The Glass Transition of a Single Macromolecule - ACS Publications

Sep 21, 2016 - and David S. Simmons*,†. †. Department of Polymer Engineering, The University of Akron, 250 South Forge St., Akron, Ohio 44325-0301...
0 downloads 0 Views 2MB Size
Download PDF
Article pubs.acs.org/Macromolecules

The Glass Transition of a Single Macromolecule Weston L. Merling,† Johnathon B. Mileski,† Jack F. Douglas,‡ and David S. Simmons*,† †

Department of Polymer Engineering, The University of Akron, 250 South Forge St., Akron, Ohio 44325-0301, United States Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States

‡

S Supporting Information *

ABSTRACT: We employ molecular simulations to show that a generic isolated macromolecule behaves as a glass-forming liquid in an extreme state of nanoconfinement. Specifically, its glass transition temperature T g is strongly suppressed with respect to a corresponding bulk-state polymer, but adsorption onto an attractive substrate can reverse this effect. Results indicate that observations of bulklike Tg in individual nanoconfined systems can result from a “compensation point” between Tg enhancement and Tg suppression. In addition to their implications for the understanding of nanostructured synthetic materials, these results are also likely relevant to the dynamics of globular and adsorbed biological macromolecules.

■

INTRODUCTION Although glass formation is commonly thought of as a macroscale phenomenon, a substantial body of recent literature has demonstrated that materials with nanoscale dimensions can exhibit a glass transition, corresponding to a precipitous drop in relaxation rate and a freezing into a state of relative inactivity. This phenomenon apparently even occurs in isolated macromolecules, including synthetic polymer chains1 and biological macromolecules such as proteins.2 Because the dynamics of macromolecules are sensitive to the presence of incipient glass formation at temperatures as great as twice the glass transition temperature,3,4 the phenomenon of glass formation in single macromolecules has profound implications for diverse problems, including the preservation5 of biological molecules, the behavior of dilute polymer blends, the performance of polymer−polymer nanocomposites,6 the fabrication of ultrastable polymer glasses by matrix-assisted pulsed laser evaporation,7 and the dynamics and biological activity of biomolecules in solution and adhered onto interfaces. Moreover, since a single molecule logically represents the smallest system in which glass formation can occur in macromolecular systems, it should provide a unique laboratory in which to probe characteristic length scales that are proposed by multiple theories of glass formation8,9 to underpin the dynamics of supercooled liquids. A large body of literature also suggests that glass formation in material domains of nanoscale extent should differ appreciably from that in bulk materials.6,10−25 This literature suggests that the presence of an interface can induce long-range (tens of nanometers) gradients in segmental dynamics.15,26−28 For example, polymers confined in thin films or in nanoparticles surrounded by a soft medium exhibit reductions in their glass transition temperature Tg that can exceed 100 K for the smallest system dimensions studied.29 On the basis of these © XXXX American Chemical Society

observations, one might expect the dynamics of a globular macromolecule in dilute solution to be greatly accelerated from its bulk state. Furthermore, since this literature indicates that the details of a bounding interface (such as interfacial energy and softness) substantially impact the dynamics of a contacting material,14,30,31 adhesion on a substrate should also impact the dynamics of an isolated macromolecule. In apparent contrast to this body of literature, Tress et al., in a recent paper in Science, reported that the dielectric segmental relaxation of isolated chains of poly(2-vinylpyridine) on a silica substrate was similar to that observed in the same polymer in a bulk state.32,33 Since a single macromolecule can logically be viewed as the extreme limit of nanoconfinement, this has been interpreted as compelling evidence that nanoconfinement does not substantially alter glass formation,34 a perspective in line with a series of papers arguing that observations of altered Tg and dynamics under nanoconfinement are artifacts resulting from proposed experimental artifacts such as inadequate equilibration.35−37 If correct, this conclusion would have major implications for the properties of synthetic polymers, biomacromolecules, and nanostructured materials more broadly. It would imply that nanostructured and nanoconfined materials should exhibit segmental dynamics indistinguishable from bulk, with large implications for development and understanding of these materials’ properties. Moreover, it would indicate that the dynamics of disordered, globular proteins and other disordered biomacromolecular domains should be insensitive to both crowding and adhesion to substrates, since within this view a globular, amorphous macromolecule’s dynamics behave in the Received: August 8, 2016 Revised: September 8, 2016

A

DOI: 10.1021/acs.macromol.6b01461 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

with diameter σ = 1.0 in LJ units, fixed on an FCC lattice at a density of 1.4, with the 111 face exposed to the polymer chain, consistent with previously published work.47 We vary interfacial energy by varying the ratio εmw/εmm of monomer−wall to monomer−monomer LennardJones interaction strength from 0.4 to 1.1. We compare the dynamics and glass formation behavior of these simulations to that of a bulk melt of the same polymer model with chain length 20 and subject to a comparable simulation history. Four entirely separate simulations are performed for each set of conditions probed to allow for statistical replication. Simulations are performed in the LAMMPS molecular dynamics environment48 using a RESPA time integration scheme,49 with pair interactions calculated on the outermost loop with a time step of 0.003τLJ and bond forces calculated 3 times as often. Temperature is controlled via the Nosé−Hoover thermostat with a damping parameter of 2τLJ. Simulations are equilibrated through a temperature quench and annealing procedure comparable to experiments. Specifically, chains are initially equilibrated at a high temperature of T = 1.5 for 350 million timesteps (ts), followed by a temperature ramp to T = 0.1 at a rate of 10−5T/τLJ. Configurations saved at regular temperature intervals are then subject to an additional equilibration of duration 3.5 × 106 ts when T > 1.0 or 3.5 × 107 ts when T ≤ 1.0. Data are then collected from runs continued from these equilibrations. In summary, we consider the system to be in equilibrium at a given temperature if and only if it was subjected to a fixed-temperature equilibration period of at least 100 times its mean alpha relaxation time, as determined from the decay of the self-part of the intermediate scattering function (described below). This type of criterion for equilibration, which has been widely employed in other recent simulation studies,26,27,30,41,45,46,50−54 is illustrated graphically in Figure 1 for the case of the 1000-bead chain in a vacuum. For single chains in a vacuum, the linear and angular momentum are zeroed out and the chain is recentered in the box every 333 ts during quench and equilibration steps but not during data collection. For comparison to single-chain glass formation data, we perform simulations of glass formation in a melt of 20-bead polymer chains interacting via the same force field as the single chain polymers above. Melts consist of 100 chains, with periodic boundary conditions. These

same manner regardless of whether it is in crowded bulk-like state, a dilute solution state, or near an interface. Resolving this apparent contradiction is thus a matter of significant theoretical and practical interest. Moreover, glass formation in individual macromolecules remains a poorly understood phenomenon requiring further investigation in its own right. In order to address this challenge, we employ molecular dynamics simulations to characterize the glassformation behavior of model single macromolecule chains in order to determine whether and how their dynamics and glass transition differ from the bulk and how they are affected by adhesion to a substrate. Our results indicate that glass formation in a single molecule is consistent with an extreme state of nanoconfinement, similar to that reported in ultrathin films and small polymeric nanoparticles. As with those systems, polymer−substrate interactions can have an enormous impact on the molecule’s relaxation dynamics.

■

METHODS

We consider glass formation in single bead−spring polymer chains of length 256 or 1000 beads. Simulations employ an attractive bead− spring polymer model, extended from the work of Kremer and Grest,38 that has been widely employed in the literature, and results throughout the paper are presented in standard Lennard-Jones (LJ) dimensionless units38−40 of temperature T, time τLJ, and energy ε. The Kremer− Grest model has previously been shown to exhibit glass formation behavior in qualitative agreement with experimental polymers in a variety of respects.41−46 In order to avoid heterogeneously nucleated chain crystallization when the polymer is brought into contact with a rigid crystalline wall, we slightly modify the polymer model by reducing the bond length as described in a previous publication.47 We have previously shown that this alteration strongly enhances crystallization resistance by enhancing packing frustration that emerges from a mismatch in the model’s bonded and nonbonded interaction length scales.47 In this revised model, nonbonded beads interact via a LennardJones (LJ) 12−6 interaction

⎡⎛ σ ⎞12 ⎛ σ ⎞6 ⎤ E LJ(r ) = 4ε⎢⎜ ⎟ − ⎜ ⎟ ⎥ ⎝r⎠ ⎦ ⎣⎝ r ⎠

(1)

with ε and σ both equal to one for monomer−monomer interactions, as in the standard Kremer−Grest model. This interaction is truncated at a range of 2.5σ, with the energy (but not force) shifted to zero at this point. As described below, throughout these simulations we maintain a value of εmm equal to one for segment−segment interactions and vary only the wall−polymer interaction in simulations of adsorbed chains. Bonded beads interact via the finitely extensible nonlinear elastic (FENE) potential E FENE(r ) =

⎡ ⎡⎛ σ ⎞12 ⎛ σ ⎞6 ⎤ ⎛ r ⎞2 ⎤ 1 KR 0 2 ln⎢1 − ⎜ ⎟ ⎥ + 4ε⎢⎜ ⎟ − ⎜ ⎟ ⎥ + ε ⎝r⎠ ⎦ ⎢⎣ 2 ⎝ R 0 ⎠ ⎥⎦ ⎣⎝ r ⎠ (2)

As in the standard Kremer−Grest model, K = 30 and ε = 1.0, maintaining the standard Kremer−Grest energy scale for bonded interactions; however, R0 and σ are reduced from their standard values of 1.5 and 1.0, respectively, to 1.3 and 0.8, yielding a greater resistance to crystallization.47 Each simulation employs a single polymer chain composed of 256 or 1000 beads. As each bead in this model corresponds to approximately a Kuhn segment, the longer of these two chains can be understood as corresponding to a molecular weight in the hundreds of thousands for a typical polymer. One set of simulations is composed of the chain in vacuum only, while a second set models the chain adhered on a crystalline substrate. The substrate consists of LJ beads

Figure 1. Illustration of the criterion for equilibration described in the text, for simulations of the 1000-bead chain in vacuum described in the text at temperatures of T = 0.75 (red squares) and T = 0.38 (blue diamonds). The segmental relaxation time, defined as the time at which self-part of the intermediate scattering function Fs(k,t) (y-axis of figure) decays to a value of 0.2 (shown by the correspondingly colored circle at each temperature), must be no greater than 1% of the isothermal equilibration period. Since the equilibration period is of approximately equal length to the data collection time, this implies that this segmental relaxation function will report at least 2 decades of time after the relaxation time at every in-equilibrium temperature, as shown here. B

DOI: 10.1021/acs.macromol.6b01461 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules systems are initially equilibrated at zero pressure and T = 1.5 for 100 000 τLJ and are then quenched at a rate of 10−6T/τLJ. Configurations saved at regular temperature intervals are then subject to an additional equilibration at fixed temperature and zero pressure. The duration of this equilibration is 10 000 τLJ for T ≥ 0.68 or 100 000 τLJ for T < 0.68. The average density of the system over the four trials at each temperature is then determined, and the system size is subject to a slight rescaling to achieve this mean density, after which the system is subject to a brief equilibration in the NVT ensemble. Data are then collected from runs continuing from these equilibrated configurations. As with the single chain systems, we consider the system to be in equilibrium at a given temperature if and only if it was subjected to a fixed-temperature equilibration period of at least 100 times its mean alpha relaxation time. Simulations of the bulk system are performed using a RESPA time integration scheme, with an outer time step of 0.01 τLJ for nonbonded interactions and an inner time step of 0.0025 τLJ used for bonded interactions. Structural relaxation is quantified by the self-part of the intermediate scattering function Fs(k,t),55 calculated at a wavenumber k of 7.07, near the first peak in the monomer structure factor for this model bead− spring polymer (shown for several representative temperatures in the bulk polymer system in Figure 2). This k is also chosen to be

Figure 3. Single 256-bead polymer chain in isolation (top left) and on a crystalline substrate with monomer/wall interaction parameter εmw = 0.4 (top right) and 1.0 (bottom right). 1000-bead polymer chain on a crystalline substrate with monomer/wall interaction parameter εmw = 1.05 (bottom left). Bonds are shown for the top left image only, and the apparent bead size is somewhat reduced in that image for clarity.

liquid medium is similar to the same material surrounded by a gas or vacuum,30 making this a reasonable model for glass formation of a globular macromolecule in solution. Our results indicate that the Tg of an isolated polymer chain is strongly suppressed relative to bulk, with a commensurate enhancement in the rate of relaxation. In order to confirm that our results are not the outcome of a particular Tg convention, we employ two conventions for Tg and verify that the results are consistent. We first consider Tg as determined calorimetrically, based on the position of a change in slope of the system’s energy. This calorimetric Tg is defined as the intersection of linear fits to the liquid and glassy temperature ranges for the energy, as shown in Figure 4a. Because of the weak change in slope at Tg and the intrinsically large thermodynamic noise in these single-molecule systems, the resulting Tg value exhibits a dependence on the temperature ranges used for the above linear fits. In order to account for this, we average single-chain calorimetric Tg over four separate trials and 12 different choices of temperature range for these linear fits (a single temperature range was used in the bulk as results are less sensitive to the selected range in this case; results from individual fits shown in the Supporting Information). As shown by Table 1, calorimetric Tg is suppressed by an average of 36.6 ± 4.8% in the 256-bead chain and 22.4 ± 3.2% in the 1000-bead chain. As shown by Figures 4b and 4c, this shift in the pseudothermodynamic Tg is reflected in the globule’s dynamics: the relaxation rate as measured by the self-part of the intermediate scattering function (comparable to time-offlight incoherent neutron scattering) is greatly accelerated compared to a comparable bead−spring polymer in the bulk melt state. As shown in Table 1, the dynamic Tg, defined here (as in several earlier simulation studies30,45,46,53) as the temperature at which τα = 103τLJ, where the simulations begin to fall from equilibrium, is reduced by 30.8 ± 0.3%, an amount nearly as great as the calorimetric Tg reduction. A somewhat smaller dynamic Tg suppression of 17.7 ± 0.1% is observed in the 1000-bead globule, consistent with the smaller surface-to-volume ratio of this chain. The observation of a large suppression in Tg and associated enhancement in overall and interfacial dynamics is evidently

Figure 2. Representative plots of structure factor for the bulk polymer system described in the text at T = 1.0 (blue diamonds), T = 0.6 (red squares), and T = 0.45 (green triangles). comparable to the wavenumber employed in numerous recent simulation studies, such that results here should be comparable to other recent simulations of bead−spring polymers in the bulk and nanoconfinement.26,27,30,41,42,45,53,56−58 Consistent with prior simulation studies,26,27,30,42,45,53,54 the segmental structural relaxation time τα is defined as the time at which Fs(k,t) = 0.2, employing a stretched exponential form for data smoothing and interpolation. Local dynamics are quantified by first sorting monomers into bins based on their position and then performing this same analysis on particles located within each bin at some initial reference time.

■

RESULTS Chain in a Vacuum. We begin by considering the glass formation behavior of these individual polymer chains in a vacuum. In the temperature range relevant to glass formation, these chains assume a collapsed globular state, shown in Figure 3, consistent with the understanding that polymer chains in a vacuum or gas assume a collapsed globular state rather than an ideal random walk.59−61 While we have not observed a transition to an expanded coil state in these simulations, it is evidently above the maximal temperature of 1.5 probed in these simulations, with prior simulation and theory work suggesting that it lies in the temperature range of 2 to 3.61−63 256-bead and 1000-bead chain globules exhibit mean surface radii of ≈4σ and ≈6σ, respectively, near Tg, corresponding to ≈4 or ≈6 nm.38−40 The glass transition of a polymer surrounded by a soft C

DOI: 10.1021/acs.macromol.6b01461 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

significant dynamic Tg suppression emerges from wellequilibrated data without any possibility of additive contamination, ruling out complications that have been argued lead to spurious observations of nanoconfinement effects on Tg.35−37 Adsorbed Polymer Chains. Is there any way to reconcile these results with observations of bulk-like dielectric relaxation dynamics in P2VP chains adsorbed on a silica substrate? To answer this question, we simulate individual polymer chains adsorbed on a crystalline substrate over a range of interfacial energies. We vary the interfacial energy by varying the ratio εmw/εmm of monomer−wall to monomer−monomer LennardJones interaction strength from 0.4 to 1.05. Simulations at several weaker wall interactions were observed to separate from the wall, indicating that a desorption transition for this system is below εmw/εmm = 0.4. We therefore exclude simulations with εmw/εmm < 0.4 as being unrepresentative of well-adsorbed chains. We also exclude results for appreciably stronger interactions, where the chain tends to collapse to a monolayer. Results presented here are therefore for well-adsorbed, nonmonolayer chains. As shown by Figure 5, when a polymer chain is only weakly attracted to the interface, it exhibits a pronounced suppression

Figure 5. Glass transition temperatures of substrate-adhered 256-bead (red) and 1000-bead (blue) polymer chains, determined via the τα = 103τLJ convention described in the text and normalized by the bulk value, as a function of monomer−wall interaction strength. Solid lines are linear fits to the data.

in Tg. However, with increasing surface attraction, the polymer’s Tg increases linearly up to a “compensation point” where a bulklike Tg is found, in the range εmw/εmm ≈ 1.0−1.1. This linear crossover from Tg suppression to Tg enhancement with increasing surface adhesion strength appears to be a general result, with similar trends observed in supported thin films14,27,64 and in simulations of multi-nanolayered polymers.30 More broadly, this phenomenon is similar to surfaceinteraction-induced compensation effects in thermodynamic transitions, including the second-order phase transition temperature of spin models and phase separating fluids,65,66 the collapse of polymers tethered to an interacting boundary,67 and self-assembly processes such as protein folding in confined cavities.68 Explicit calculation shows that the problem of calculating the shift of the critical temperature in spin systems undergoing second-order phase transitions and the problem of calculating the change of free energy of confined polymers are very closely related.66,69 It is then reasonable that a corresponding compensation phenomenon should emerge in nanoconfined glass-forming liquids in contact with surfaces, where the change of polymer free energy with confinement is related to the sign of the shift of the glass transition from its bulk value. Could the bulklike Tg observed by Tress et al.32 be associated with this compensation point rather than reflecting a general

Figure 4. Glass-formation behavior of a representative trial (one of four) of the single 256-bead chain in a vacuum (red) and 1000-bead chain in a vacuum (blue) in comparison to bulk melt (green): (a) total energy vs temperature with representative linear fits to glassy and melt regions; (b) self-part of the intermediate scattering function for T = 0.55 (diamonds), T = 0.50 (squares), and T = 0.45 (triangles); (c) τα vs temperature.

Table 1. Glass Transition Temperature of Isolated 256-Bead and 1000-Bead Single Polymer Chains vs Bulk Melt system

calorimetric Tg

dynamic Tg

256-bead 1000-bead bulk

0.250 ± 0.017 0.288 ± 0.011 0.371 ± 0.007

0.307 ± 0.001 0.364 ± 0.000 0.443 ± 0.000

robust to the definition of Tg, with a mean reduction of Tg by 33.7% in the 256-bead chain when averaged across these two conventions. In terms of the Tg of polystyrene, for example, the result for the 256-bead chain corresponds to a reduction of approximately 126 K relative to the bulk. This is comparable to the experimental observation of a 122 K suppression in the Tg of a 3 nm thick polystyrene filma thickness similar to the diameter of the presently simulated globule.23 This finding of a D

DOI: 10.1021/acs.macromol.6b01461 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules absence of nanoconfinement effects on Tg? Figure 5 suggests that compensation occurs when the monomer−substrate attractive interaction is modestly stronger than the monomer−monomer attractive interaction. This corresponds to a wetting substrate, as indicated by the highly “flattened” chain configuration shown in Figure 3. Consistent with these predictions, the polymer−substrate pair examined by Tress et al.P2VP on silicaexhibits very favorable polymer−substrate interactions due to strong monomer−substrate hydrogen-bonding interactions.32 Furthermore, the chain height profiles they report, based upon AFM measurements, reveal a highly flattened chain configuration (i.e., globules that are 50 nm wide and 2 nm high),32 consistent with our results for these chains near the compensation point. These correspondences suggest that the bulk-like Tg reported by Tress et al.32 results from proximity to a compensation point at which suppressed dynamics near an attractive substrate compensate for a tendency toward enhanced mobility at the free interface. Interfacial Gradients. Beyond changes in the mean Tg, how should we expect the distribution of relaxation behavior to change from the bulk in this system? As shown in Figure 6, the enhancement in overall chain dynamics is driven by a reduction in relaxation time near the globule surface, comparable to observations at the free surface of freestanding and supported films. This observation has implications for the coupling of polymer nanoparticles’ and proteins’ dynamics to their

environments. For example, a similarly mobile surface layer observed in simulations of metallic nanoparticles is suggested to have a substantial impact on these particles’ catalytic properties.70 This finding also has important implications for the understanding of the physical origin of shifts in Tg in these single polymer chains relative to the bulk. Several theoretical treatments have suggested that shifts with chain length in the temperature of established thermodynamic transitions such as crystallization and coil−globule transitions in single chains are driven by finite size effects.71,72 There is also some evidence for a role of finite-size effects on the glass transition of nanoconfined liquids, especially small-molecule liquids confined to pores.73 In contrast, the dominance of surface gradients seen in Figure 6 (for τα) and Figure 7 (for Tg) suggests that the Tg alterations observed here relative to bulk are driven by an interface effect rather than by a finite size effect. This is

Figure 7. Local Tg of surface-adsorbed 256-bead (a) and 1000-bead (b) polymer chains as a function of distance from the substrate. Filled symbols of different colors denote different values of the polymer/wall interaction, as follows: εmw/εmm = 0.4 (blue diamonds), 0.6 (red squares), 0.8 (green triangles), 1.0 (purple circles), and 1.05 (orange diamonds, 1000-bead only). Open circles denote Tg for the isolated chain in a vacuum as a function of distance from its center of mass. The number of points included is lower for higher εmw because the adsorbed globule becomes thinner with increasing wall attraction. Inset of (a) shows a cutaway of the isolated chain, with each segment colored by the mean Tg at its distance from the chain center of mass based on a linear fit to the isolated chain Tg-gradient data (the open circles in part a), and with dark blue indicating the highest local Tg and dark red the lowest.

Figure 6. τα (solid points, left axis) and ρ (hollow points, right axis) normalized by their bulk values as a function of distance from center of mass of the 256-bead (a) and 1000-bead (b) isolated chains at T = 0.55 (diamonds), T = 0.50 (squares), and T = 0.45 (triangles). E

DOI: 10.1021/acs.macromol.6b01461 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

in nanoconfined Tg. The observation of bulk-like dielectric relaxation dynamics in P2VP chains on a silica substrate,32 in particular, appears likely to result from this compensation effect. A direct experimental test of this proposition would require a study of dielectric relaxation in P2VP chains on a series of rigid surfaces with a range of interfacial energies. We suggest that similar compensation effects might be responsible for observation of nearly bulklike Tg in certain other nanoconfined systems35−37 and several polymer nanocomposites.77 Indeed, surface interactions of an adsorbed polymer can result in enhancement of, suppression of, or no impact on relaxation dynamics depending on the strength of the interaction. For this reason, general conclusions regarding nanoconfinement effects on the glass transition should be based on consistent data spanning multiple interfacial energies and/or “softnesses” of confinement.

consistent with a number of earlier simulation and experimental studies pointing toward a dominance of interfacial effects in determining T g alterations in nanoconfined polymers.15,17,52,74,75 This potential difference in the mechanism of alterations in the temperature of the glass transition relative to alterations in the temperatures of a number of indisputably thermodynamic transitions in single chains and under nanoconfinement will likely remain an important issue for future work in this area. As shown by Figure 7, the near-interface spatial distribution of dynamics in this single chain is a function of the wall− substrate interaction strength in adsorbed chains. For chains with high εmw, near the compensation point, the gradient in dynamics through the globule is truncated. This can be understood based upon experiments by the Torkelson group in which they observed a minimum length scale for the establishment of fully developed gradients in mobility.15 Since, near the compensation point, strong wall−chain attractions cause the chain to become thin and widely spread on the interface, the bulklike mean relaxation time obtained at that point is accompanied by a nearly bulklike distribution of relaxation times. This observation is again consistent with the experimental results of Tress et al., who reported an excess in the long-time tail of the relaxation spectrum (which they attributed to a reduced-mobility layer near the substrate), but not an appreciable enhancement in the fast-relaxing region of the spectrum. While they interpreted this finding as evidence for a lack of nanoconfinement effects, we find that it emerges from the very small thickness of the globule (2 to 3 nm), comparable to the thickness of ≈2.5σ (1.25−2.5 nm in real units) observed here for adsorbed chains with εmw/εmm = 1.0. Evidently, the adsorbed globule is so thin that it cannot fully exhibit suppressed dynamics at the substrate and enhanced dynamics at the free surface simultaneously.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.6b01461. Tables of 256-bead and 1000-bead isolated chain calorimetric Tg determined by several temperature fit ranges (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (D.S.S.). Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under Grant DMR1310433. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Grant OCI-1053575 (XSEDE Grant DMR130011).

■

CONCLUSIONS These results indicate that an isolated globular macromolecule can be viewed as a polymeric nanoparticle for the purposes of understanding its glass transition and segmental dynamics. The qualitative behavior reported here is therefore likely applicable to ultrastable, lightweight polymer glasses produced by matrixassisted pulsed laser evaporation (MAPLE), where enhanced surface mobility in vapor-suspended precursor polymer nanoparticles may contribute to the realization of an ultrastable glassy film.7 The large Tg suppression observed here may also account for or at least contribute to the relatively low Tg’s (commonly in the range of 200 K) often found in globular proteins76 despite their typically relatively strong interactions. These results further indicate that molecular crowding or adsorption of biomacromolecules on solid substrates should generally reduce their relaxation rates relative to dilute solution. This effect grows as molecule−substrate interactions become increasingly strongly attractive and for strong interactions can even lead to vitrification at temperatures above the Tg of the molecule in a densely packed bulk state. Since these effects on dynamics are found to persist to temperatures greater than 2Tg, for a globular biomacromolecule with a Tg in the vicinity of 200 K, adhesion to a substrate can be expected to impact dynamics within biologically relevant temperature ranges. These results also suggest that conclusions regarding the nature of nanoconfinement effects on dynamics and glass formation generally cannot be drawn from individual confined systems because of possible proximity to a compensation point

■

REFERENCES

(1) Dokholyan, N. V.; Pitard, E.; Buldyrev, S. V.; Stanley, H. E. Glassy Behavior of a Homopolymer from Molecular Dynamics Simulations. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2002, 65, 30801. (2) Vitkup, D.; Ringe, D.; Petsko, G. A.; Karplus, M. Solvent Mobility and the Protein “Glass” Transition. Nat. Struct. Biol. 2000, 7, 34−38. (3) Aharoni, S. M. TR: A New Characteristic Temperature for Thermoplastic Polymers. J. Polym. Sci., Polym. Symp. 1973, 42, 795− 805. (4) Dudowicz, J.; Freed, K. F.; Douglas, J. F. Generalized Entropy Theory of Polymer Glass Formation. In Advances in Chemical Physics; Wiley: 2008; Vol. 137, pp 125−222. (5) Cicerone, M. T.; Douglas, J. F. β-Relaxation Governs Protein Stability in Sugar-Glass Matrices. Soft Matter 2012, 8, 2983−2991. (6) Rharbi, Y. Reduction of the Glass Transition Temperature of Confined Polystyrene Nanoparticles in Nanoblends. Phys. Rev. E 2008, 77, 31806. (7) Guo, Y.; Morozov, A.; Schneider, D.; Chung, J. W.; Zhang, C.; Waldmann, M.; Yao, N.; Fytas, G.; Arnold, C. B.; Priestley, R. D. Ultrastable Nanostructured Polymer Glasses. Nat. Mater. 2012, 11, 337−343. (8) Adam, G.; Gibbs, J. H. On the Temperature Dependence of Cooperative Relaxation Properties in Glass-Forming Liquids. J. Chem. Phys. 1965, 43, 139−146.

F

DOI: 10.1021/acs.macromol.6b01461 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

Glass Temperature, Rubbery Stiffening, and Flow. Macromolecules 2012, 45, 2453−2459. (30) Lang, R. J.; Merling, W. L.; Simmons, D. S. Combined Dependence of Nanoconfined Tg on Interfacial Energy and Softness of Confinement. ACS Macro Lett. 2014, 3, 758−762. (31) Guo, Y.; Zhang, C.; Lai, C.; Priestley, R. D.; D’Acunzi, M.; Fytas, G. Structural Relaxation of Polymer Nanospheres under Soft and Hard Confinement: Isobaric versus Isochoric Conditions. ACS Nano 2011, 5, 5365−5373. (32) Tress, M.; Mapesa, E. U.; Kossack, W.; Kipnusu, W. K.; Reiche, M.; Kremer, F. Glassy Dynamics in Condensed Isolated Polymer Chains. Science 2013, 341, 1371−1374. (33) Kremer, F.; Tress, M.; Mapesa, E. U. Glassy Dynamics and Glass Transition in Nanometric Layers and Films: A Silver Lining on the Horizon. J. Non-Cryst. Solids 2015, 407, 277−283. (34) Russell, T. P. Polymers Find Plenty of Wiggle Room at the Bottom. Science 2013, 341, 1351−1352. (35) Serghei, A.; Kremer, F. Metastable States of Glassy Dynamics, Possibly Mimicking Confinement-Effects in Thin Polymer Films. Macromol. Chem. Phys. 2008, 209, 810−817. (36) Serghei, A.; Tress, M.; Kremer, F. The Glass Transition of Thin Polymer Films in Relation to the Interfacial Dynamics. J. Chem. Phys. 2009, 131, 154904. (37) Tress, M.; Erber, M.; Mapesa, E. U.; Huth, H.; Müller, J.; Serghei, A.; Schick, C.; Eichhorn, K.-J.; Voit, B.; Kremer, F. Glassy Dynamics and Glass Transition in Nanometric Thin Layers of Polystyrene. Macromolecules 2010, 43, 9937−9944. (38) Kremer, K.; Grest, G. S. Dynamics of Entangled Linear Polymer Melts: A Molecular-dynamics Simulation. J. Chem. Phys. 1990, 92, 5057−5086. (39) Baschnagel, J.; Varnik, F. Computer Simulations of Supercooled Polymer Melts in the Bulk and in Confined Geometry. J. Phys.: Condens. Matter 2005, 17, R851−R953. (40) Slimani, M. Z.; Moreno, A. J.; Colmenero, J. Heterogeneity of the Segmental Dynamics in Lamellar Phases of Diblock Copolymers. Macromolecules 2011, 44, 6952−6961. (41) Betancourt, B. A. P.; Douglas, J. F.; Starr, F. W. Fragility and Cooperative Motion in a Glass-Forming Polymer−nanoparticle Composite. Soft Matter 2012, 9, 241−254. (42) Hanakata, P. Z.; Douglas, J. F.; Starr, F. W. Local Variation of Fragility and Glass Transition Temperature of Ultra-Thin Supported Polymer Films. J. Chem. Phys. 2012, 137, 244901. (43) Starr, F. W.; Douglas, J. F. Modifying Fragility and Collective Motion in Polymer Melts with Nanoparticles. Phys. Rev. Lett. 2011, 106, 115702. (44) Starr, F. W.; Sastry, S.; Douglas, J. F.; Glotzer, S. C. What Do We Learn from the Local Geometry of Glass-Forming Liquids? Phys. Rev. Lett. 2002, 89, 125501. (45) Ruan, D.; Simmons, D. S. Glass Formation near Covalently Grafted Interfaces: Ionomers as a Model Case. Macromolecules 2015, 48, 2313−2323. (46) Mangalara, J. H.; Simmons, D. S. Tuning Polymer Glass Formation Behavior and Mechanical Properties with Oligomeric Diluents of Varying Stiffness. ACS Macro Lett. 2015, 4, 1134−1138. (47) Mackura, M. E.; Simmons, D. S. Enhancing Heterogenous Crystallization Resistance in a Bead-Spring Polymer Model by Modifying Bond Length. J. Polym. Sci., Part B: Polym. Phys. 2014, 52, 134−140. (48) Plimpton, S. J. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1−19. (49) Tuckerman, M.; Berne, B. J.; Martyna, G. J. Reversible Multiple Time Scale Molecular Dynamics. J. Chem. Phys. 1992, 97, 1990−2001. (50) Lacevic, N.; Starr, F. W.; Schroder, T. B.; Glotzer, S. C. Spatially Heterogeneous Dynamics Investigated via a Time-Dependent FourPoint Density Correlation Function. J. Chem. Phys. 2003, 119, 7372− 7387. (51) Starr, F. W.; Douglas, J. F.; Sastry, S. The Relationship of Dynamical Heterogeneity to the Adam-Gibbs and Random First-

(9) Kirkpatrick, T. R.; Thirumalai, D. Random First-Order Phase Transition Theory of the Structural Glass Transition. In Structural Glasses and Supercooled Liquids; Wolynes, P. G., Lubchenko, V., Eds.; John Wiley & Sons, Inc.: 2012; pp 223−236. (10) Jackson, C. L.; McKenna, G. B. The Glass Transition of Organic Liquids Confined to Small Pores. J. Non-Cryst. Solids 1991, 131−133, 221−224. (11) Keddie, J. L.; Jones, R. A. L.; Cory, R. A. Size-Dependent Depression of the Glass Transition Temperature in Polymer Films. Europhys. Lett. EPL 1994, 27, 59−64. (12) Forrest, J.; Dalnoki-Veress, K.; Dutcher, J. Interface and Chain Confinement Effects on the Glass Transition Temperature of Thin Polymer Films. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1997, 56, 5705−5716. (13) Zheng, X.; Rafailovich, M. H.; Sokolov, J.; Strzhemechny, Y.; Schwarz, S. A.; Sauer, B. B.; Rubinstein, M. Long-Range Effects on Polymer Diffusion Induced by a Bounding Interface. Phys. Rev. Lett. 1997, 79, 241−244. (14) Fryer, D. S.; Peters, R. D.; Kim, E. J.; Tomaszewski, J. E.; Nealey, P. F.; White, C. C.; Wu, W. L. Dependence of the Glass Transition Temperature of Polymer Films on Interfacial Energy and Thickness. Macromolecules 2001, 34, 5627. (15) Ellison, C. J.; Torkelson, J. M. The Distribution of GlassTransition Temperatures in Nanoscopically Confined Glass Formers. Nat. Mater. 2003, 2, 695−700. (16) Baschnagel, J.; Varnik, F. Computer Simulations of Supercooled Polymer Melts in the Bulk and in Confined Geometry. J. Phys.: Condens. Matter 2005, 17, R851−R953. (17) Priestley, R. D.; Ellison, C. J.; Broadbelt, L. J.; Torkelson, J. M. Structural Relaxation of Polymer Glasses at Surfaces, Interfaces, and In Between. Science 2005, 309, 456−459. (18) Roth, C. B.; Dutcher, J. R. Glass Transition and Chain Mobility in Thin Polymer Films. J. Electroanal. Chem. 2005, 584, 13−22. (19) Akabori, K.-I.; Tanaka, K.; Takahara, A.; Kajiyama, T.; Nagamura, T. Substrate Effect on Mechanical Relaxation of Polystyrene in Ultrathin Films. Eur. Phys. J.: Spec. Top. 2007, 141, 173−180. (20) Inoue, R.; Kanaya, T.; Nishida, K.; Tsukushi, I.; Telling, M. T. F.; Gabrys, B. J.; Tyagi, M.; Soles, C.; Wu, W. -l Glass Transition and Molecular Mobility in Polymer Thin Films. Phys. Rev. E 2009, 80, 31802. (21) McKenna, G. B. Ten (or More) Years of Dynamics in Confinement: Perspectives for 2010. Eur. Phys. J.: Spec. Top. 2010, 189, 285−302. (22) Richert, R. Dynamics of Nanoconfined Supercooled Liquids. Annu. Rev. Phys. Chem. 2011, 62, 65−84. (23) Wang, J.; McKenna, G. B. A Novel Temperature-Step Method to Determine the Glass Transition Temperature of Ultrathin Polymer Films by Liquid Dewetting. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 1343−1349. (24) Arabeche, K.; Delbreilh, L.; Saiter, J.-M.; Michler, G. H.; Adhikari, R.; Baer, E. Fragility and Molecular Mobility in Micro- and Nano-Layered PC/PMMA Films. Polymer 2014, 55, 1546−1551. (25) Ediger, M. D.; Forrest, J. A. Dynamics near Free Surfaces and the Glass Transition in Thin Polymer Films: A View to the Future. Macromolecules 2014, 47, 471−478. (26) Lang, R. J.; Simmons, D. S. Interfacial Dynamic Length Scales in the Glass Transition of a Model Freestanding Polymer Film and Their Connection to Cooperative Motion. Macromolecules 2013, 46, 9818− 9825. (27) Hanakata, P. Z.; Douglas, J. F.; Starr, F. W. Interfacial Mobility Scale Determines the Scale of Collective Motion and Relaxation Rate in Polymer Films. Nat. Commun. 2014, 5, 4163. (28) Paeng, K.; Swallen, S. F.; Ediger, M. D. Direct Measurement of Molecular Motion in Freestanding Polystyrene Thin Films. J. Am. Chem. Soc. 2011, 133, 8444−8447. (29) O’Connell, P. A.; Wang, J.; Ishola, T. A.; McKenna, G. B. Exceptional Property Changes in Ultrathin Films of Polycarbonate: G

DOI: 10.1021/acs.macromol.6b01461 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules Order Transition Theories of Glass Formation. J. Chem. Phys. 2013, 138, 12A541−12A541−18. (52) Marvin, M. D.; Lang, R. J.; Simmons, D. S. Nanoconfinement Effects on the Fragility of Glass Formation of a Model Freestanding Polymer Film. Soft Matter 2014, 10, 3166−3170. (53) Ruan, D.; Simmons, D. S. Roles of Chain Stiffness and Segmental Rattling in Ionomer Glass Formation. J. Polym. Sci., Part B: Polym. Phys. 2015, 53, 1458−1469. (54) Simmons, D. S.; Douglas, J. F. Nature and Interrelations of Fast Dynamic Properties in a Coarse-Grained Glass-Forming Polymer Melt. Soft Matter 2011, 7, 11010−11020. (55) Hansen, J.-P.; McDonald, I. R. Theory of Simple Liquids; Elsevier Academic Press: London, 2006. (56) Betancourt, B. A. P.; Douglas, J. F.; Starr, F. W. String Model for the Dynamics of Glass-Forming Liquids. J. Chem. Phys. 2014, 140, 204509. (57) Shavit, A.; Riggleman, R. A. Influence of Backbone Rigidity on Nanoscale Confinement Effects in Model Glass-Forming Polymers. Macromolecules 2013, 46, 5044−5052. (58) Shavit, A.; Riggleman, R. A. Physical Aging, the Local Dynamics of Glass-Forming Polymers under Nanoscale Confinement. J. Phys. Chem. B 2014, 118, 9096−9103. (59) Simmons, D. S.; Sanchez, I. C. A Model for a Thermally Induced Polymer Coil-to-Globule Transition. Macromolecules 2008, 41, 5885−5889. (60) Simmons, D. S.; Sanchez, I. C. Pressure Effects on Polymer Coil−Globule Transitions near an LCST. Macromolecules 2010, 43, 1571−1574. (61) Simmons, D. S.; Sanchez, I. C. Scaled Particle Theory for the Coil−Globule Transition of an Isolated Polymer Chain. Macromolecules 2013, 46, 4691−4697. (62) Luna-Bárcenas, G.; Gromov, D. G.; Meredith, J. C.; Sanchez, I. C.; de Pablo, J. J.; Johnston, K. P. Polymer Chain Collapse near the Lower Critical Solution Temperature. Chem. Phys. Lett. 1997, 278, 302−306. (63) Ortiz-Estrada, C. H.; Luna-Bárcenas, G.; Alvarado, F. J.; Gonzalez-Alatorre, G.; Sanchez, I. C.; Castillo-Tejas, J.; Manero-Brito, O.; Ramírez, N. F.; García, S. R. V. Polymer Chain Collapse in Supercritical Fluids. 1. Molecular Simulation Results. Macromol. Symp. 2009, 283−284, 250−265. (64) Torres, J. A.; Nealey, P. F.; de Pablo, J. J. Molecular Simulation of Ultrathin Polymeric Films near the Glass Transition. Phys. Rev. Lett. 2000, 85, 3221−3224. (65) Li, H.; Paczuski, M.; Kardar, M.; Huang, K. Surface Ordering and Finite-Size Effects in Liquid-Crystal Films. Phys. Rev. B: Condens. Matter Mater. Phys. 1991, 44, 8274−8283. (66) Ishinabe, T. Self-avoiding Lattice Walk Confined between Two Planes Interacting with Them. J. Chem. Phys. 1985, 83, 4151−4158. (67) Douglas, J. F.; Wang, S. Q.; Freed, K. F. Flexible Polymers with Excluded Volume at a Penetrable Interacting Surface. Macromolecules 1987, 20, 543−551. (68) Rathore, N.; Knotts, T. A.; de Pablo, J. J. Confinement Effects on the Thermodynamics of Protein Folding: Monte Carlo Simulations. Biophys. J. 2006, 90, 1767−1773. (69) Domb, C. Critical Temperature of Finite Systems in D Dimensions. J. Phys. A: Math., Nucl. Gen. 1973, 6, 1296. (70) Zhang, H.; Kalvapalle, P.; Douglas, J. F. String-like Collective Atomic Motion in the Interfacial Dynamics of Nanoparticles. Soft Matter 2010, 6, 5944. (71) Taylor, M. P.; Aung, P. P.; Paul, W. Partition Function Zeros and Phase Transitions for a Square-Well Polymer Chain. Phys. Rev. E 2013, 88, 12604. (72) Rampf, F.; Binder, K.; Paul, W. The Phase Diagram of a Single Polymer Chain: New Insights from a New Simulation Method. J. Polym. Sci., Part B: Polym. Phys. 2006, 44, 2542−2555. (73) Alcoutlabi, M.; McKenna, G. B. Effects of Confinement on Material Behaviour at the Nanometre Size Scale. J. Phys.: Condens. Matter 2005, 17, R461−R524.

(74) Paeng, K.; Richert, R.; Ediger, M. D. Molecular Mobility in Supported Thin Films of Polystyrene, Poly(methyl Methacrylate), and poly(2-Vinyl Pyridine) Probed by Dye Reorientation. Soft Matter 2011, 8, 819−826. (75) Simmons, D. S. An Emerging Unified View of Dynamic Interphases in Polymers. Macromol. Chem. Phys. 2016, 217, 137−148. (76) Tournier, A. L.; Xu, J.; Smith, J. C. Translational Hydration Water Dynamics Drives the Protein Glass Transition. Biophys. J. 2003, 85, 1871−1875. (77) Moll, J.; Kumar, S. K. Glass Transitions in Highly Attractive Highly Filled Polymer Nanocomposites. Macromolecules 2012, 45, 1131−1135.

H

DOI: 10.1021/acs.macromol.6b01461 Macromolecules XXXX, XXX, XXX−XXX