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Computational Calorimetry of PNIPAM Cononsolvency in Water/Methanol Mixtures Cahit Dalgicdir, Francisco Rodriguez-Ropero, and Nico F. A. van der Vegt J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b05960 • Publication Date (Web): 21 Jul 2017 Downloaded from http://pubs.acs.org on July 22, 2017

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The Journal of Physical Chemistry

Computational Calorimetry of PNIPAM Cononsolvency in Water/Methanol Mixtures Cahit Dalgicdir,† Francisco Rodr´ıguez-Ropero,†,‡ and Nico F. A. van der Vegt∗,† †Eduard-Zintl-Institut f¨ ur Anorganische und Physikalische Chemie, Center of Smart Interfaces, Technische Universit¨ at Darmstadt, Germany ‡Current address: Department of Physics and Center of Molecular Study of Soft Condensed Matter, Illinois Institute of Technology, Chicago, Illinois 60160, USA E-mail: [email protected]

Abstract We revisit the mechanism for cononsolvency of PNIPAM in water/methanol mixtures. Using extensive molecular dynamics simulations we calculate the calorimetric enthalpy of the PNIPAM collapse transition and observe a unique fingerprint of PNIPAM cononsolvency which is analysed in terms of microscopic interactions. We find that polymer hydration is the determining factor for PNIPAM collapse in the cononsolvency regime. In particular, it is shown that methanol frustrates the ability of water to form hydrogen bonds with the amide proton and therefore causes polymer collapse.

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Introduction Poly(N-isopropylacrylamide) (PNIPAM) is soluble in water as well as in methanol, however it becomes insoluble when these two good solvents are mixed in a certain range of methanol concentrations. This intriguing phenomenon is called cononsolvency. Although it has been known for many years, 1–3 its molecular-level explanation 4–9 remains incomplete and has led to some controversy in the recent literature. 10,11 There have been several ideas reported in the literature on the molecular origin of this phenomenon. Okada and Tanaka proposed a cooperative hydration mechanism in which the formation of a amide-water hydrogen bond (H-bond) facilitates the formation of further polymer-water H-bonds. 12 As a result of this cooperativity, the chain collapses very fast when the temperature is increased and these H-bonds are broken. Tanaka extended this model by assuming that methanol molecules, due to competitive hydrogen bonding with the polymer, interfere with the cooperativity of hydration. As a results of this competition, the total solvent coverage of the chain passes through a minimum in a certain methanol concentration range leading to chain collapse. 5,13,14 Related to these ideas, Pica and Graziano recently conjectured that methanol interaction with PNIPAM leads to a geometric frustration in which the overall number of solvent H-bonds with the polymer decreases and the polymer collapses. 9 Based on molecular dynamics (MD) simulations with a generic polymer and solvent model, Mukherji et al. proposed that the cononsolvency phenomenon is instead driven by strong methanol interactions with the polymer. 7 The MD simulations performed with this model, in which polymer-water interactions are repulsive and polymer-methanol interactions are attractive, show that the polymer chain collapses due to sticky methanolbridging interactions between distant monomers along the chain. Polymer coil-to-globule collapse can however also be predicted without assuming strong methanol interactions with the chain. 15,16 Apart from mechanisms that are based on direct polymer-solvent interactions, indirect mechanisms have been proposed as well. Zhang and Wu proposed that methanol-water 2


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complexes are formed when methanol is added to the aqueous PNIPAM solution. 4 Because methanol-water complex formation leads to a decrease in the concentration of ”free” water molecules that are available to hydrate the PNIPAM chain, the solvent quality decreases and the polymer collapses. Recently, Bischofberger et al. pointed out that the solvent composition where the PNIPAM lower critical solution temperature (LCST) passes through a minimum correlates with the solvent composition where the excess enthalpy of mixing of the solvent mixture becomes minimal. 6 Based on this correlation, the authors concluded that the hydrogen bonded water network, strengthened by the presence of the cosolvent, is decisive in the cononsolvency phenomenon. The molecular-scale cononsolvency mechanisms proposed in the literature can in principle be investigated with detailed-atomistic MD simulations. Such an approach requires that the solvation shell structure and energetics of extended chain sequences and collapsed chain sequences are compared. Because there exists no unique collapsed structure, the structural degeneracy has to be accounted for in order to achieve a representative sampling. In practise, this is an extremely challenging task. Not only should the simulated PNIPAM chain be long enough to observe clearly distinguishable extended and compact structures, the MD simulations should also be run long enough to observe a sufficiently large number of transitions between such structures. The first requirement can be met with a chain composed of 40 NIPAM monomers as was shown in previous work by two of the present authors. 8,17 Transitions between extended and collapsed structures of a 40-mer PNIPAM chain however occur on time scales of 50-100 ns in water at 300 K. 17 Cononsolvency has been reported (based on cloud point measurements) for a low molecular weight (5 kDa) PNIPAM sample which corresponds to a chain length of 44 NIPAM repeat units. 18 For such short chains, it is unlikely that cononsolvency can also be observed in properties that characterize the average chain dimension such as the radius of gyration (Rg ). The conformational entropy of polymer chains results from flexible degrees of freedom at the smallest length scales and, therefore, coil-to-globule collapse can only be observed in

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chain conformational properties for sufficiently long chains. 19 It is therefore unlikely that an advanced sampling method, used to examine the free energy of a relatively short 40-mer chain along a collective variable (such as Rg ), will provide a convincing indication of cononsolvency. In this work, we instead use a large-scale conformational sampling approach to examine solvation energies of collapsed and extended structures. The difference between these two energies is assumed to characterize the desolvation of the chain that gives rise to the endothermic heat effect, experimentally measured at the LCST transition. 1,3,6 The large-scale conformational sampling approach used in this work involves 1600 MD simulations of independent 40-mer structures, sampled 0.1 µs each. This approach provides the sampling required to observe a unique cononsolvency fingerprint in the energy difference between extended and collapsed structures. The approach furthermore provides the information required to analyze the polymer-solvent and solvent-solvent interactions that are assumed to govern cononsolvency in the different theoretical models discussed above. The data obtained in this work indicate that PNIPAM cononsolvency at 300 K and 1 bar occurs due to changes in polymer-water interactions, as assumed in the theoretical model of Tanaka et al. 5 and conjectured by Pica and Graziano in a recent paper. 9

Methods Simulation All MD simulations were carried out with the Gromacs 4.6.7 package 20 using cubic simulation boxes. A single atactic 40-mer PNIPAM chain was simulated in a series of 1600 MD simulations (different starting structures and different water-methanol solvent compositions) of maximally 0.1 µs each (see SI for details). The systems were simulated under constant pressure (1 bar) and constant temperature (300 K) conditions using the Parrinello-Rahman barostat 21 (τP = 1.0 ps) and Nose-Hoover thermostat 22 (τT = 0.5 ps). The OPLS-AA force-field 23 was used for PNIPAM, the rigid SPC/E model for water, 24,25 and the Kirkwood-Buff force-field for methanol. 26 With this PNIPAM and water model

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consonsolvency 27,28 and urea-induced PNIPAM collapse 17,29,30 has been previously reported. All bonds were constrained using the LINCS algorithm. 31,32 A van der Waals cutoff of 1.4 nm was used without long-range dispersion corrections for energy and pressure. Long range electrostatic interactions were calculated using the Particle Mesh Ewald method 33 with a real space cutoff of 1.4 nm, a grid spacing of 0.12 nm and an interpolation order of 10−4 . 33 An integration timestep of 2 fs was used. The initial PNIPAM conformations for the MD simulations were chosen from a uniform distribution of the radius of gyration obtained by Metadynamics 34 simulations performed with the PLUMED toolkit 35 with Rg as the collective variable. The initial conformations were energy minimized using the Steepest Descent algorithm until convergence and then equilibrated for 50000 steps in the canonical ensemble (NVT) and then for at least 100000 steps in the isothermal-isobaric ensemble (NPT) before starting the production runs. Trajectories and energies were saved every 500 frames (1 ps). The conformations with a Rg -value above 1.45 nm were considered as extended and a Rg -value below 1.1 nm as collapsed. Using this criterion the differences between the average energies, number of hydrogen bonds, and solvent accessible surface area (SASA) were calculated. Analysis The partitioning of the energy terms into polymer-polymer, polymer-solvent and solvent-solvent was done using the ““-rerun” option of GROMACS’ mdrun tool. The contributions from each of the molecule types and/or their pairs were separately computed by considering only these relevant molecule types in the trajectories. The singled out contributions were then calculated by addition or subtraction of these energies. Solvent accessible surface areas 36 were calculated using the g sas tool of GROMACS with a probe radius of 0.14 nm. A hydrogen bond was identified where the distance between donor and acceptor is lower than 0.25 nm and donor-acceptor-hydrogen angle is higher than 150◦ using the MDAnalysis software package 37 where the unique hydrogen bonds were counted.

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Umbrella Sampling Umbrella sampling 38 simulations were performed to calculate potentials of mean force (PMFs) along the radial coordinate r separating the centers of mass of two NIPAM molecules in different methanol-water mixtures. A harmonic potential was applied on the distances with a force constant of 1000 kJ/(mol nm2 ). For shorter distances between the monomers a larger force constant was utilized when necessary. The PMF 39 was calculated using the Weighted Histogram Analysis Method (WHAM) 40 with GROMACS’ g wham tool. 41 Ten independent sets of umbrella sampling simulations were performed using different initial configurations each with 33 windows ranging between 0.26 to 1.9 nm. Prior to production runs the initial configurations were energy minimized for 10000 steps or until convergence using steepest descent algorithm, and subsequently equilibrated for 20000 and 100000 steps under NVT and NPT conditions, respectively. Finally the umbrella sampling simulations were carried out for 5 ns under NPT ensemble (300 K and 1 bar). For a more accurate error estimation we performed bootstrapping 42 on the complete histograms 200 times. 43 The convergence of the PMFs were checked by dividing the total simulation into four equal parts. The entropic contribution proportional to kB T ln(4πr2 ) was removed from the PMFs, where kB is the Boltzmann constant and T the temperature, and the curves were shifted to zero using the average values between the distances 1.7 and 1.9 nm.

Results and Discussion Sampling The slow chain relaxation of PNIPAM makes it hard to sample the conformational space of the chain even for microsecond long simulations. 44,45 Therefore, to enhance the sampling of the phase space, we considered 200 independent PNIPAM 40-mer conformations that were each sampled in 0.1 µs MD simulations at 300 K and 1 bar. During the 0.1 µs MD simulations, reversible transitions occur between extended and collapsed chain conformations (Fig. 1). This procedure was followed for 8 different methanol-water compositions thus amounting to an overall number of 1600 MD simulations of 0.1 µs each (see Supporting

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(mole fraction), depending on molecular weight. 2 The collapse enthalpy, ∆HE→C , and collapse entropy, ∆SE→C , are both positive but decrease with the addition of small amounts of methanol, becoming vanishingly small at the point where Ttr reaches a minimum. 3,6,47 Because a Ttr depression is observed when small amounts of methanol are added, the ∆SE→C decrease does not fully compensate the ∆HE→C decrease. The ∆SE→C decrease can be understood based on insights obtained in recent MD simulations studies. In pure water, the collapse of PNIPAM leads to loss of amide-water hydrogen bonds and desolvation of nonpolar groups. Due to the corresponding increase in translational entropy of the solvent molecules, ∆SE→C is large and positive. In the cononsolvency regime, excess methanol accumulates in the first solvation shell of the E-chain and the C-chain, expelling hydration water for both of these two conformational states. 8 Therefore, the polymer collapses with a significantly smaller gain in solvent translational entropy. There may be different explanations for why the ∆SE→C decrease does not entirely compensate the ∆HE→C decrease. One explanation, supported by calculations, is that the configurational entropy of the collapsed chain is significantly larger in the presence of methanol than in pure water. 8 While solvent translational entropy contributions rapidly diminish when methanol is added, the configurational entropy of the collapsed chain increases, thus providing a compensating positive contribution to ∆SE→C . As a result, ∆SE→C decreases slower than it would in case configurational entropy effects had played no role. The configurational entropy must therefore be considered in the cononsolvency phenomenon, an insight which has been referred to as an ”emerging view of entropic chain collapse”. 10 Clearly, this does not state that ”the original LCST transition is entropy driven”. 11 Computational Calorimetry So far, MD simulations have not provided an explanation of the ∆HE→C decrease reported by calorimetric measurements. The energies of methanol binding to the C-state and to the E-state of PNIPAM have previously been determined with MD simulations, showing no significant differences (cf. Fig. 5 in Ref 8 ). Hence, if

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(Fig. 3A) with a larger rate of decrease at low methanol concentrations. This nonlinear behaviour is the determining factor for the cononsolvency minimum observed in Fig. 2A: Small amounts of methanol remove the desolvation-energy penalty which prevents polymer collapse in pure water. The polymer-methanol energy component shown in Fig. 3B shows that polymer-methanol interactions oppose chain collapse. Moreover, this energy contribution increases linearly with the bulk methanol concentration. Therefore, changes in polymer hydration should be considered to describe the PNIPAM coil-to-globule collapse transition. Mechanisms that exclusively rely on methanol interactions provide an incomplete picture. The inset in Fig. 3A shows that the E- and C-chains lose favorable interaction with water when methanol is added. E-chains however lose favorable interactions with water faster than pps on methanol concenC-chains. This causes the observed nonlinear dependence of ∆UE→C

tration. The inset in Fig. 3B shows that the overall methanol interaction with the E-chain is larger than with the C-chain. Methanol van der Waals interactions with solvent-exposed isopropyl groups explain this observation (see SI Fig. S3). Above 20% methanol, this interaction drives the globule-to-coil reentrance. We note that the rapid increase of Ttr , experimentally observed at 20% methanol, 18 occurs not only because of polymer-methanol interactions but also because ∆SE→C becomes vanishingly small at this concentration. This entropy change remains small with further addition of methanol (above 20%) because solvent-excluded volume effects, which generally oppose chain extension, 9 decrease at larger methanol concentrations. 8 Hydrogen Bonding Fig. 4A shows the average number of polymer-solvent and amideamide hydrogen bonds (H-bonds) for collapsed and uncollapsed chains. Addition of small amounts of methanol causes a rapid initial decrease in the number of polymer-water H-bonds which is not compensated by newly-formed polymer-methanol H-bonds. Specifically, adding 20% methanol to the aqueous PNIPAM 40-mer, initially in pure water, causes a loss of approximately 20 polymer-water H-bonds which is compensated by only 10 newly formed

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that poly(N,N-diethylacrylamide) (PDEA), a tertiary amide which lacks the NH group, does not show cononsolvency. 48 It is also consistent with recent experimental data which show that poly(N-vinyl-caprolactam) (a tertiary amide) does not shows cononsolvency whereas poly(N-n-propylacrylamide) shows cononsolvency. 49 Solvent-Accessible Surface Area The isopropyl group of PNIPAM screens the solvent accessibility of the amide group. Fig. 5 shows that the solvent-accessible-surface area (SASA) of the isopropyl group is fivefold larger than the SASA of the amide group, contributing ∼ 75% to the overall SASA of PNIPAM. Therefore, the PNIPAM macromolecular surface has hydrophobic and hydrophilic domains, both for collapsed and extended chains (Fig. 5). Water molecules, due to their small size, can form hydrogen bonds with the sterically-screened amide group rendering PNIPAM (sparsely) soluble at room temperature and causing phase separated PNIPAM (above the LCST) to contain substantial amounts of water compared to hydrophobic materials. 50 Tanaka et al. 5,18 conjectured the idea that water molecules cooperatively hydrate PNIPAM through a mechanism in which formation of H-bonds with an amide group is facilitated by water H-bonding with adjacent amide groups. According to these authors, methanol blocks the formation of cooperatively hydrated chain sequences leading to rapid dehydration and collapse of the chain. 5,18 Methanol preferentially interacts with the solvent-exposed isopropyl groups 8 (through weak van der Waals and hydrophobic interactions) but can form H-bonds with the amide group as well. However, methanol interaction with the isopropyl group, or methanol H-bonding to the amide, leads to a smaller overall number of H-bonds formed (Fig. 4A). This can be explained considering steric effects. Because of their larger size (than water), methanol molecules geometrically frustrate pathways for water molecules to access the sterically-screened amide group. It is interesting to compare the number of solvent H-bonds with collapsed and extended chains in Fig. 4A. If we consider the difference between H-bonds with extended and collapsed chains, we see that polymer collapse in the cononsolvency region below 20% methanol leads

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NIPAM-NIPAM Aggregation Recently, Mochizuki et al. showed that cononsolvency can be observed in the aggregation of small solutes in water/methanol mixtures. 51,52 Similarly, we tested the monomer of PNIPAM for such a behavior (see the chemical structure in SI Fig. S5). Fig. 6A shows the pair PMF for the interaction between two NIPAM molecules in different water-methanol mixtures. Fig. 6B shows the aggregation constant K defined as K =

R 1.4 0

exp [−VP M F (r)/kB T ]4πr2 dr at 300 K and 1 bar in different water/methanol

mixtures. In pure water (Fig. 6A; blue curve), the PMF curve has a minimum at 0.50 nm, which shifts monotonically upward with methanol addition. The aggregation constant K (Fig. 6B) does not show a large difference between pure water and low methanol concentrations, however at high methanol concentrations K decreases. Thus, the association of NIPAM molecules in the dilute solution limit does not display cononsolvency in water/methanol mixtures. This is quite interesting because it suggests that, in contrast with a single monomer, cooperative solvation effects associated with the solvation of a PNIPAM chain are important to understand the observed cononsolvency effect for PNIPAM. In their cooperative hydration model, Tanaka et al. 5 assume that water molecules H-bonded to the amide NH create additional space for the neighboring water molecules by displacing the isopropyl groups. Such a collective displacement results in a cooperative effect for the polymer and cannot be observed in the aggregation behavior of only two monomers. For the two NIPAM molecules, the amide groups are more exposed to the solvent molecules compared to NIPAM monomers in a PNIPAM chain where chain connectivity introduces correlations between (de)solvation of neighboring chain segments. The decrease of the association constant observed in Fig. 6B at high methanol concentrations is consistent with the picture that the globule-to-coil reentrant transition occurs due to methanol van der Waals interactions with the chain (see discussion of Fig. 3B).

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understanding of the role of the amide in the chain. Furthermore, the effects of temperature on the solvent composition around the polymer chain would provide additional insight into the cononsolvency mechanism. Supporting Information One table containing information on simulation lengths, and five figures showing radius of gyration distributions, electrostatic and Lennard-Jones contributions to the solvation energy for the system and its components, the effect of different radius of gyration criteria on the energy change upon collapse and the chemical structure of the NIPAM monomer. Acknowledgements The MD simulations were performed on the Lichtenberg High Performance Computer of the Technische Universität Darmstadt, Germany. The authors are indebted to Viktor Klippenstein for his help with setting up and computing NIPAM-NIPAM potentials of mean force. NvdV acknowledges Jan Heyda for several insightful discussions.

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Computational Calorimetry of PNIPAM ... - ACS Publications

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