility of PMO in water is often cited as a counterexample but follows from its much higher crystal melting temperature compared to that of PEO and other polyethers. The crystal melting temperature of PMO is 457 K compared to 342 K for PEO; other polyethers have similarly low crystal melting temperatures, e.g., 330 K for poly(tetramethylene oxide) and 347 K for poly(hexamethylene oxide).4 Although PEO is water soluble at ambient temperatures, the polymer becomes less soluble with increasing temperature until phase separation occurs at a lower critical solution temperature (LCST). This LCST also depends on the polymer chain length. Specifically, the LCST decreases with increasing chain length and approaches an asymptote near the normal boiling temperature of water for polymer molecular weights greater than ∼104 g/mol.5,6 The LCST behavior of aqueous PEO solutions has attracted a great deal of theoretical attention due to its technological significance in protein purification and crystallization7 * Corresponding author. Ohio State University. E-mail: Paulaitis.1@ osu.edu. Tel.: (614) 247-8847. Fax: (614) 292-3769. † Tulane University. E-mail: [email protected].

and in applications of the polymer brush properties of PEO film coatings.8 However, no consensus on the molecular mechanism for phase separation has emerged.3,9 Kjellander and Florin2 analyzed the PEO chain-length dependence of the LCST by fitting experimental values for the LCST to a free-energy expression formally identical to the Flory-Huggins equation but with a temperature-dependent Flory interaction parameter. They found unfavorable entropy and favorable enthalpy contributions to the Flory parameter and interpreted the unfavorable entropy contribution as a net loss in configurational entropy associated with waters of hydration minus the gain in configurational entropy of the polymer chain. Since the configurational entropy of the polymer chain depends on chain length, a qualitative explanation for the PEO chainlength dependence of the LCST follows from the higher favorable configurational entropy of the shorter chains. Interestingly, it was also noted that the unfavorable entropy and favorable enthalpy contributions to the Flory parameter are also signatures of hydrophobic interactions. A similar temperature dependence for the hydration thermodynamics of dimethoxy ether has also been cited as a component to the aqueous phase behavior of PEO.10 Karlstro¨m et al.11-13 proposed a mechanism for LCST behavior based on favorable electrostatic interactions between PEO and water coupled to temperature-dependent changes in the local polymer conformation. This mechanism was motivated by the observation that the preferred gauche conformation of the OCCO dihedral angle of PEO in water at ambient temperatures has a large local dipole moment and that the temperature dependence of this gauche preference decreases with increasing temperature. Thus, favorable electrostatic interactions with water at ambient temperatures become less significant at higher temperatures as the polymer populates on average conformations with lower local dipole moments, and as a result, phase separation occurs with increasing temperature. Thermodynamic models based on hydrogen bonding between PEO and water have also been proposed to explain the LCST behavior.14-16 Matsuyama and Tanaka14 applied a Flory-

10.1021/ie051131h CCC: $33.50 © 2006 American Chemical Society Published on Web 02/18/2006

5532

Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006

Huggins free-energy expression with chemical association to fit the experimental temperature-composition phase diagrams for mixtures of water and PEO of different molecular weights. They found that phase separation occurs in their model because hydrogen bonds between the ether oxygens of PEO and water break with increasing temperature. A recent extension16 of this model also takes into account water-water hydrogen bonding to give more realistic values for the hydrogen bonding interaction parameters as well as the temperature dependence of the Flory parameter for non-hydrogen-bonding interactions. This improved model assumes, however, a temperature-dependent Flory parameter characteristic of nonassociating polymers that does not admit hydrophobic interactions. We show here that dimethyl ether (DME) (CH3OCH3), which we take to represent the PEO monomer, exhibits a solubility minimum in water with increasing temperature, albeit at temperatures above the normal boiling point of water. This solubility minimum is similar to the solubility minimum exhibited by simple nonpolar gases and liquid hydrocarbons in water as a function of temperature17,18 and is often cited as providing the thermodynamic driving force for protein unfolding with decreasing as well as increasing temperature19 and the temperature minimum observed in the critical micelle concentration of both ionic and nonionic surfactants in aqueous solution.20,21 Thus, DME, or equivalently the monomer of PEO, can be thought of as an intrinsically hydrophobic species. Polymerization to form PEO reduces the mixing entropy of the monomers, allowing this intrinsic hydrophobicity to dominate the solubility behavior and drive phase separation at elevated temperatures. At ambient temperatures, the unlimited miscibility of PEO and water is driven by strong attractive interactions between the monomer and water, whereas the hydrophobicity of the monomer is the primary driving force for phase separation at a LCST. Theoretical Considerations The thermodynamic quantity of central importance in our analysis is the hydration free energy or excess chemical potential of the solute in aqueous solution. The excess chemical potential, µ/s , is related to the chemical potential of the solute in aqueous solution by

µs ) kT ln(FsΛs3/qs) + µ/s

(1)

where kT is the thermal energy, Fs is the solute number density in solution, Λs is the thermal de Broglie wavelength, and qs is the internal partition function of the solute. By convention we have adopted the standard state of Ben-Naim22 in which the solute excess chemical potential in the liquid is measured relative to the chemical potential of the solute in a vacuum. The distribution of solute between aqueous solution and the ideal gas is directly related to this excess chemical potential by

βµ/s ) -ln(Fs/FIG s ) ≡ -ln Keq

(2)

where β ) 1/kT and Keq is the Ostwald partition coefficient. The excess chemical potential can be separated into two contributions: the free energy for creating a cavity in water large enough to accommodate the excluded volume of the solute and the free energy associated with attractive solute-water intermolecular interactions.17 The free energy of cavity formation in water is derived here from an information theory model of hydrophobic hydration.23 In the context of this model, cavity

formation is tied to Gaussian fluctuations in the water density as determined by the water-water pair correlation function. In the context of perturbation theory, nonspecific van der Waals interactions can be treated in a mean-field sense as being linear with respect to the solvent density. To an excellent approximation then, the excess chemical potential of simple nonpolar solutes in water at infinite dilution is given by24 2 βµ/∞ cav ) a + bFw

(3a)

βµ/∞ vdW ) c/T + dFw/T

(3b)

/∞ /∞ 2 βµ/∞ s ) βµcav + βµvdW ) a + bFw + c/T + dFw/T

(3c)

where Fw is the number density of water. The first two terms in eq 3c correspond to the free energy of cavity formation where the parameters a and b correlate with the molecular size of the solute and the compressibility of liquid water (water density fluctuations), respectively. The last two terms correspond to the free-energy contribution due to solute-water attractive interactions. For a cavity-like, purely repulsive solute in water (c ) d ) 0), eq 3c predicts a maximum in βµ/∞ s that corresponds to a solubility minimum at 277 K, the density maximum of pure liquid water. The effect of adding attractive solute-water interactions is to shift this solubility minimum to higher temperatures. We analyze the LCST behavior for aqueous PEO solutions by applying eq 3 to calculate the temperature dependence of the excess chemical potential of dimethyl ether. To draw a connection between this excess chemical potential and the LCST, we consider the effect on solution thermodynamic properties of polymerizing the monomer to form PEO. FloryHuggins theory provides a first-order approximation to the effect of polymerization on mixture thermodynamics. In FloryHuggins theory, the free energy of a mixture of PEO (subscript p) and water (subscript w) is given by25

βAFH ) Np ln Φp + Nw ln Φw + χpwrNpΦw +

χppr NΦ + 2 p p χww N Φ (4) 2 w w

where Ni and Φi are, respectively, the number and volume fractions of species i, r is the ratio of the polymer to water molar volumes, and χij is the Flory interaction parameter for pairs of monomeric units of species i and j. The criterion for phase separation is

[

χ ≡ χpw -

]

(χpp +χww) (1 + r1/2)2 g 2 2r

(5)

where the equality holds for critical phase separation. Equation 5 assumes that χ is independent of concentration, which is an approximation for aqueous PEO solutions.6 For nonassociating polymer solutions, χ typically decreases with increasing temperature, and thus, phase separation only occurs with decreasing temperaturesi.e., at an upper critical solution temperature (UCST). More complex functions of temperature can be obtained depending on the temperature dependence of the individual χij for each ij pair. Below, we examine the temperature dependence of these individual interaction parameters that leads to LCST behavior. We start by deriving expressions for the Flory interaction parameters of the pure polymer and pure liquid water in terms

Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006 5533

of their excess chemical potentials. From eq 4 and standard thermodynamic relations,

βµ/pure p )

χpp r 2

(6a)

βµ/pure w )

χww 2

(6b)

and

From eq 2, the excess chemical potential of a pure component is given as / βµpure i ) ln

vap Fpure i

(7)

liq Fpure i

along the saturation curve where the vapor phase is assumed to be an ideal gas. The right-hand side of eq 7 is negative and a monotonically increasing function of temperature, since the latent heat of condensation is negative. Thus, the interaction parameters for the pure components make positive contributions to χ, which decreases monotonically with temperature such that only a UCST can be obtained. For LCST behavior then, χpw must be an increasing function of temperature. To obtain this interaction parameter, we derive the excess chemical potential for the polymer at infinite dilution in water from eq 4,

βµ/∞ p

(

)

χww ) ln r - (1 - r) + χpw r 2

Ucav(r) )

{

ULJ(r) +  r e 21/6σ 0

r > 21/6σ

(10)

where ULJ is the LJ potential function and σ and  are the LJ diameter and well depth, respectively. The cavity free energy was determined using a coupling parameter, λ, that linearly scaled σ and  from 0 (no cavity) to 1 (full cavity-water interactions). These simulations were carried out in twenty stages corresponding to λ values between 0.025 and 0.975 in increments of 0.05 with perturbations of ∆λ ) (0.025. The cavity hydration free energy was evaluated as 20

(8)

and then apply eq 3 with the parameters for dimethyl ether to calculate βµ/∞ p . The criterion for critical phase separation is obtained from eq 5,

βµ/∞ (1 + r1/2)2 DME - ln rDME - rDME + 1 ) rDME 2r

mean combining rule. Electrostatic interactions were calculated using the generalized reaction field method.31,32 Both LJ and electrostatic interactions were truncated at 9 Å. To calculate the hydration free energy of DME from simulation, the chemical potential was separated into three contributions corresponding to excluded volume interactions, dispersion/van der Waals interactions, and electrostatic interactions. The first contribution is given by the free energy of cavity formation in water, while the last two are due to solute-water attractive interactions. The excluded volume contribution was calculated as the work required to grow a DME-shaped cavity into water. Cavity-water interactions were evaluated assuming the Weeks-Chandler-Andersen (WCA) separation of LJ interactions33 for the interaction of water with each heavy-atom solute site

(9)

where µ/∞ DME and rDME are the excess chemical potential and volume ratio of DME, respectively. We have assumed here that χpp can be neglected relative to χww and χpw since the magnitude of water-water and water-polymer interactions are expected to be stronger than those between the monomeric units of PEO. The assumption that |χww| . |χpp| is consistent with the experimental observation that the boiling and critical temperatures of dimethyl ether, -24 °C and 127 °C, respectively, are well below those of water: 100 °C and 374 °C. Simulation Methods. Canonical ensemble Monte Carlo (MC) simulations of a single DME molecule in a periodic box of 215 water molecules were performed over a range of temperatures from 260 to 480 K in increments of 20 K. The water density corresponding to each temperature was set to the density of pure liquid water along the saturation curve26 and extrapolated into the supercooled region.27 Each simulation consisted of 50 000 MC passes for equilibration, followed by 500 000 MC passes for calculating thermodynamic averages (one MC pass is equivalent to one attempted move for each molecule in the simulation box). Water was modeled using the SPC/E potential,28 which provides an accurate description of water’s thermodynamic properties over a wide range of temperatures.29 DME united-atom Lennard-Jones (LJ) parameters, bond lengths, and bond angles were taken from the potential model for alkyl ethers developed by Briggs et al.30 The DME-water cross LJ interaction parameter was obtained by applying the geometric

µ/cav

)

* * [∆µcav (λi + ∆λ) - ∆µcav (λi - ∆λ)] ∑ i)1

(11)

where34

∆µ/cav(λi ( ∆λ) ) -kT ln〈exp{-β[Ucav(λi ( ∆λ) Ucav(λi)]}〉i (12) and the subscripted brackets 〈‚‚‚〉i indicate averaging over configurations generated at the fixed value, λi. Attractive dispersion interactions in the WCA separation are given by

Udisp(r) ) ULJ(r) - Ucav(r)

(13)

The hydration free-energy contribution from these interactions was determined in a manner analogous to the cavity hydration free energy, except that the coupling parameter directly scaled the dispersion interactions as λUdisp(r). Electrostatic contributions to the hydration free energy were determined by expressing the exponential in eq 12 as a cumulant expansion. When the dimethyl ether charges are scaled linearly by λ, the following expression for the electrostatic charging free energy,

1 µ/elec(λ ) 0f1) ) (〈V〉1/2-1/x12 + 〈V〉1/2 + 1/x12) (14) 2 is exact to fourth order.35 Here, V is the electrostatic interaction energy between the dimethyl ether and water. When this expression is applied to charging a water molecule in water, the electrostatic contribution to the hydration free energy is indistinguishable within the statistical uncertainties of the simulation from that determined by including higher-order terms in the expansion. We therefore expect this expression to work well for DME, since electrostatic interactions are weaker for DME than for water. Rather than quantifying structure using standard radial distributions, we use proximal correlations, which provide a

5534

Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006

more accurate representation of the local solvent ordering. Proximal pair correlation functions for water oxygens and hydrogens around the ether oxygen and methyl groups of DME are used to describe the hydration water structure around the solute. The proximal correlation function for a solute consisting of n equivalent sites is defined in terms of the conditional probability of finding a water molecule at rw given that the n solute sites are located at (r1, ..., rn),

F(rw|r1,...,rn) ≈ Fwgprox(|ri - rw|)

(15)

with i such that |ri - rw| ) minj)1,...,n|ri - rw|. The proximal correlation function, gprox(r), characterizes the local density of water oxygens and hydrogens around site i relative to the bulk water density. Proximal correlation functions and their determination from simulation are discussed in detail elsewhere.36-40 Our objective in calculating these proximal correlation functions is to compare the hydration water structure around the methyl groups of dimethyl ether to that around a single methane molecule in water and the hydration water structure around the ether oxygen of dimethyl ether to that around the oxygen atom of a single water molecule in water to gain insight, respectively, into the hydrophobic and hydrogen-bonding character of this hydration water structure. For the general case, where the n solute sites are not equivalent, eq 15 can be generalized as

F(rw|r1,...,rn) ≈ Fwgprox,i(|ri - rw|)

(16)

with i such that (|ri - rw| - Ri) ) minj)1,...,n(|rj - rw| - Rj), where Ri is the effective radius of site i and gprox,i(r) is the proximal correlation function for site i. The effective radius for a particular site is determined iteratively as the radius at which the proximal correlation function for that site first equals ones i.e., gprox,i(Ri) ) 1salthough alternate definitions can be applied. In general, the proximal correlation functions are distinct from the standard radial distribution functions. The differences between these two measures of hydration structure result from the incorporation of excluded volume information for polyatomic solutes into the radial distribution functions. The definition of the proximal correlation function avoids this by following the contour of the solute surface. Previous simulation studies have demonstrated that the proximal correlation functions are insensitive to the solute topology and are determined, in large part, by the solute site functionality.36-40 We presently quantify the hydration structure near dimethyl ether using the proximal correlation function to untangle the different chemical functionalities of the solute. Results and Discussion In Figure 1, βµ/∞ s obtained from simulation is plotted as a function of temperature. At low temperatures, βµ/∞ s is negative, indicating a high solubility in water, but changes sign with increasing temperature and exhibits a maximum (solubility minimum) at a temperature above the normal boiling temperature of water. The chemical potential determined from simulation differs from that determined from the experimental solubility of DME in water at 25 °C by only ∼1 kT.41,42 Our simulation results are also in good quantitative agreement with the results reported by Sanchez and co-workers for DME hydration over a comparable temperature range.43 The solid curve in this figure is a fit of βµ/∞ s to eq 3 with a ) -7.04 ( 0.17, b ) 21 000 ( 180 Å,6 c ) 2 200 ( 180 K, and d ) -233 000 ( 6 000 Å3K, where error bars are reported as one standard deviation. The excellent fit gives us confidence that

Figure 1. Solution thermodynamics of dimethyl ether in water as a function of temperature. The symbols denote the following: open circlessβµ/s for dimethyl ether at infinite dilution in water; filled circlessexcluded volume contribution to βµ/s ; filled trianglesscontribution to βµ/s due to dimethyl ether-water attractive LJ interactions; open trianglesscontribution to βµ/s due to both LJ and electrostatic attractive interactions; and filled squaress experimental value of -βµ/s for dimethyl ether at infinite dilution in water determined from solubility measurements.40,41 The lines denote the following: the long dashed curve is the fit of βµ/cav using eq 3a (a ) -7.04 ( 0.17 and b ) 21 000 ( 180 Å6); the short dashed curve is the fit of βµ/vdW using eq 3b (c ) 2 200 ( 180 K and d ) -233 000 ( 6 000 Å3‚K); and the solid curve is a fit of βµ/s using eq 3c.

we can use eq 3 with these parameters to calculate separately those contributions corresponding to the free energy of cavity formation (eq 3a) and dimethyl ether-water attractive interactions (eq 3b). Indeed, we observe that the simulation results for βµ/cav are in close agreement with the values calculated from eq 3a. We also note that eliminating the attractive interactions increases the chemical potential and shifts its maximum value (i.e., solubility minimum) to ∼280 K, which is close to the density maximum of liquid water as predicted by the information theory model of hydrophobic hydration. The expression for the attractive energetic contribution to the free energy (eq 3b) is likewise in close agreement with dimethyl ether-water attractive (dispersion plus electrostatic) interactions obtained from simulation. Also plotted in this figure are the simulation results for the attractive dispersion interactions, not incorporating electrostatic interactions. We see that these interactions make the major contribution to the total interaction free energy, while electrostatic interactions account for a smaller fraction (∼30%) of the total interaction free energy. The last observation suggests that hydrogen bonding, which is dictated by electrostatic interactions in the context of this model, plays only a minor role in the hydration of dimethyl ether, or equivalently, the PEO monomer. Hydrogen bonding between PEO oligomers and water, however, has been extensively explored and correlated with the solution behavior of the polymer.44 To examine hydrogen bonding and the hydration structure near DME, we compare water oxygen and hydrogen proximal correlation functions for the two methyl groups and the ether oxygen to those for a single methane molecule and a single water molecule in water. Figure 2a and b compare water oxygens and hydrogens, respectively, around the methyl groups of DME and a single methane at 300 K. We see that the hydration water structure is largely unaffected by the charge on the methyl groups and connectivity of the methyl groups of DME to the ether oxygen and is essentially equivalent to that around methane. The methyl groups of DME are hydrated as if they were an isolated hydrophobic methanes in water. We would

Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006 5535

Figure 3. Lower critical solution temperatures for aqueous poly(ethylene oxide) solutions as a function of polymer molecular weight. The open and filled triangles are experimental values from Sakei et al.5 and Bae et al.6 The curve is predicted using eq 9 with rDME equal to 2.14 evaluated from the room-temperature densities of PEO (1.14 g/cm3) and water (0.997 g/ cm3). The filled circle indicates the predicted minimum polymer molecular weight for which phase separation occurs (degree of polymerization of 18 and a critical temperature of 441 K).

Figure 2. Correlation functions for ether, methane, and water in water at 300 K obtained from simulation. The individual figures from top to bottom show (a) proximal correlation between water oxygens and the methyl groups of dimethyl ether (solid curve) and the radial distribution function of water oxygens about a solitary methane (dashed curved); (b) proximal correlation between water hydrogens and the methyl groups of dimethyl ether (solid curve) and the radial distribution function of water hydrogens about a solitary methane (dashed curved); (c) proximal correlation between water oxygens and the dimethyl ether oxygen (solid curve) and the radial distribution function of water oxygens about the water oxygen (dashed curved); and (d) proximal correlation between water hydrogens and the dimethyl ether oxygen (solid curve) and the radial distribution function of water hydrogens about the water oxygen (dashed curved).

not expect this conclusion to change if a second methyl group is added at the ends of dimethyl ether to mimic the polymerization of the monomer to form PEO.36 In Figure 2c and d, the water oxygen and hydrogen proximal correlation functions with the ether oxygen are compared to the radial distribution functions for water at 300 K. The water oxygen-ether oxygen proximal correlation function (Figure 2c) is sharply peaked at r ) 2.8 Å, in agreement with the water oxygen-oxygen radial distribution function. Similar qualitative comparisons can be made for the water hydrogen correlations. Notably, the water hydrogen-ether oxygen proximal correlation function displays two split peaks, as observed in the water hydrogen-water oxygen radial distribution function (Figure 2d). The comparison allows us to identify the primary peak in the water hydrogen-ether oxygen proximal correlation function at ∼2 Å as that associated with water hydrogen bonding to the ether oxygen. The secondary peak at ∼3.2 Å indicates hydrogens from waters in the primary hydration that are available for hydrogen bonding with outer shell waters. The same analysis with increasing temperature gives a qualitatively similar picture, though the extent of hydrogen bonding diminishes in agreement with previous studies.44 We conclude that water hydrogen bonding to the ether oxygen of dimethyl ether, or equivalently, the ether oxygen of the PEO monomer, is an intrinsic feature of the hydration water structure. However, the smaller role electrostatic contributions play relative to dispersion interactions (Figure 1) and the similar temperature dependence of these contributions over the broad temperature range explored indicate a more passive role for hydrogen bonding in the LCST behavior of aqueous PEO solutions which can be lumped into a single van der Waals-like expression. This conclusion is supported by the success of eq 3b in accurately capturing the temperature dependence of the hydration free energy of dimethyl ether in Figure 1. Below, we consider how the solubility minimum for dimethyl ether in water gives rise to LCST behavior for PEOwater solutions. The molecular weight dependence of the LCST for PEO in water predicted using eq 9 is shown in Figure 3. Overall, the predicted phase behavior is in semi-quantitative agreement with the experimental observation. The predicted asymptotic value of the LCST in the limit of infinite polymer chain length is

5536

Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006

388 K, in reasonable agreement with the experimental value of 372 K for a PEO molecular weight of 106 g/mol.5,6 Moreover, the predictions and the experimental results both indicate that phase separation occurs only when the polymer chain length reaches a critical value. The shortest PEO chain length for which LCST behavior has been measured is 49, which is approximately three times greater than the critical chain length predicted using eq 9. The discrepancy can be attributed to several assumptions that were made in the implementation of Flory-Huggins theory. For example, the assumption of an infinitely dilute polymer solution is less likely to hold as the polymer chain length decreases. Moreover, the assumption of a concentrationindependent Flory interaction parameter is known to lead to differences between predicted and measured phase envelopes associated with the LCST. We also neglected certain solution interactions, most notably the contribution due to direct monomer-monomer interactions. Indeed, fitting the experimental LCST curve to get χpp yields values that are small in magnitude, as expected, but physically reasonable, and it improves the agreement with the experiment by lowering the critical PEO chain length for LCST behavior while shifting the corresponding LCST to high temperatures (results not shown). Clearly, these assumptions need to be sorted out, although their impact on the predicted LCST behavior in Figure 3 is not expected to change the underlying physical picture or the central role that monomer hydrophobicity plays in the phase separation. Conclusions Despite structural features in the proximal correlation functions which point to hydrogen bonding, the calculations presented here indicate that the hydration free-energy contribution attributed to attractive electrostatic interactions is smaller in magnitude than that for attractive Lennard-Jones dispersion interactions between DME and water. Thus, while the hydrogenbonding structure may reflect the thermodynamics underlying the LCST behavior of PEO in water, the present analysis suggests that the intrinsic hydrophobicity of the PEO monomer alone is sufficient to induce phase separation with increasing temperature. We note that LCST phase behavior has been observed in asymmetric tetraalkylammonium salts in aqueous solution, which are unable to participate in hydrogen bonding with water and for which hydrophobic effects clearly play a significant role in their hydration.45-47 Although this study has not addressed the issue of how conformational changes with temperature might drive phase separation, several examples can be given suggesting that, while conformational changes with increasing temperature occur, they are not the thermodynamic driving force for phase separation. For example, tetrahydrofuran exhibits a solubility minimum in water with increasing temperature and a LCST at 70-72 °C.48,49 However, despite its chemical similarity to PEO, the ability of tetrahydrofuran to undergo conformational changes is prohibited by its ring structure. Butoxyethanol is also chemically related to PEO and has a LCST in water of 42 °C.50 The molecular length of butoxyethanol is, however, much shorter than the chain length for PEO oligomers, which are completely miscible in water at this temperature. In addition, aqueous tetrahydrofuran or butoxyethanol solutions phase separate at temperatures well below the normal boiling point of water in contrast to the case of aqueous PEO solutions. The primary difference between these solutes and PEO is that they have a greater number of nonpolar methylene groups per ether oxygen. From the perspective of the mechanism for phase separation based on hydrophobic hydration considered here, the LCSTs of tetrahydrofuran and

butoxyethanol are shifted to lower temperatures as a consequence of the greater hydrophobicity of these species compared to that of PEO. Acknowledgment H.S.A. gratefully acknowledges support from an ORAU Ralph E. Powe Award. Financial support from the National Science Foundation (CTS-0078491) is also gratefully acknowledged (M.E.P.). This research has benefited from conversations with Eric Kaler, Lawrence Pratt, and Dilipkumar Asthigiri. The good company of Ed Glandt during many annual meetings of the Mid-Atlantic Thermodynamics Conference is warmly acknowledged. Literature Cited (1) Zalipsky, S.; Harris, J. M. Introduction to chemistry and biological applications of poly(ethylene glycol). ACS Symp. Ser. 1997, 680, 1. (2) Kjellander, R.; Florin, E. Water-structure and changes in thermalstability of the system poly(ethylene oxide)-water. J. Chem. Soc., Faraday Trans. 1 1981, 77, 2053. (3) Israelachvili, J. The different faces of poly(ethylene glycol). Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 378. (4) Wunderlich, B. Macromolecular Physics, Vol. 3 Crystal Melting; Academic Press: New York, 1980. (5) Sakei, S.; Kuwahara, N.; Nakata, M.; Kaneko, M. Upper and lower critical solution temperatures in poly (ethylene glycol) solutions. Polymer 1976, 17, 685. (6) Bae, Y. C.; Lambert, S. M.; Soane, D. S.; Prausnitz, J. M. Cloudpoint curves of polymer solutions from thermooptic measurements. Macromolecules 1991, 24, 4403. (7) Kulkami, A. M.; Chatterjee, A. P.; Schweizer, K. S.; Zukoski, C. F. Effects of poly(ethylene glycol) on protein interactions. J. Chem. Phys. 2000, 113, 9863. (8) Elbert, D. L.; Hubbell, J. A. Surface treatments of polymers for biocompatibility. Annu. ReV. Mater. Sci. 1996, 26, 365. (9) Halperin, A.; Leckband, D. E. From ship hulls to contact lenses: Repression of protein adsorption and the puzzle of PEO. C.R. Acad. Sci. IV Phys. 2000, 365. (10) Smith, G. D.; Bedrov, D. Roles of enthalpy, entropy, and hydrogen bonding in the lower critical solution temperature behavior of poly(ethylene oxide)/water solutions. J. Phys. Chem. B 2003, 107, 3095. (11) Karlstro¨m, G. A new model for upper and lower critical solution temperatures in poly(ethylene oxide) solutions. J. Phys. Chem. 1985, 89, 4962. (12) Engkvist, O.; Karlstro¨m, G. A Monte Carlo simulation study of the temperature dependence for the conformation distribution of 1,2dimethoxyethane in water. J. Chem. Phys. 1997, 106, 2411. (13) Bedrov, D.; Borodin, O.; Smith, G. D. Molecular dynamics simulations of 1,2-dimethoxyethane/water solutions. 1. Conformational and structural properties. J. Phys. Chem. B 1998, 102, 5683. (14) Matsuyama, A.; Tanaka, F. Theory of solvation-induced reentrant phase separation in polymer solutions. Phys. ReV. Lett. 1990, 65, 341. (15) Bekiranov, S.; Bruinsma, R.; Pincus, P. Solution behavior of poly(ethylene oxide) in water as a function of temperature and pressure. Phys. ReV. E 1997, 55, 577. (16) Dormidontova, E. E. Role of competitive PEO-water and waterwater hydrogen bonding in aqueous solution PEO behavior. Macromolecules 2002, 35, 987. (17) Pollack, G. L. Why gases dissolve in liquids. Science 1991, 251, 1323. (18) Economou, I. G.; Tsonopoulos, C. Associating models and mixing rules in equations of state for water/hydrocarbon mixtures. Chem. Eng. Sci. 1997, 52, 511. (19) Brandts, J. F. The thermodynamics of protein denaturation. I. The denaturation of chymotrypsinogen. J. Am. Chem. Soc. 1964, 86, 4291. (20) Chen, L. J.; Lin, S. Y.; Huang, C. C. Effect of hydrophobic chain length of surfactants on enthalpy-entropy compensation of micellization. J. Phys. Chem. B 1998, 102, 4350. (21) Chen, L. J.; Lin, S. Y.; Huang, C. C.; Chen, E. M. Temperature dependence of critical micelle concentration of polyoxyethylenated nonionic surfactants. Colloids Surf., A 1998, 135, 175. (22) Ben-Naim, A.; Marcus, Y. Solvation thermodynamics of nonionic solutes. J. Chem. Phys. 1984, 81, 2016.

Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006 5537 (23) Hummer, G.; Garde, S.; Garcı´a, A. E.; Paulaitis, M. E.; Pratt, L. R. An information theory model of hydrophobic interactions. J. Phys. Chem. B 1998, 102, 10469. (24) Garde, S.; Garcı´a, A. E.; Pratt, L. R.; Hummer, G. Temperature dependence of the solubility of nonpolar gases in water. Biophys. Chem. 1999, 78, 21. (25) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953. (26) Sandler, S. I. Chemical and Engineering Thermodynamics, third ed.; Wiley and Sons: New York, 1998. (27) Hare, D. E.; Sorensen, C. M. Densities of supercooled H2O and D2O in 25-micron glass capillaries. J. Chem. Phys. 1986, 84, 5085. (28) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The missing term in effective pair potentials. J. Phys. Chem. 1987, 91, 6269. (29) Alejandre, J.; Tildesley, D. J.; Chapela, G. A. Molecular dynamics simulation of the orthobaric densities and surface tension of water. J. Chem. Phys. 1995, 102, 4574. (30) Briggs, J. M.; Matsui, T.; Jorgensen, W. L. Monte Carlo simulations of liquid alkyl ethers with the OPLS potential functions. J. Comput. Chem. 1990, 11, 958. (31) Hummer, G.; Soupasis, D. M.; Neumann, M. Computer simulation of aqueous Na-Cl electrolytes. J. Phys. Cond. Mater. 1994, 6, A141. (32) Hummer, G.; Pratt, L. R.; Garcı´a, A. E. Hydration free energy of water. J. Phys. Chem. 1995, 99, 14188. (33) Weeks, J. D.; Chandler, D.; Andersen, H. C. Role of repulsive forces in determining the equilibrium structure of simple liquids. J. Chem. Phys. 1971, 54, 5237. (34) Zwanzig, R. High-temperature equation of state by a perturbation method. I. Nonpolar gases. J. Chem. Phys. 1954, 22, 1420. (35) Hummer, G.; Szabo, A. Calculation of free-energy differences from computer simulations of initial and final states. J. Chem. Phys. 1996, 105, 2004. (36) Ashbaugh, H. S.; Paulaitis, M. E. Entropy of hydrophobic hydration: Extension to hydrophobic chains. J. Phys. Chem. 1996, 100, 1900. (37) Ashbaugh, H. S.; Garde, S.; Hummer, G.; Kaler, E. W.; Paulaitis, M. E. Conformational equilibria of alkanes in aqueous solution: Relationship to water structure near hydrophobic solutes. Biophys. J. 1999, 77, 645. (38) Ashbaugh, H. S.; Paualitis, M. E. Effect of solute size and solutewater attractive interactions on hydration water structure around hydrophobic solutes. J. Am. Chem. Soc. 2001, 123, 10721. (39) Ashbaugh, H. S.; Pratt, L. R.; Paulaitis, M. E.; Clohecy, J.; Beck, T. L. Deblurred observation of the molecular structure of an oil-water interface. J. Am. Chem. Soc. 2005.

(40) Garde, S.; Hummer, G.; Garcı´a, A. E.; Pratt, L. R.; Paulaitis, M. E. Hydrophobic hydration: Inhomogeneous water structure near nonpolar molecular solutes. Phys. ReV. E 1996, 53, R4310. (41) Hine, J.; Weimar, R. D. Carbon basicity. J. Am. Chem. Soc. 1965, 87, 3387. (42) Hine, J.; Mookerjee, P. K. Structural effects on rates and equilibriums. XIX. Intrinsic hydrophilic character of organic compounds. Correlations in terms of structural contributions. J. Org. Chem. 1975, 40, 292. (43) Stone, M. T.; Veld, P. J. I. t.; Lu, Y.; Sanchez, I. C. Hydrophobic/ hydrophilic solvation: Inferences from Monte Carlo simulations and experiments. Mol. Phys. 2002, 100, 2773. (44) Smith, G. D.; Bedrov, D.; Borodin, O. Molecular dynamics simulation study of hydrogen bonding in aqueous poly(ethylene oxide) solutions. Phys. ReV. Lett. 2000, 85, 5583. (45) Kleemeier, M.; Schro¨er, W.; Weinga¨rtner, H. Critical behavior of the ionic system n-propyl-tri-n-butylammonium iodide plus water near its upper and lower consolute point. J. Mol. Liq. 1997, 73, 74, 501. (46) Weinga¨rtner, H. (Liquid plus liquid) phase equilibria in electrolyte solutions. Effect of pressure on closed-loop behavior of (a tetra-alkylammonium salt plus water). J. Chem. Thermodyn. 1997, 29, 1409. (47) Weinga¨rtner, H.; Klante, D.; Schneider, G. M. High-pressure liquid-liquid immiscibility in aqueous solutions of tetra-n-butylammonium bromide studied by a diamond anvil cell technique. J. Solution Chem. 1999, 28, 435. (48) Sorensen, C. M. Dynamic light-scattering study of tetrahydrofuran and water solutions. J. Phys. Chem. 1988, 92, 2367. (49) Oleinikova, A.; Weinga¨rtner, H. Liquid-liquid coexistence curves of re-entrant phase transitions beyond the asymptotic range: Tetrahydrofuran plus water and tetrahydrofuran plus heavy water. Phys. Chem. Chem. Phys. 2002, 4, 955. (50) Koehler, R. D.; Schubert, K.-V.; Strey, R.; Kaler, E. W. The Lifshitz line in binary-systems: Structures in water/C4E1 mixtures. J. Chem. Phys. 1994, 101, 10843.

ReceiVed for reView October 10, 2005 ReVised manuscript receiVed January 11, 2006 Accepted January 17, 2006 IE051131H