Study of the Polymer Length Dependence of the Single Chain

Aug 10, 2012 - Ashley K. Tucker* and Mark J. Stevens. Sandia National Laboratories, Albuquerque, New Mexico 87185-1395, United States. Macromolecules ...
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Study of the Polymer Length Dependence of the Single Chain Transition Temperature in Syndiotactic Poly(N‑isopropylacrylamide) Oligomers in Water Ashley K. Tucker* and Mark J. Stevens Sandia National Laboratories, Albuquerque, New Mexico 87185-1395, United States S Supporting Information *

ABSTRACT: Aqueous solutions of poly(N-isopropylacrylamide) (PNIPAM) exhibit a temperature responsive change in conformation. When the temperature is increased, the polymer transitions from an extended coil conformation to a collapsed structure. We performed molecular dynamics simulations of aqueous solutions of single chain, syndiotactic PNIPAM oligomers over a wide range of temperatures and varying degrees of polymerization to elucidate the effect of oligomer length on the single chain transition temperature, T1. We have reproduced recent measurements of the transition temperature increasing with decreasing oligomer chain length. Examination of the chain structure reveals that conformations above T1 bend to bring hydrophobic segments together to shield them from the water. The constraints of the dihedral dynamics require elevated temperatures for shorter chains to bend sharply enough in order to undergo the transition. This result is confirmed by calculations of the solvent accessible surface area, which shows an increase in shielding of the hydrophobic groups with increasing oligomer length above T1.

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and intramolecular aggregation.9,10 Experimental data have been presented that indicate the interactions between intrachain, polymer segments drive the structural collapse. The driving interactions between polymer intrachain segments include hydrophobic interactions of the isopropyl tail groups as well as the possibility of hydrogen bond formation between the amide oxygen and nitrogen. A large body of experimental work on PNIPAM has aimed to understand the LCST of PNIPAM. FTIR experiments on aqueous solutions of PNIPAM have indicated that above the LCST fewer polymer−water hydrogen bonds occur, and thus the polymer chain is dehydrated, and that hydrophobic interactions of the isopropyl groups cause the collapse of the extended chain.24 Furthermore, dielectric relaxation techniques have found that PNIPAM chains in solution show fewer hydrating waters near the polymer above the LCST, where solutions of monomer only show constant hydration above and below the LCST.25,26 Laser light scattering has also been used to probe the role of hydrogen bonding between the polymer and water during the transition by adding varying concentrations of methanol, changing the hydrogen-bonding character of the solvent. With increasing methanol concentration, a reentrant LCST transition was observed, indicating that hydrogen bonding plays a role in the single chain transition and the LCST transition observed in solutions of PNIPAM.7 Some atomistic simulations have studied PNIPAM, primarily a single chain in solution. Typically, a temperature above and

INTRODUCTION Poly(N-isopropylacrylamide) (PNIPAM) is a well-studied polymer that exhibits a lower critical solution temperature (LCST) in water. Below this temperature, the polymer is in an extended state, while above this temperature, the polymer collapses into a globule state due to diminishing solubility of the polymer. The thermoresponsivity of this particular polymer in aqueous solution imparts PNIPAM with interesting behavior in a variety of settings.1−4 The LCST is governed by the balance of polymer−solvent interactions and polymer−polymer interactions. This process has been observed experimentally5−16 and also in simulations.17−21 Not only do solvent−polymer interactions and polymer intrachain interactions affect the LCST, chain length has also been shown to influence the LCST. Recent interest in nanoparticles coated with PNIPAM oligomers has led to the discovery of the chain length dependence of transition temperature Tc.22 These microcalorimetry and turbidity experiments studied the transition temperature with respect to chain length of PNIPAM oligomers and found that by increasing chain length, the transition temperature decreased. We have performed simulations to examine the chain length dependence of the LCST transition and to characterize the single chain structure. PNIPAM single chains exhibit the coil-to-globule transition in water for high molecular weight, single chains at T1 = 32 °C.12,13,16 Laser light scattering experiments of extremely dilute solutions of nearly monodisperse PNIPAM found the coil-toglobule transition to occur as well as determined two thermodynamically stable intermediate states between the extended coil and fully collapsed globule in the single chain transition.11,13,23 The LCST transition is comprised of inter© 2012 American Chemical Society

Received: April 9, 2012 Revised: July 26, 2012 Published: August 10, 2012 6697

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absence of periodic image interactions. The polymer backbone was fully extended prior to energy minimization using a conjugate gradient algorithm and a subsequent NVT run. We treat a polymer chain in the syndiotactic state, which will have the greatest change in structure in the transition since the syndiotactic chain is the most extended conformation in the low-temperature state. Experimentally, it is known that a stereochemical dependence exists in the LCST temperature.29 For example, the syndiotactic chain has a sharper transition than the atactic.29 However, the major points that we make characterizing the chain-length-dependent transition in oligomers do not change with tacticity. We verify this by performing simulations of the N = 18 oligomer with an atactic conformation at T = 280, 290, 295, and 310 K. These results are provided in the Supporting Information. The all-atom MD simulations were performed at a constant pressure and temperature using the LAMMPS simulation package.30 The interactions were simulated using the OPLS force field31 and the TIP3P water model.32 The heteroatomic Lennard-Jones parameters were determined using the geometric mixing rule, and the cutoff for the real-space component of the electrostatic portion of the potential and the van der Waals forces was 10.0 Å. The electrostatic interactions were treated using the particle−particle particle−mesh (PPPM) technique33 implemented in LAMMPS, and an rms accuracy of 10−4 was used for the PPPM method. The bond lengths and the angles of the water molecules were constrained using the SHAKE algorithm.34 The time step was 2 fs. The production runs of the simulations were carried out in the NPT ensemble, employing the Nose−Hoover thermostat with a relaxation time of 100 fs. The pressure was kept constant at 1.0 atm using the Nose−Hoover barostat with a relaxation time of 500 fs. Temperatures of the simulations in this work range from T = 280 K up to 360 K. Long simulations of at least 100 ns were run to determine if the coilto-globule transition occurs. After a clear transition was observed, the simulation times were extended to at least another 100 ns to ensure that the collapsed structure was indeed the preferred structure at that specific temperature and pressure.

below the experimental, long chain Tc have been treated. Simulations of the effect of tacticity in a PNIPAM trimer have found lower hydrophilicity for the isotactic PNIPAM trimer in comparison to the syndiotactic conformer.27 An effect due to solution composition has also been observed via molecular dynamics on NIPAM monomer in water/methanol mixtures28 similar to the laser light scattering experiments of Wu et al.7 Like the experiment, the hydrogen-bonding behavior of water was altered in the molecular dynamics simulation by adding varying concentrations of methanol and thus created a concentration-dependent effect on interactions between the solvent and NIPAM monomer. Desolvation of the monomer was found to occur with increasing methanol content. Molecular dynamics simulations were also utilized to observe the hydrogen-bonding behavior in PNIPAM oligomers with 50 monomer units at two temperatures, above and below the experimentally observed LCST.18 The oligomers studied showed negligible temperature dependence on the number of hydrogen bonds between PNIPAM and water. However, a decrease in the number of waters in the first hydration shell at simulations performed above the LCST were observed.18 Also, the hydrogen-bonding network of water surrounding PNIPAM oligomer below the LCST has been shown to differ from the network formed above the LCST.21 In this work, a computational study of a single, syndiotactic PNIPAM oligomer in solution at several temperatures is performed. Increasing temperature, and therefore diminishing the solubility of PNIPAM in water, induces collapse of the oligomer; however, the chain length limits the extent to which the oligomer can fold, thus inducing the possibility for chain length dependence of the single chain transition temperature, T1(N). We use the notation T1 to distinguish the single chain transition from the LCST, Tc, that occurs in solution due to chain contraction and aggregation events. We therefore aim to understand the temperature dependence of T1 in terms of the structure of the chain. A limitation of previous simulations of PNIPAM is the treatment of only two temperatures; no one has determined the transition temperature for the force field used or considered the effect of chain length on T1. Various degrees of polymerization were studied, with oligomers comprised of N = 3, 8, 11, 18, and 30 monomer units. We know that the dihedral transition in a hydrocarbon backbone limit the degree of chain bending for short chains. In order for the chain to coil, multiple correlated dihedral transitions must occur. The shorter the chain, the less likely for such coiling to occur. This will reduce the likelihood of the collapsed state above T1. We performed simulations as a function of temperature (T = 280− 360 K) to ensure that the full transition is captured by our simulations. The results are presented in terms of the radius of gyration of the polymer as well as a discussion of the resulting hydrogen-bonding statistics between water and the polymer as well as intrachain hydrogen bonds.

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RESULTS The aim of this work is to examine the oligomer length dependence on the transition temperature. We will examine how the oligomer structure differs from the long polymer structure which, below Tc, has a random coil structure compared to the collapsed conformation that exists at temperatures above Tc. In order to examine this transition, the radius of gyration, RG, is determined as a function of temperature for each oligomer studied. The ratio of the average radius of gyration versus RG(280 K) for each degree of polymerization is given as a function of temperature in Figure 1. A clear transition from the extended state of the polymer to a collapsed conformation is observed for varying degrees of polymerization, namely N = 11, 18, and 30 monomer units. Representative time-dependent RG values above and below the transition temperature for N = 18 are provided in the Supporting Information. In this figure, the temperature at which the polymer transitions from the extended conformation to the folded conformation is clearly dependent upon the length of the oligomer; as the oligomer length increases, the transition temperature decreases, where at N = 30 we observe T1 ∼ 300 K, which is near the experimental Tc of high molecular weight PNIPAM. The transition from extended to collapsed conformations become more pronounced with increasing polymer length. RG values of the collapsed structure decrease relative to the extended conformation as N increases, up until N = 30. The apparent nonmonotonic change in the trend for the N = 30 oligomer will be shown below to be due to an N dependence in the conformation below Tc, which is the normalization factor used in Figure 1. The low-temperature

METHOD

Molecular dynamics (MD) simulations were performed on a single PNIPAM molecule in water. We studied chains with N = 3, 8, 11, 18, and 30 monomer units. Experimentally, N = 30 was found to have the long-chain Tc value.22 Both ends of the polymer were terminated with hydrogen atoms, and the initial polymer chain was surrounded by TIP3P water molecules. Three-dimensional periodic boundary conditions were employed with a cubic simulation box. The simulation box size was increased accordingly with increasing polymer length with values of L = 40 Å for the shortest oligomer, N = 3, L = 60 Å for N = 8−18 and L = 120 Å for N = 30. Box sizes were chosen to ensure the 6698

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Figure 1. Ratio between the radius of gyration at a given temperature vs the RG at T = 280 K. This image shows the extent of the collapsed conformation and the location of the transition temperature, Tc, for N = 3 (black circles), 8 (red squares), 11 (green diamonds), 18 (blue triangles), and 30 (purple, inverted triangles). Error bars are the standard deviation of the time average.

configuration of N = 30 has a coiled conformation and thus makes the transition of the N = 30 oligomer appear to have a weaker transition. Further discussion will be provided below. When the polymer length is decreased to 8 monomer units, no clear transition emerges, although RG values at high temperature tend to be smaller than the values at low T (below 320 K). The differences are well within the uncertainty reported. Finally, the trimer data (black circles in Figure 1) clearly show no transition in the temperature range of T = 280−360 K. We will show below that because the chain is short, it is not able to fold the carbon backbone of the polymer enough to show an overall change in the RG. In order to gain more understanding into the structural transition than from just the average RG values, we have examined the distribution of the RG values. Figure 2 shows the distribution of RG values, f(RG), as a function of oligomer length and temperature. The distributions and average RG values were determined by analyzing the time interval after a stable conformation was found. For the data provided, the time intervals are at least 100 ns for each temperature and oligomer length. The distributions provided in Figure 2 are obtained by counting the occurrences of a specific RG value within a bin size of 0.25 Å. The bins are normalized so that the area under each curve is unity. At N = 3 (Figure 2a) there is clearly no change in the distribution as a function of T. At N = 8, a transition is also not observed; however, a slight temperature dependence in the distribution of RG is observed, indicated by the drop in peak height as well as broadening of the peak at high temperatures. When N is increased to 11 monomer units, two states are clearly observed: the extended state and the collapsed state. The extended peak is centered at RG ∼ 8.5 Å, and the second peak occurs at 6.4 Å at higher temperatures. When the oligomer length is further increased to N = 18 and 30, more than two states are observed. At N = 18 the lowest two temperature distributions are broader and distinct from other temperatures. In comparison to the N = 30 low-T distributions, the N = 18 distributions go to larger RG. This suggests that N = 30 can bend at low T in ways that N = 18 cannot; we show below that this is indeed true. This difference explains why N = 18 has a lower ratio in Figure 1 than N = 30; the RG(280 K) is larger for

Figure 2. Distribution of RG with respect to temperature for varying degrees of polymerization, N = 3 (a), 8 (b), 11 (c), 18 (d), and 30 (e).

N = 18, reducing the ratio. The distributions above the transition are similar to that for smaller N, but with a corresponding larger average RG. A physical representation, as a function of N, can be obtained from snapshots of typical backbone conformations and are provided in Figure 3. No transition was observed in the trimer

Figure 3. Backbone conformations for varying degrees of polymerization, N, when the temperature is below the transition temperature, T1(N), and when the temperature is greater than T1. For the N = 8 oligomer, a concrete transition is not observed, but multiple conformations above the temperature at which oscillations between folded and extended conformations are shown. Each bead represents one monomer, i.e., two carbon atoms. 6699

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data, and all of the structures remained straight chains due to the inability of the short chain to fold; therefore, they are not included in Figure 3. Two examples of high-temperature conformations are provided for the N = 8 oligomer in Figure 3. While there is a slight change in the conformation of the N = 8 oligomer with increasing temperature, a concrete transition to a stable compact structure is not observed. At low T there are no sharp bends. At high T, there are bends observed in the backbone, but the structure is not collapsed. The key feature is that the N = 8 oligomer cannot bend and bring the hydrophobic moieties into contact with each other at high temperatures; therefore, the N = 8 oligomer cannot fold, and there is no transition. The need for sufficient bending to yield contact becomes clear in the N = 11 conformations. At N = 11, we see the “U”shaped structure that causes contact between two chain segments that enables the chain to shield some of its hydrophobic parts from the surrounding water. At N > 11, the oligomers are sufficiently long, so that more than one bend in the backbone is possible. The N = 18 and 30 oligomers show folded structures that shield hydrophobic moieties from the solvent; these structures clearly possess more folds. Evidently, by N = 30 the chain length is sufficiently long to allow enough folds that large N behavior is reached. In addition, at N = 30 the low-temperature conformations are different. At this length the chain is long enough to have substantial bending in the low-T state. We know bending should occur at some chain length because in the limit of large N, the polymer is in a good solvent at these temperatures and should have a random walk conformation. The data show that at N ≤ 18 the good solvent conformations are not coiled. Coiling begins somewhere near N = 30. Upon increasing the oligomer length to near 3 times the experimentally determined persistence length, N ≥ 10,35 behavior of the large N limit emerges because the chain is flexible enough to yield conformations within the random walk distribution. Thus, the transition at N = 30 occurs at the polymeric (large N) value. The distributions of the end-to-end distance also show this pattern of increased folding with increasing oligomer length. The end-to-end distribution data are provided in the Supporting Information. Since the transition involves the shielding of hydrophobic segments, the amount of accessible surface area to the water should decrease above the transition. The conformations shown in Figure 3 indicate such a structure. We thus calculate the solvent accessible surface area (SASA) and plot the ratio SASA(T)/SASA(280 K) in Figure 4. The SASA is calculated using the variant of the Shrake−Rupley algorithm36 provided in the VMD package,37 with a probe radius of 1.4 Å. The SASA data as a function of T more clearly displays the transition than the plot of the structure data (Figure 1). Above the transition the SASA decreases sharply and the drop is larger for longer chains. Thus, the longer oligomers are able to fold into structures that bring more of the hydrophobic moieties into contact shielding them from the solvent. For example, the SASA data for N = 11 show a sharp transition around 315 K, matching the transition between the extended and collapsed conformations observed in the f(RG) data. The SASA ratio is monotonically decreasing as a function of N, in contrast to the RG ratio. The SASA data indicate that although RG(280 K) (see Figure 1) for N = 30 is smaller than for N = 18, the change in SASA ratio is actually larger for N = 30. The structural and SASA data show that N = 30 is able to fold more than N = 18 in order to reduce the SASA, in agreement with intuition.

Figure 4. Solvent accessible surface area with respect to temperature normalized by the values of the extended structure at low temperature for increasing oligomer length, N = 8 (black circles), 11 (red squares), 18 (green diamonds), and 30 (blue triangles). The error bars give the standard deviation of the time average.

Polymer length dependence on the transition temperature of PNIPAM oligomer solutions has been measured previously using turbidity experiments.22 A qualitative comparison between the temperatures obtained in this work to the experimentally determined Tc values is provided in Figure 5.

Figure 5. Transition temperatures, T1 (K), for the polymer simulated (black squares) compared to experimental Tc values determined by Shan et al.22 Experimental data (red squares) are determined at an oligomer concentration of 20 mg/mL for the trimer and at 5 mg/mL for the other oligomers.

Simulation T1 values are determined from Figure 1. The midpoint of the initial transition from the extended conformation to the folded conformation in Figure 1 are the T1 values reported with the error bars estimated from the figure also. The experimental work of Shan et al. is performed on polymer solutions of atactic oligomers. Previous work has indicated a slight temperature dependence due to tacticity,29 but this difference in T1 due to tacticity is within our error bars reported. The Supporting Information also shows that for the N = 18 oligomer there was no change in the transition temperature between the atactic and syndiotactic conformers within the error bars of our measurements. Therefore, we are not claiming that there is no difference in the transition 6700

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require well-separated monomers to be brought together via bends in the chain. As has been pointed out above, for the shortest oligomers in this study such bends do not happen at low T. For sufficiently long chains with bending below T1, intrachain hydrogen bonding causes an unfavorable decrease of conformational entropy. The same favorable interactions can be obtained by hydrogen bonds forming between the polymer’s hydrophilic groups and water without the conformational constraint. Therefore, a low number of intrachain hydrogen bonds is observed in the low-T state. When the polymer is in the high-T conformation, intramolecular hydrogen bonds expose the hydrophobic groups to the water, which is unfavorable; therefore, it is still advantageous to have the PNIPAM hydrogen bondable groups exposed to water as in the low-T conformations. In summary, the intramolecular number of hydrogen bonds should be small and not strongly Tdependent.

temperature due to tacticity; only that it is within our error bars, and most importantly, the underlying causes of the transition are independent of tacticity. While the error bars in Figure 5 seem somewhat large, the simulation runs were quite long in order to obtain a clear transition. Because of this, obtaining more independent statistics needed to shrink the error bars is prohibitive. However, we have developed an understanding of the relationship between the structure of the chain and the transition. Considering no transition was observed in the N = 3 and N = 8 in the simulations, it is likely that the experimentally observed transition for these N values is due to aggregation of more than one chain and not solely the folding of the single chain. Given that these chain lengths are shorter than the measured persistence length, the absence of a single chain transition is to be expected. The experimental Tc values are not determined from infinitely dilute solutions, i.e., single chain samples. Previous work has suggested that the transition observed in solutions of PNIPAM where the concentration is below the overlap concentration occurs by the simultaneous contraction of single chains and interparticle aggregation.9,10 The chain length dependence of the single chain transition is, therefore, not the whole story, but the interchain transition is not independent of the single chain transition. The conformations formed by the single chain transition will affect aggregation of multiple chains and therefore the global LCST. Previous simulation and experimental work has focused on the hydrogen-bonding behavior of the polymer and the changes after the polymer has undergone the coil-to-globule transition.17−21,38 A majority of this work has shown a decrease in the hydrogen bonding between PNIPAM and water as well as an increase in intrachain hydrogen bonds when the collapsed state is compared to the extended state. However, most of this work has focused on concentrated polymer solutions and polymer networks. When single chains in water are studied via molecular dynamics, the overall change in the number of hydrogen bonds above and below the LCST is negligible,18 but a change in the structure of the water molecules in the first hydration shell is observed with the onset of the transition with decreasing solvation of the oligomer observed above the LCST.21 For the systems studied in this work, the hydrogenbonding statistics for each oligomer were determined. The criteria used was a bond length d < 3.0 Å and an angle θ > 150.0°.39,40 No statistical change in hydrogen bonding between the polymer and water was observed between the extended and collapsed conformation. In order to ensure that the results were not due to the choice of the criteria, a slightly longer bond distance d < 3.3 Å with θ > 150.0° was also tested, and again, no statistical change in hydrogen bonding was observed. The fact that the number of polymer−water hydrogen bonds seems insensitive to the conformation of the chain is reasonable considering that whether extended or folded, the hydrophilic groups remain exposed to the solvent. When the polymer has folded, in order to shield the hydrophobic moieties from water, the hydrophilic groups must maintain contact with water. This is consistent with previous computational work studying the hydrogen bonding of a N = 50 oligomer in water.18 The intrachain hydrogen bonds were also investigated, and only a slight increase was observed with increasing temperature. The number of such hydrogen bonds is small compared to the number of water−polymer hydrogen bonds. In the low-T state intrachain hydrogen bonds (not between neighbor monomers)

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DISCUSSION The results of these simulations have important implications for using PNIPAM oligomers in systems where the transition is a key part of the function. The simulation data have shown that very short oligomers (N ≤ 8) do not possess a single chain transition because a sufficient bending of the chain does not occur for such short chains. Equivalently, chain lengths below the persistence length cannot change conformations sufficiently to have a transition. Thus, such short chains in isolation cannot be used in a system that requires a switchable volume change. For N ≥ 11 the transition does occur, and T1 decreases with N until at N = 30 the long chain limit value of T1 is reached. The conformations of these intermediate length chains above T1 involve the folding of the chain on to itself in order to aggregate hydrophobic segments and shield them from the water. They can be used in isolation as switchable molecules. These oligomer conformations have implications for nanoparticles coated with PNIPAM, which was the original interest of the experimental work that observed the N-dependent Tc.22 In these coatings, the chains typically will not be in isolation and this fundamentally alters the behavior. Particularly with the oligomers that possess the transition and can change shape, the coverage of the oligomers on the nanoparticle will play an important role. If the NIPAM oligomers are attached to a nanoparticle at low T in the extended conformation, they could pack quite densely. At such dense coverages, the high-T folded structure would be precluded. On the other hand, if coating of the nanoparticle occurs in the high-T state, then the maximum coverage will be smaller. In this case, a transition to below T1 will open a lot of volume including unoccupied sites on the nanoparticle. The unoccupied sites would be at least 50%. The behavior of the LCST of oligomers grafted to nanoparticles differs drastically from the single chain solutions. The experimental work has shown that when coated on the surface of a nanoparticle, the transition temperature of the solution, Tc, of PNIPAM oligomers increases with increasing chain length,22 i.e., the opposite behavior of the single, free chain T1. A closer examination of the data show that only the shortest oligomer has a Tc much different than the long-chain value, which suggests that Tc does not change much for most oligomers when grafted to a nanoparticle. The transition observed for these coated nanoparticles must be due to hydrophobic screening by interchain aggregation and the exclusion of water, which is a different process than the single chain case. As noted above, the coverage plays a significant role 6701

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Macromolecules in the nature of the coating. At high coverage the single chain conformational change cannot occur, which implies that the transition observed is due to a different behavior. The amount of water within the coating will depend on the coverage, too. Even at high coverage, there will be free volume within the coating for water to occupy.41 The geometry of a linear chain grafted to a nanoparticle necessarily results in either some free volume near the ends of the chains or gaps between regions of chains, particularly at facet edges. The transition would then be due to these water molecules leaving these regions above Tc as the chains aggregate to shield their hydrophobic parts. This mechanism is equivalent to that in a PNIPAM gel, and the Tc(N) should be similar to the long-chain value for that reason. The dependence on interactions between chains instead of a single chain conformational change explains why most of the PNIPAM-coated nanoparticles have a Tc close to the long-chain value. In the experiments, the shortest chain (N = 3) is the only oligomer with a Tc clearly below the long-chain value and requires a separate explanation. We can only speculate not having done simulations of coated nanoparticles that coverage may be playing a role for such a small oligomer. There is typically a difference in the ease of forming high coverage coatings between very short and long molecules, and this factor could easily yield a different Tc, but to fully address this issue is beyond the present work.

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REFERENCES

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CONCLUSIONS In this work, MD simulations of a single, syndiotactic PNIPAM oligomer chain in water demonstrate a chain-length-dependent transition temperature. These results are similar to experimentally determined Tc values.22 Using the simulation data, we are able to connect the chain length dependence of the transition temperature to chain length dependent structures. For the shortest oligomers studied (N ≤ 8), no transition was observed over the temperature ranges simulated. This result is consistent with single chains shorter than the persistence length not having a transition. At N = 11 a clear transition from an extended to collapsed conformation is observed. At this chain length, the chain can bend into a “U”-shaped conformation that shields hydrophobic segments above the transition temperature. At N > 11 monomers the emergence of intermediate structures between the fully extended and fully folded structures are observed. As chain length increases, the oligomer is able to access a wider range of folded structures above the transition from dihedral rotations bringing hydrophobic segments into contact, shielding them from the solvent. We find at N = 30 not only can the chain form a collapsed state above T1 it also can form a good solvent coiled structure below T1. Thus, the large N limit for T1 is reached by N = 30. ASSOCIATED CONTENT

S Supporting Information *

Supplemental Figures 1−4. This material is available free of charge via the Internet at http://pubs.acs.org.

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ACKNOWLEDGMENTS

Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under Contract DE-A-C04-94AL85000. This research was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract DE-AC02-05CH11231.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 6702

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dx.doi.org/10.1021/ma300729z | Macromolecules 2012, 45, 6697−6703