Unfolding of a Single Polymer Chain from the Single Crystal by Air

2 days ago - Abstract Image. Understanding the mechanisms of the ... of PEO chain (PDF). View: ACS ActiveView PDF | PDF | PDF w/ Links | Full Text HTM...
0 downloads 0 Views 3MB Size
Download PDF
Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

pubs.acs.org/Macromolecules

Unfolding of a Single Polymer Chain from the Single Crystal by Air-Phase Single-Molecule Force Spectroscopy: Toward Better Force Precision and More Accurate Description of Molecular Behaviors Peng Yang,† Yu Song,†,‡ Wei Feng,†,§ and Wenke Zhang*,† †

State Key Laboratory of Supramolecular Structure and Materials, College of Chemistry, ‡Institute of Theoretical Chemistry, and Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China

§

Downloaded via UNIV OF SOUTH DAKOTA on September 5, 2018 at 00:28:22 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: Understanding the mechanisms of the mechanical deformation of lamellar crystals at the molecular level is of prime importance to rational design of advanced crystalline polymer materials. Single-molecule force spectroscopy (SMFS) can directly characterize molecular behavior and kinetic parameters that are masked in ensemble measurements. However, current SMFS approach cannot sufficiently manipulate a single molecule in air, which is the real working condition for most crystalline polymer materials. Here, we establish an air-phase atomic force microscopy (AFM)-based SMFS method that allows the unfolding of a single helical poly(ethylene oxide) (PEO) chain from the single crystal in air. Our results show that the mechanostability of PEO stem and unfolding potential are significantly enhanced in air compared with the case in liquid. The airphase SMFS method can achieve a much better force precision of 4 pN even at rapid stretching velocity of ∼100 μm/s. Moreover, some intermediate states (e.g., the movement of helical loop within the crystal phase), which were not detectable by using liquid-phase SMFS, have been identified by air-phase SMFS. Therefore, this proposed approach opens new ways for investigating the nanomechanical properties and corresponding molecular mechanism of polymer materials used in solvent-free state.

■

SMFS experiment is generally performed in liquid,32−42 despite that most of the semicrystalline polymer materials are used in air. Thus, an air-phase SMFS method must be developed because the large gap between polymer−solvent and polymer− air interfacial tensions would lead to differences in molecular behavior and kinetic parameters.32,33 Optical and magnetic tweezers43,44 cannot detach the particles from the substrate due to the huge interfacial adhesion, thereby failing to stretch a single molecule in air. By contrast, atomic force microscopy (AFM) enables the tip to overcome interfacial adhesion and is an ideal technique for measuring single-molecule mechanical response under ambient conditions. Furthermore, the extremely weak hydrodynamic drag makes it possible for air-phase SMFS to enhance the stretching velocity and force precision.45−50 In this regard, scholars in materials science and related fields aim to develop an air-phase SMFS method that can reach the pulling velocity used by conventional mechanical test22,51 and can be applied to all commercial AFMs. In this paper, we expand the application of the AFM-based SMFS method to air-phase study of the force-induced unfolding of a single polymer chain from single crystals. The air-phase AFM-based SMFS method is established by optimizing the environment humidity, cantilever stiffness, and AFM tip hydrophobicity. We further examine the molecular behavior, the

INTRODUCTION Crystalline polymer materials are generally composed of crystalline lamellae alternating with amorphous regions, forming a highly interconnected network.1−4 This sandwich structure enables the intercrystalline chain connections (known as tie chains) to stretch significantly at the initial elastic deformation and undergo stress-induced melting and recrystallization of the crystalline lamellae during severe plastic deformation.5−7 Therefore, the crystal phase plays a key role in defining the mechanical properties of crystalline polymer materials; understanding the molecular mechanisms in lamellar crystals during mechanical deformation is of fundamental importance to the development of advanced crystalline polymer materials.8−13 However, the nanometer thickness of lamellar crystals limits the direct characterization of molecular behavior and dynamics during mechanical deformation. This issue can be addressed by forced unfolding of a single polymer chain from the single crystals in the solvent-free state (e.g., in air), which is the real working condition for most crystalline polymer materials. Single-molecule force spectroscopy (SMFS) has been a powerful means to investigate inter- or intramolecular interactions at the single-molecule level.14−21 The corresponding molecular behavior and kinetic parameters can be derived from single-molecule measurements.14,22−24 The single-molecule mechanics provide the temporal structural information when the length of the unfolded chain is measured with subnanometer precision.16,25−29 The kinetic parameters can be probed by varying the loading rate.22,23,30,31 However, traditional © XXXX American Chemical Society

Received: July 17, 2018 Revised: August 23, 2018

A

DOI: 10.1021/acs.macromol.8b01544 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

Both gas streams were mixed at different ratios to achieve different levels of relative humidity and poured into the liquid cell of the AFM instrument containing one outlet and inlet and sealed with an O-ring. The humidity was measured by a sensor (iTHX-W3, Omega, USA). SMFS. All AFM-based SMFS experiments in air and liquid were performed on a NanoWizardII BioAFM (JPK Instrument AG, Berlin, Germany). Detailed descriptions on the operation of the AFM imaging and SMFS experiment were reported in a previous work. 34 Silicon cantilevers (OTESPA-R3, 26 N/m, Bruker, Germany) were used for representative AFM imaging in air. For SMFS experiment, PEO single crystals were first imaged by tapping mode in air or liquid. A crystal was selected and zoomed in and the instrument was switched to contact mode. The bare or functionalized AFM tip (MLCT-E, 0.2 N/m, Bruker) was allowed to execute random approach−contact−retract (at contact force of 0.3−2 nN and contact time of 0.1−3 s) cycles on the selected area of the crystal surface. Over 80 force−distance (F−D) curves were obtained at each pulling speed (0.02, 0.1, 0.5, 1, 2, 10, 20, 50, and 100 μm/s). We determined the cantilever stiffness k (pN/nm) for each cantilever prior to each individual use of cantilever using the thermal noise method.61 F−D curves were obtained at a sampling rate of 10000 Hz, and 102−105 data points were collected on each curve. For some F−D curves obtained with small cantilever, an interference artifact was present and can be removed using the method developed by Perkins et al.16 We analyzed the resulting F−D curves using the following wormlike chain (WLC) model: ÄÅ ÉÑ −2 kBT ÅÅÅ 1 ij x yz 1 x ÑÑÑÑ Å FWLC = Å jj1 − zz − + ÑÑ Lp ÅÅÅÅÇ 4 k L{ 4 L ÑÑÑÖ (1)

surrounding-environment effect, and the unfolding energy landscape. The air-phase SMFS method can achieve high force precision even at a rapid stretching velocity. Some new intermediate states (e.g., the movement of helical loop within the crystal phase), which were not detectable by using liquid phase SMFS, have been identified by air-phase SMFS. Thus, this airphase SMFS method offers a new way to study a broad range of polymer materials in condensed states at the molecular level.

■

MATERIALS AND METHODS

Chemicals and Materials. Poly(ethylene oxide) (HS-PEOOCH3, Mn = 48.5K g/mol, PDI = 1.05) and polystyrene (Mn = 29K g/mol, PDI = 1.1) were purchased from Polymer Source Inc., CAN. Amyl acetate, ethyl acetate, and hexadecane were obtained from Sigma-Aldrich LLC. 3-Aminopropyldimethylmethoxysilane was acquired from Fluorochem, UK. All other chemical reagents were of analytical reagent grade and used as received without further purification. High-purity deionized water (dH2O > 18 MΩ·cm) from a Millipore System was adopted to prepare all aqueous solutions. Preparation of Functionalized Silicon Slices. Silicon slices were treated using a freshly prepared piranha solution (H2O2/H2SO4 = 3:7 in volume) for 180 min. Then silicon slices were rinsed thoroughly with deionized water to obtain hydrophilic silicon slices. After drying in an oven (around 80 °C, 180 min), the hydrophilic slices were placed into a desiccator containing P2O5 for 10 min. Subsequently, 40 μL of 3-aminopropyldimethylmethoxysilane was placed into a plastic weighing boat inside the desiccator. The desiccator was then sealed and left for 120 min at room temperature. The silanized slices were rinsed with methanol three times (20 mL per rinse) and dried under the flow of nitrogen gas. Preparation of Polystyrene (PS)-Coated Silicon Slices (PS film). PS films were prepared by spin-casting 0.2 wt % PS solution in ethyl acetate (filtered by 0.25 μm filter) onto the hydrophilic silicon slices at 2000 rpm for 60 s. The PS samples were annealed at 50 °C for 60 min and at 150 °C for 120 min to remove the residual solvent. Preparation of Functionalized AFM Tips. Silicon nitride AFM tips (MLCT or DNP, Bruker Nano, Santa Barbara, CA) with different functions were employed for SMFS experiments. The AFM cantilevers were treated with piranha solution (H2O2/H2SO4 = 3:7 in volume) for 30 min to obtain hydrophilic AFM tips (i.e., hydroxyl group modified AFM tip). The tips were then thoroughly rinsed with deionized water and dried in an oven at 80 °C for 180 min to remove any remaining water. The vapor-phase deposition method was introduced to silanize the cleaned AFM tips by suspending them in the atmosphere of 3-aminopropyldimethylmethoxysilane in a dry nitrogen-purged desiccator for 120 min at room temperature. After rinsing with methanol three times, the silanized tips were placed in an oven at 80 °C for 10 min. Preparation of PEO Single Crystals and Their Immobilization. PEO single crystals were prepared from diluted solution by selfseeding method through the methods reported in the previous work of Liu et al.34 In brief, 1 mg of PEO (48.5K g/mol) was dissolved in 10 g of amyl acetate at 60 °C for 10 min. The hot solution was transferred to a water bath at 5 °C for 4 h. The polymer solution was heated to the seeding temperature at 46 °C with a heating rate of 10 °C/min and held at this temperature for 10 min to form stabilized and uniform nuclei. The solution was then subjected to crystallization at 25, 38, or 40 °C for 2−12 h depending on the crystallization temperature. The suspension of PEO single crystals was deposited onto the silanized silicon surface and incubated for 30 min after the sample was rinsed with amyl acetate. The immobilized single crystals on the silicon surface were used for AFM imaging and SMFS experiment. Control of Relative Humidity. A method previously reported by Butt et al.52 was used to adjust the relative humidity (RH) during the SMFS experiment. A stream of nitrogen was split into a stream of pure nitrogen and a stream of water vapor-saturated nitrogen. The second stream of nitrogen was bubbled through a glass tube into pure water at different speed levels to obtain water vapor-saturated nitrogen.

where Lp is the persistence length of the polymer chain, L is the contour length of the polymer, kB is the Boltzmann constant, T is the absolute temperature, and x is the end-to-end distance of the extended single chain. F−D curves for a wide variety of polymers or biopolymers have been well described by the WLC model.11,22,32,33 The elasticity of the unfolded PEO chain was well described by the WLC model with Lp = 0.34 nm. Single-molecule pulling experiments were performed under different force loading rates to obtain the kinetic parameters of PEO unfolding. The experimental data were then fitted to the Bell−Evans model.53,54 The kinetic parameters and conceptual free-energy landscapes for the unfolding of the PEO chain from the single crystal were determined using a previously established method.55 Calculation of the PEO−Solvent Interfacial Free Energy. The PEO−solvent interfacial free energy, γPEO−sol, was calculated according to Wu’s equation:56,57

γPEO−sol = γPEO + γsol −

d d 4γPEO γsol d γPEO

+

d γsol

−

p p 4γPEO γsol p p γPEO + γsol

(2)

with p d γPEO = γPEO + γPEO

(3)

and d p γsol = γsol + γsol

(4)

where γPEO and γsol are the surface tensions of PEO and the solvent, γdPEO and γdsol are the dispersive components of PEO and the solvent, and γpPEO and γpsol are the polar components of PEO and the solvent, respectively. The surface tensions of PEO significantly vary. The surface tensions of γsol and γdsol can be calculated from Hansen solubility parameters (Table 1) developed by Beerbower:58 ij 1 yz δd 2 + 0.632δp2 + 0.632δ h 2 = 13.9jjj zzz j Vm z k {

1/3

B

γsol

(5)

DOI: 10.1021/acs.macromol.8b01544 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules Table 1. Solubility Parameters and Interfacial Free Energy Hansen solubility parametersa

interfacial free energyb

solvent

δd (MPa )

δp (MPa )

δh (MPa )

γsol (mJ/m )

γd (mJ/m )

γp (mJ/m2)

amyl acetate hexadecane air

7.48 7.97

1.52 0

3.42 0

24.69 30.35

21.32 30.35

3.37 0

1/2

1/2

1/2

2

2

polymer

γ (mJ/m2)

γd (mJ/m2)

poly(ethylene oxide)

42.90

30.90

γPEO−sol (mJ/m2) 6.60 12.00 42.90c γp (mJ/m2) 12.00

a

Hansen solubility parameters of hexadecane and amyl acetate are the values which have been reported.70 bInterfacial free energies were calculated according to the corresponding Hansen solubility parameters and Wu’s equation.56,57 cIn air, we regard surface tension of PEO as the interfacial free energy between PEO and air.71,72 and d γsol

=

0.0715Vm1/3δd 2

the force plateau can be observed during the pulling of a single PEO chain out the single crystal (Figure 1c). The pulling of polystyrene (PS) chains from a PS film surface further demonstrates the efficacy of RH control for the air-phase SMFS (Figure S1). Moreover, the hydrophobic substrate and tip, which exhibit low surface energy and weak capillarity, can also achieve the weak adhesion force59,62,63 and thus decrease the ΔD (Figure 1e). Using the stiffer cantilever is another effective method to decrease ΔD. This is evident from the data obtained using cantilevers with different spring constants at the RH of 11% (Figure 1f). The ΔD decreases 4-fold when the cantilever spring constant is increased from 0.02 to 0.2 N/m and then decreases slightly when the k is increased from 0.2 to 0.7 N/m (Figure 1g). However, the cantilever stiffness cannot be increased arbitrarily since the stiffer cantilever may result in higher force noise and perturbs the unfolding process by adding a highfrequency force modulation on the energy barrier.64−66 Considering these facts, the cantilever with k around 0.2 N/m is a more suitable choice. Taken together, a combination of the cantilever of 0.2 N/m, RH of 11%, and amino-silanized tip leads to the 35 nm ΔD, making it possible to study the unfolding of a PEO chain with the length about ∼395 nm in air. Air-Phase AFM-Based SMFS Experiment on PEO Single Crystals. We then used the above optimized experimental condition (with cantilever spring constant of 0.2 N/m, RH of 11%, and amino-silanized tip) to unfold individual PEO chain from the single crystal. We performed the air-phase SMFS experiments on the three PEO single crystal with the thickness of 7.8, 9.6, and 11.2 nm (Figure 2a,b,c). As the chains fold back and forth into 72 helical stems with direction essentially perpendicular to the crystal lamellar surface, the PEO stem can be gradually stretched out of the crystal during tip−sample separation (as the schematic shown in Figure 2d). Figure 2e shows the typical F−D curves obtained on the single crystals at a stretching velocity of 0.02 μm/s. The F−D curves display sawtooth peaks, and the gaps in between the adjacent peaks are regular. According to the previous steered molecular dynamics (SMD) simulation,67 we attribute the sawtooth peaks to the unfolding of two PEO stems (i.e., a complete fold). The contour length increments (ΔL) in between the regularly spaced peaks were estimated by the wormlike chain (WLC) model (Figure S2). The adjacent peaks were identified by using a self-developed algorithm implemented in Igor Pro (Wavemetrics, Portland) with the force over 14 pN (the force difference between a peak and its neighboring valley as shown in Figures S2 and S3). As the top panel shown in Figure 2f, ΔL in between the regularly spaced peaks are 18.0 ± 3.6, 25.0 ± 4.0, and 29.4 ± 4.6 nm for these three types of single crystals, which are proportional to the crystal thickness and corresponding to the unfolding of two stems (or one fold as shown

(6)

where Vm is the average molar volume and δd, δp, and δh are the Hansen solubility parameters due to dispersion, dipole, and hydrogen forces, respectively.

■

RESULTS AND DISCUSSION Optimizing the Air-Phase Experimental Condition for the Pulling of a Single Polymer Chain. To unfold a single polymer chain from the single crystal in the solvent-free state, we need to expand the application of AFM-based SMFS in air. The PEO single crystals were obtained through solution crystallization by using a self-seeding method and immobilized as described in our previous study.34 The AFM tip was brought to contact with the crystal surface in the selected area after AFM imaging. During retraction of the AFM tip, the PEO chain was pulled out of the single crystal producing the characteristic force plateau. For the traditional SMFS experiments in liquid, the force plateau can be identified in the force−distance (F−D) curve (the red curve in Figure 1a). In contrast, such a force plateau may get covered by the big adhesion peak in air (the blue curve in Figure 1a) since there normally exists a thin layer of water on the surface. Because of such water layer, a capillary neck will form between the AFM tip and sample surface causing the strong adhesion between them. Figure 1b is the schematic that deciphers how the interfacial adhesion influences the single-molecule measurements. While retracting from the surface of single crystal, the cantilever is forced to deflect significantly due to the strong interfacial adhesion (change from stage 1 to 2 in Figure 1b). After the rupture of the capillary bridge (Figure 1b), the cantilever rapidly relaxes (change from stage 2 to 4 in Figure 1b). Simultaneously, the polymer chain (the red chain in Figure 1b) would be pulled out of the single crystal. The magnitude of single-molecule stretching signal is relatively weak (around 0.1 nN), making it difficult to distinguish from the strong adhesion force (the inset in Figure 1a). As a result, the single-molecule force signal is severely masked in the huge adhesion zone (e.g., ΔD, which is the width of the adhesion peak marked in Figure 1a) of ∼550 nm. This would limit the usability and throughput of the air-phase SMFS experiment, and scholars must minimize the ΔD induced by interfacial adhesion for air-phase SMFS detection. Modulating the interfacial adhesion is a direct approach for decreasing ΔD. As the water capillary between the tip and substrate plays a key role in defining interfacial adhesion, it is very necessary to consider the effect of relative humidity (RH) (Figure 1c and Figure S1).52,59−61 The ΔD measured by using the cantilever of 0.2 N/m decreases from 410 to 35 nm while the RH drops from 40% to 11% (Figure 1d). At the same time, C

DOI: 10.1021/acs.macromol.8b01544 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

Figure 1. Optimization of the experimental parameters for the air-phase SMFS study of polymer single crystal. (a) Typical force−distance (F−D) curves obtained by using cantilever with spring constant k of ∼0.02 N/m in air (blue curve) and in liquid (red curve). The inset shows an enlarged version of the region below 300 pN. (b) Schematic illustration of the effect of strong capillary adhesion on the single-molecule unfolding corresponding to stages 1−4 in (a). (1) The AFM tip placed on the surface of single crystal. The inset shows that the tip contacts with a chain end of the single-crystal surface. A capillary water bridge forms in between the AFM tip and single crystal. (2) Cantilever deflected significantly before the fracture of the capillary neck. The fracture force of adhesion is marked as “Adhesion force” (see panel a). (3) After fracture, the cantilever relaxed and the polymer chain has already been stretched out of the single crystal (Lchain < ΔD). (4) Cantilever has totally relaxed. The extension range covered by adhesion (in between stage 1 and stage 4) is marked as ΔD (see panel a). (c) Typical F−D curves obtained under the relative humidity (RH) of 40% (orange curve), 20% (green curve), and 10% (purple curve). Cantilevers with spring constant k of ∼0.2 N/m were used. (d) Effect of RH on ΔD (over 200 events for each point). (e) Plots of adhesion force versus the serial number of F−D curve for three typical cases: hydrophilic silicon substrate with hydrophilic tip (Si−OH/Si3N4−OH, purple dots); hydrophobic substrate with hydrophilic tip (PS film/Si3N4− OH, orange dots); hydrophobic substrate with hydrophobic tip (PS film/Si3N4−NH2, blue dots). The RH is 15% in these experiments. (f) Typical F−D curves recorded by cantilevers with different k (25 pN/nm, red; 50 pN/nm, light blue; 190 pN/nm, purple). (g) Effect of k on ΔD under the RH of 11%. Error bars show standard deviation (s.d.).

crystal phase shortens the PEO stems and fails catastrophically at the critical length (Figure 3a), which is defined as the shortest stem in the chain motion. We found that the plateau is longer in air (blue curve in Figure 3b) than that in hexadecane (orange curve in Figure 3b). Through statistically analyzing the sawtooth plateau, the length of sawtooth plateau gives the most probable values of 13.4 nm in air (ΔL1) and 6.1 nm (ΔL2) in hexadecane (Figure 3c), which suggests that the helical motion has been enhanced in air. This phenomenon can be ascribed to the large interfacial free energy that increases the mechanical stability of the PEO stem and then suppresses the catastrophic fracture. The unfolding of a single PEO chain from the single crystals must compensate for the increase in interfacial free energy because new interfaces will be created both inside and outside the crystal. According to previous investigations,32,33 interfacial free energy affects the unfolding force. We indeed found that the unfolding force (the most probable force from middle

in Figure S2) from each single crystal (the bottom panel in Figure 2f). Therefore, the regularly sawtooth peaks reveal that the PEO folds are mechanically unfolded predominantly one by one, serving as a precise fingerprint to identify the unfolding of a single PEO chain from single crystals in air. Different Molecular Behaviors of the Single-Molecule Unfolding in Air and in Liquid. Interestingly, a close inspection of F−D curves as shown in Figure 2e reveals that there exists small sawtooth peaks in each major peak (see Figure 3b and Figure S2). Such a phenomenon was not observed in our previous liquid phase study.32 According to our previous SMD simulations results,67,68 the 72 helix repeats of the PEO chain are unfolded one by one in the helical motion (Figure S4) during stretching. The small sawtooth peaks can be attributed to the helical motion of the PEO chain (including the PEO loop) along the helical structure in a rotating manner during the unfolding of the PEO stems from the single crystal. During the unfolding, the helical motion of the PEO chain within the D

DOI: 10.1021/acs.macromol.8b01544 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

Figure 2. Air-phase AFM-based SMFS experiment on PEO single crystals. The AFM images of PEO single crystals (Mn = 48.5K g/mol) crystallized at Tc of (a) 25, (b) 38, and (c) 40 °C in amyl acetate dilute solution. A height profile in the selected area of the crystal is also included in the bottom panel. Scale bars stand for 1 μm in (a), (b), and (c). (d) Schematic of unfolding of single PEO chain from single crystal. (e) The typical F−D curves obtained from PEO single crystals with different thickness of 11.2, 9.6, and 7.8 nm at the stretching velocity of 0.02 μm/s. Contour length increments (ΔL) between the adjacent peaks estimated by using wormlike chain (WLC) model (dashed lines). (f) Histograms of ΔL and corresponding stem number obtained in single crystal with thickness of 7.8 nm (red line, N = 203), 9.6 nm (blue line, N = 205), and 11.2 nm (orange line, N = 172). The dashed lines are the corresponding Gaussian fits.

regions of the F−D curves, Figure S5) increases from 48 ± 15 pN in the hexadecane to 89 ± 7 pN in air (Figure 3d and further comparison in Figure S6). The corresponding interfacial tension increases from 12.0 mJ/m2 (γPEO−hexadecane) to 42.9 mJ/m2 (γPEO−air), which were calculated using Wu’s equation56,57 (see Materials and Methods and Table 1). These results confirm that the microenvironments surrounding the single crystal have pronounced impact on the force to stretch the PEO chain out the single crystal. The larger interfacial tension between air and PEO significantly enhances the mechanostability of the PEO chain within single crystals. Notably, these data demonstrate the necessity and importance of SMFS detection of the crystalline (as well as amorphous) polymer materials under the solvent-free condition. These results further prove that the microenvironments surrounding polymer single crystals have significant effect on the unfolding process. A further comparison on the F−D curves in air and in hexadecane is shown in Figure 3b; there is a huge difference in the force fluctuation. For the sake of clarity, the F−D curve in liquid was smoothed by the built-in algorithm (box smoothing, which computes the average of the values over the specified number of neighboring values centered about the point)

implemented in Igor pro (the raw F−D curve is shown in Figure S7). In spite of smoothing, the force fluctuation in liquid is still larger than that in air (without smoothing). The force of the baseline fluctuates within −40 to 40 pN peakto-peak in liquid (bottom panel in Figure 3e). In contrast, the F−D curves exhibited much smaller fluctuation in air (top panel in Figure 3e). The average force precision of the commercial cantilever is improved from 23 pN in liquid to 4 pN in air (see Figure 3e,f) without further modification, which is calculated from the Allan deviation [σF(t) = (1/2⟨(F̅ n+1 − F̅ n)2⟩t)1/2].65,69 This phenomenon can be explained by the fluctuation− dissipation theorem.46,65 According to this model, the improvement in the force precision is a direct result of the weak hydrodynamic drag in air. Notably, the F−D curve obtained at the velocity of 100 μm/s still has a high force precision (Figure 3f). The high force precision and improved mechanostability of PEO stem in air even make it possible to identify some intermediate during the unfolding (the sawtooth in the plateau shown in Figure 3b and Figure S2). These intermediate states (e.g., the movement of helical loop within the crystal phase, Figure S4)57 were not detectable by using liquid-phase SMFS.33 E

DOI: 10.1021/acs.macromol.8b01544 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

Figure 3. Comparison of the F−D curves obtained in air (blue curve) and in hexadecane (yellow curve). (a) Interpretation of the sequence of events taking place when unfolding of one complete PEO fold (containing two stems). Black solid arrows (from state 1 to state 2 or from state 2 to state 3) show the shortening of the fold. The dashed arrows (from state 3 to state 4 or from state 2 to state 4) show the catastrophic fracture of the shortened fold in air (blue arrows) and in hexadecane (orange arrow), respectively. (b) Close inspection and comparison of F−D curves obtained in air (original curve without smooth) and in hexadecane (the gray black curve obtained by box smoothing with a point parameter of 11 and the orange curve obtained by box smoothing with a point parameter of 101). The contour length of the sawtooth plateau in each peak, estimated by WLC model, is defined as ΔL1 in air (the top panel) and ΔL2 in hexadecane (the bottom panel). h1/h2 = ΔL1/ΔL2. (c) Histograms of ΔL1 and ΔL2 (over 200 events) obtained in 9.8 nm single crystals. Gaussian fitting (black dashed line) gives the most probable value shown in each histogram. (d) Histograms of unfolding forces obtained from 9.8 nm PEO single crystals in air (blue bar) and in hexadecane (orange bar) with stretching velocity of 0.02 μm/s. The dashed lines are the corresponding Gaussian fits. (e) The baselines (i.e., the noise level) of F−D curves in (b). Histograms show the force distributions of baselines, with average force precisions calculated from the Allan deviation65,69 of 23 pN in liquid and 4 pN in air, respectively. (f) The force precisions at different retraction velocities obtained by the V-shaped (diamond) and rectangle cantilever (square) from liquid (solid markers) and air (hollow markers).

Effect of Microenvironment on the Energy Landscapes of the Unfolding. To elucidate the microenvironment effect on the mechanism of force-induced unfolding, dynamic force spectroscopy (DFS) was employed to reveal the free-energy landscape. Because of the extremely low viscosity of air and resulting weak hydrodynamic drag on the cantilever beam, the air-phase SMFS method can diminish the squeezing effect (i.e., an increment of the hydrodynamic drag while the AFM tip is close to the surface).45,46,73,74 The range affected by the squeezing effect (distance Z) is significantly smaller in air than that in liquid (Figure S8). The distance Z reaches around 960 nm at a retraction velocity of 100 μm/s in liquid. In contrast, the distance Z is only 49 nm at the same velocity in air (Figure S8c,d). As a result, the air-phase SMFS method can significantly expand the pulling velocity range of commercial cantilevers. Figure 4a illustrates the typical F−D curves obtained in air at stretching velocities of 0.02, 2, 20, and 100 μm/s. To minimize the effect of nonspecific tip−sample adhesion and polymer chain end on the unfolding force, we statistically analyzed the forces in the middle region of the F−D curves (see Figure S5). The unfolding force increases from 89 ± 7 pN (0.02 μm/s) to 133 ± 7 pN (100 μm/s) (Figure S9). At a high stretching velocity, the sawtooth peaks become indistinct due to the reduced data points on each F−D curve and reduced relaxation time during the unfolding of the polymer loop on the top

surface of the single crystal. The unfolding force was plotted as a function of the logarithm of the loading rate (ln rf) (Figure 4b). The linear correlation between the unfolding force and ln rf indicates the presence of a single energy barrier during the unfolding process. The Bell−Evans model53,54 can be used to fit the data relatively well, producing kinetic parameters for the unfolding. According to the parameters obtained in the DFS experiment (Table S1), we can draw the conceptual free energy landscapes for the unfolding of the PEO chain from the PEO single crystal under different conditions, as shown in Figure 4c. The reaction coordinate distance (xβ) from the folded to the transition state is 0.39 nm in amyl acetate, 0.42 nm in hexadecane, and 0.75 nm in air, which increases with increasing PEO−medium interfacial energy. In addition, the energy barrier for the unfolding of the PEO chain also increases with increasing interfacial tension (see Table S1 and Figure 4c). These results further demonstrate that the microenvironments that surround the polymer single crystal significantly affect the energy landscapes of the unfolding process. Therefore, the airphase SMFS method can provide more accurate molecularlevel information about the origin of the mechanical properties of polymer materials. Moreover, air-phase SMFS method can easily expand the pulling velocity range of commercial cantilevers without further modification,44 which further proves the advantage of air-phase SMFS method. F

DOI: 10.1021/acs.macromol.8b01544 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

0.02 to 100 μm/s) using the normal cantilever without further modification. Moreover, our results show that the surrounding environment can significantly affect the kinetic behavior during the force-induced melting of the polymer crystal. Some new intermediate states (e.g., the movement of helical loop within the crystal phase), which were not detectable by using liquidphase SMFS, have been identified by air-phase SMFS. Therefore, the molecular behavior and kinetic parameters revealed by the air-phase SMFS method will be relevant to a large number of polymer systems used in solvent-free environment. Data on the nanoscopic dynamics of the lamellar crystal will be useful for the rational design of advanced crystalline polymer materials. With further advancement in AFM, the proposed air-phase SMFS methodology is applicable to the study of a broad range of polymer materials in condensed states (both crystalline and amorphous states) at the molecular level. The molecular behavior and kinetic parameters revealed by the air-phase SMFS method will serve as a guide for rational design of high-performance polymer materials used in air.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b01544. Figures S1−S9: effect of the relative humidity (RH) on the F−D curves obtained on polystyrene (PS) film; interpretation of the peaks in the F−D curve; histogram of the magnitude of force fluctuation between peak and valley in the baseline and sawtooth peak; snapshots and F−D obtained by SMD simulations; data points used for statistical analysis of the unfolding forces in the sawtooth plateau region; histograms of unfolding forces obtained in different microenvironments with stretching velocity of 2 μm/s; raw and smoothed F−D curve obtained in hexadecane at a velocity of 0.02 μm/s; comparison on the quality of SMFS data obtained in liquid and in air; force distribution of the sawtooth peaks obtained at different pulling speed in air; Table S1: kinetic parameters for the unfolding of PEO chain (PDF)

■

Figure 4. Dynamic force spectroscopy. (a) Typical F−D curves obtained on PEO single crystal in air at different stretching velocities: 0.02, 2, 20, and 100 μm/s. (b) Loading rate dependence of the unfolding forces (over 80 F−D curves for each loading rate). The solid black line is the fit of the Bell−Evans model with fitting parameters of xβ = 0.75 nm in air (blue solid squares), xβ = 0.42 nm in hexadecane (orange hollow diamonds), and xβ = 0.39 nm in amyl acetate (purple hollow circles). Error bars show standard deviation (s.d.). (c) Conceptual free energy landscapes for the unfolding of PEO chain from the single crystal in air (blue line), in hexadecane (orange line), and in amyl acetate (purple line).

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (W.Z.). ORCID

Wenke Zhang: 0000-0002-4569-6035 Author Contributions

P.Y. and Y.S. contributed equally to this work. Notes

The authors declare no competing financial interest.

■

■

CONCLUSION In summary, we have successfully extended the application of the AFM-based SMFS on single polymer chain from the liquid phase to the air phase by diminishing the strong adhesion (between the AFM tip and substrate) caused mainly by the capillary force. Adhesion can be tuned by the cantilever stiffness, environment humidity, and surface hydrophobicity of the AFM tip and substrate to fit the needs of a particular experiment. The air-phase SMFS method we established here can be easily used on all commercial AFMs. This approach improves the force precision from ∼23 to ∼4 pN and can work in a very broad range of the pulling speed (e.g., from

ACKNOWLEDGMENTS This work was funded by National Natural Science Foundation of China (21525418, 21474041, 91127031, and 21504030), the National Basic Research Program (2013CB834503), and the Program for New Century Excellent Talents in University (NCET).

■

REFERENCES

(1) Men, Y. F.; Rieger, J.; Strobl, G. Role of the Entangled Amorphous Network in Tensile Deformation of Semicrystalline Polymers. Phys. Rev. Lett. 2003, 91, 095502. (2) De Rosa, C.; Auriemma, F.; Ruiz de Ballesteros, O. R. A Microscopic Insight into the Deformation Behavior of Semicrystalline

G

DOI: 10.1021/acs.macromol.8b01544 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules Polymers: the Role of Phase Transitions. Phys. Rev. Lett. 2006, 96, 167801. (3) Jabbari-Farouji, S.; Lame, O.; Perez, M.; Rottler, J.; Barrat, J.-L. Role of the Intercrystalline Tie Chains Network in the Mechanical Response of Semicrystalline Polymers. Phys. Rev. Lett. 2017, 118, 217802. (4) Li, L.; Zhong, Z.; de Jeu, W. H.; Dijkstra, P. J.; Feijen, J. Crystal Structure and Morphology of Poly(l-lactide-b-d-lactide) Diblock Copolymers. Macromolecules 2004, 37, 8641−8646. (5) López-Barrón, C. R.; Zeng, Y.; Schaefer, J. J.; Eberle, A. P. R.; Lodge, T. P.; Bates, F. S. Molecular Alignment in Polyethylene during Cold Drawing Using In-Situ SANS and Raman Spectroscopy. Macromolecules 2017, 50, 3627−3636. (6) Wang, D.; Shao, C.; Zhao, B.; Bai, L.; Wang, X.; Yan, T.; Li, J.; Pan, G.; Li, L. Deformation-Induced Phase Transitions of Polyamide 12 at Different Temperatures: An in Situ Wide-Angle X-ray Scattering Study. Macromolecules 2010, 43, 2406−2412. (7) Lin, Y.; Li, X.; Meng, L.; Chen, X.; Lv, F.; Zhang, Q.; Zhang, R.; Li, L. Structural Evolution of Hard-Elastic Isotactic Polypropylene Film during Uniaxial Tensile Deformation: The Effect of Temperature. Macromolecules 2018, 51, 2690−2705. (8) Mandelkern, L. The Relation between Structure and Properties of Crystalline Polymers. Polym. J. 1985, 17, 337−350. (9) Hiss, R.; Hobeika, S.; Lynn, C.; Strobl, G. Network Stretching, SlipProcesses, and Fragmentation of Crystallites during Uniaxial Drawing of Polyethylene and Related Copolymers. A Comparative Study. Macromolecules 1999, 32, 4390−4403. (10) Keten, S.; Xu, Z.; Ihle, B.; Buehler, M. J. Nanoconfinement Controls Stiffness, Strength and Mechanical Toughness of β-Sheet Crystals in Silk. Nat. Mater. 2010, 9, 359−367. (11) Jabbari-Farouji, S.; Rottler, J.; Lame, O.; Makke, A.; Perez, M.; Barrat, J.-L. Plastic Deformation Mechanisms of Semicrystalline and Amorphous Polymers. ACS Macro Lett. 2015, 4, 147−150. (12) Zhu, S.; Lempesis, N.; in 't Veld, P. J.; Rutledge, G. C. Molecular Simulation of Thermoplastic Polyurethanes under Large Tensile Deformation. Macromolecules 2018, 51, 1850−1864. (13) Liu, Y.; Cui, K.; Tian, N.; Zhou, W.; Meng, L.; Li, L.; Ma, Z.; Wang, X. Stretch-Induced Crystal−Crystal Transition of Polybutene1: An in Situ Synchrotron Radiation Wide-Angle X-ray Scattering Study. Macromolecules 2012, 45, 2764−2772. (14) Rief, M.; Gautel, M.; Oesterhelt, F.; Fernandez, J. M.; Gaub, H. E. Reversible Unfolding of Individual Titin Immunoglobulin Domains by AFM. Science 1997, 276, 1109−1112. (15) Wei, W.; Sun, Y.; Zhu, M.; Liu, X.; Sun, P.; Wang, F.; Gui, Q.; Meng, W.; Cao, Y.; Zhao, J. Structural Insights and the Surprisingly Low Mechanical Stability of the Au−S Bond in the Gold-Specific Protein GolB. J. Am. Chem. Soc. 2015, 137, 15358−15361. (16) Yu, H.; Siewny, M. G.; Edwards, D. T.; Sanders, A. W.; Perkins, T. T. Hidden Dynamics in the Unfolding of Individual Bacteriorhodopsin Proteins. Science 2017, 355, 945−950. (17) Wu, J.; Li, P.; Dong, C.; Jiang, H.; Bin, X.; Gao, X.; Qin, M.; Wang, W.; Bin, C.; Cao, Y. Rationally Designed Synthetic Protein Hydrogels with Predictable Mechanical Properties. Nat. Commun. 2018, 9, 620−630. (18) Milles, L. F.; Schulten, K.; Gaub, H. E.; Bernardi, R. C. Molecular Mechanism of Extreme Mechanostability in a Pathogen Adhesin. Science 2018, 359, 1527−1533. (19) Cui, S.; Liu, C.; Zhang, X. Simple Method to Isolate Single Polymer Chains for the Direct Measurement of the Desorption Force. Nano Lett. 2003, 3, 245−248. (20) Wang, D.; Russell, T. P. Advances in Atomic Force Microscopy for Probing Polymer Structure and Properties. Macromolecules 2018, 51, 3−24. (21) Cui, S.; Liu, C.; Wang, Z.; Zhang, X.; Strandman, S.; Tenhu, H. Single Molecule Force Spectroscopy on Polyelectrolytes: Effect of Spacer on Adhesion Force and Linear Charge Density on Rigidity. Macromolecules 2004, 37, 946−953. (22) Chung, J.; Kushner, A. M.; Weisman, A. C.; Guan, Z. Direct Correlation of Single-Molecule Properties with Bulk Mechanical

Performance for the Biomimetic Design of Polymers. Nat. Mater. 2014, 13, 1055−1062. (23) Hosono, N.; Kushner, A. M.; Chung, J.; Palmans, A. R.; Guan, Z.; Meijer, E. W. Forced Unfolding of Single-Chain Polymeric Nanoparticles. J. Am. Chem. Soc. 2015, 137, 6880−6888. (24) Watabe, H.; Nakajima, K.; Sakai, Y.; Nishi, T. Dynamic Force Spectroscopy on a Single Polymer Chain. Macromolecules 2006, 39, 5921−5925. (25) Liu, N.; Peng, B.; Lin, Y.; Su, Z.; Niu, Z.; Wang, Q.; Zhang, W.; Li, H.; Shen, J. Pulling Genetic RNA out of Tobacco Mosaic Virus Using Single-Molecule Force Spectroscopy. J. Am. Chem. Soc. 2010, 132, 11036−11038. (26) Kim, E.-S.; Kim, J. S.; Lee, Y.; Choi, K. Y.; Park, J. W. Following the DNA Ligation of a Single Duplex Using Atomic Force Microscopy. ACS Nano 2012, 6, 6108−6114. (27) Kim, Y.; Kim, E.-S.; Lee, Y.; Kim, J.-H.; Shim, B. C.; Cho, S. M.; Lee, J. S.; Park, J. W. Reading Single DNA with DNA Polymerase Followed by Atomic Force Microscopy. J. Am. Chem. Soc. 2014, 136, 13754−13760. (28) Lee, Y.; Kim, Y.; Lee, D.; Roy, D.; Park, J. W. Quantification of Fewer than Ten Copies of a DNA Biomarker without Amplification or Labeling. J. Am. Chem. Soc. 2016, 138, 7075−7081. (29) Li, Q.; Scholl, Z. N.; Marszalek, P. E. Capturing the Mechanical Unfolding Pathway of a Large Protein with Coiled-Coil Probes. Angew. Chem., Int. Ed. 2014, 53, 13429−13433. (30) He, C.; Hu, C.; Hu, X.; Hu, X.; Xiao, A.; Perkins, T. T.; Li, H. Direct Observation of the Reversible Two-State Unfolding and Refolding of an α/β Protein by Single-Molecule Atomic Force Microscopy. Angew. Chem., Int. Ed. 2015, 54, 9921−9925. (31) Alsteens, D.; Newton, R.; Schubert, R.; Martinez-Martin, D.; Delguste, M.; Roska, B.; Muller, D. J. Nanomechanical Mapping of First Binding Steps of a Virus to Animal Cells. Nat. Nanotechnol. 2016, 12, 177−183. (32) Gunari, N.; Balazs, A. C.; Walker, G. C. Force-induced GlobuleCoil Transition in Single Polystyrene Chains in Water. J. Am. Chem. Soc. 2007, 129, 10046−10047. (33) Li, I. T. S.; Walker, G. C. Interfacial Free Energy Governs Single Polystyrene Chain Collapse in Water and Aqueous Solutions. J. Am. Chem. Soc. 2010, 132, 6530−6540. (34) Liu, K.; Song, Y.; Feng, W.; Liu, N.; Zhang, W.; Zhang, X. Extracting a Single Polyethylene Oxide Chain from a Single Crystal by a Combination of Atomic Force Microscopy Imaging and SingleMolecule Force Spectroscopy: toward the Investigation of Molecular Interactions in Their Condensed States. J. Am. Chem. Soc. 2011, 133, 3226−3229. (35) Xue, Y. R.; Li, X.; Li, H. B.; Zhang, W. K. Quantifying Thiol− Gold Interactions Towards the Efficient Strength Control. Nat. Commun. 2014, 5, 4348−4356. (36) Li, C.-H.; Wang, C.; Keplinger, C.; Zuo, J.-L.; Jin, L.; Sun, Y.; Zheng, P.; Cao, Y.; Lissel, F.; Linder, C.; You, X.-Z.; Bao, Z. A Highly Stretchable Autonomous Self-Healing Elastomer. Nat. Chem. 2016, 8, 618−624. (37) Zhang, H.; Li, X.; Lin, Y.; Gao, F.; Tang, Z.; Su, P.; Zhang, W.; Xu, Y.; Weng, W.; Boulatov, R. Multi-Modal Mechanophores Based on Cinnamate Dimers. Nat. Commun. 2017, 8, 1147−1156. (38) Huang, W.; Zhu, Z.; Wen, J.; Wang, X.; Qin, M.; Cao, Y.; Ma, H.; Wang, W. Single Molecule Study of Force-Induced Rotation of Carbon−Carbon Double Bonds in Polymers. ACS Nano 2017, 11, 194−203. (39) Lyu, X.; Song, Y.; Feng, W.; Zhang, W. Direct Observation of Single-Molecule Stick−Slip Motion in Polyamide Single Crystals. ACS Macro Lett. 2018, 7, 762−766. (40) Grebikova, L.; Whittington, S. G.; Vancso, J. G. AngleDependent Atomic Force Microscopy Single-Chain Pulling of Adsorbed Macromolecules from Planar Surfaces Unveils the Signature of an Adsorption-Desorption Transition. J. Am. Chem. Soc. 2018, 140, 6408−6415. H

DOI: 10.1021/acs.macromol.8b01544 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules (41) Bao, Y.; Qian, H.-j.; Lu, Z.-Y.; Cui, S. Revealing the Hydrophobicity of Natural Cellulose by Single-Molecule Experiments. Macromolecules 2015, 48, 3685−3690. (42) Luo, Z.; Zhang, A.; Chen, Y.; Shen, Z.; Cui, S. How Big Is Big Enough? Effect of Length and Shape of Side Chains on the SingleChain Enthalpic Elasticity of a Macromolecule. Macromolecules 2016, 49, 3559−3565. (43) Zhang, W.; Zhang, X. Single Molecule Mechanochemistry of Macromolecules. Prog. Polym. Sci. 2003, 28, 1271−1295. (44) Neuman, K. C.; Nagy, A. Single-Molecule Force Spectroscopy: Optical Tweezers, Magnetic Tweezers and Atomic Force Microscopy. Nat. Methods 2008, 5, 491−505. (45) Roters, A.; Johannsmann, D. Distance-Dependent Noise Measurements in Scanning Force Microscopy. J. Phys.: Condens. Matter 1996, 8, 7561−7577. (46) Viani, M. B.; Schäffer, T. E.; Chand, A.; Rief, M.; Gaub, H. E.; Hansma, P. K. Small Cantilevers for Force Spectroscopy of Single Molecules. J. Appl. Phys. 1999, 86, 2258−2262. (47) Janovjak, H.; Struckmeier, J.; Muller, D. J. Hydrodynamic Effects in Fast AFM Single-Molecule Force Measurements. Eur. Biophys. J. 2005, 34, 91−96. (48) Liu, R.; Roman, M.; Yang, G. Correction of the Viscous Drag Induced Errors in Macromolecular Manipulation Experiments Using Atomic Force Microscope. Rev. Sci. Instrum. 2010, 81, 063703. (49) Bull, M. S.; Sullan, R. M. A.; Li, H.; Perkins, T. T. Improved Single Molecule Force Spectroscopy Using Micromachined Cantilevers. ACS Nano 2014, 8, 4984−4995. (50) Rico, F.; Gonzalez, L.; Casuso, I.; Puig-Vidal, M.; Scheuring, S. High-Speed Force Spectroscopy Unfolds Titin at the Velocity of Molecular Dynamics Simulations. Science 2013, 342, 741−743. (51) Chen, Y.; Kushner, A. M.; Williams, G. A.; Guan, Z. Multiphase Design of autonomic Self-Healing Thermoplastic Elastomers. Nat. Chem. 2012, 4, 467−472. (52) Farshchi-Tabrizi, M.; Kappl, M.; Cheng, Y.; Gutmann, J.; Butt, H. J. On the Adhesion between Fine Particles and Nanocontacts: An Atomic Force Microscope Study. Langmuir 2006, 22, 2171−2184. (53) Bell, G. I. Models for the Specific Adhesion of Cells to Cells. Science 1978, 200, 618−627. (54) Evans, E.; Ritchie, K. Dynamic Strength of Molecular Adhesion Bonds. Biophys. J. 1997, 72, 1541−1555. (55) Liu, N.; Chen, Y.; Peng, B.; Lin, Y.; Wang, Q.; Su, Z.; Zhang, W.; Li, H.; Shen, J. Single-Molecule Force Spectroscopy Study on the Mechanism of RNA Disassembly in Tobacco Mosaic Virus. Biophys. J. 2013, 105, 2790−800. (56) Wu, S. Surface and Interfacial Tensions of Polymer Melts: I. Polyethylene, Polyisobutylene, and Polyvinyl acetate. J. Colloid Interface Sci. 1969, 31, 153−161. (57) Wu, S. Calculation of Interfacial Tension in Polymer Systems. J. Polym. Sci., Part C: Polym. Symp. 1971, 34, 19−30. (58) Beerbower, A. Surface free energy: A new relationship to bulk energies. J. Colloid Interface Sci. 1971, 35, 126−132. (59) Sedin, D. L.; Rowlen, K. L. Adhesion Forces Measured by Atomic Force Microscopy in Humid Air. Anal. Chem. 2000, 72, 2183−2189. (60) Rozhok, S.; Sun, P.; Piner, R.; Lieberman, M.; Mirkin, C. A. AFM Study of Water Meniscus Formation between an AFM Tip and NaCl Substrate. J. Phys. Chem. B 2004, 108, 7814−7819. (61) Feiler, A. A.; Stiernstedt, J.; Theander, K.; Jenkins, P.; Rutland, M. W. Effect of Capillary Condensation on Friction Force and Adhesion. Langmuir 2007, 23, 517−522. (62) Eastman, T.; Zhu, D.-M. Adhesion Forces between SurfaceModified AFM Tips and a Mica Surface. Langmuir 1996, 12, 2859− 2862. (63) Burnham, N. A.; Dominguez, D. D.; Mowery, R. L.; Colton, R. J. Probing the Surface Forces of Monolayer Films with an AtomicForce Microscope. Phys. Rev. Lett. 1990, 64, 1931−1934. (64) Liphardt, J.; Onoa, B.; Smith, S. B.; Tinoco, I.; Bustamante, C. Reversible Unfolding of Single RNA Molecules by Mechanical Force. Science 2001, 292, 733−737.

(65) Edwards, D. T.; Faulk, J. K.; Sanders, A. W.; Bull, M. S.; Walder, R.; LeBlanc, M. A.; Sousa, M. C.; Perkins, T. T. Optimizing 1-μs-Resolution Single-Molecule Force Spectroscopy on a Commercial Atomic Force Microscope. Nano Lett. 2015, 15, 7091−7098. (66) Stigler, J.; Ziegler, F.; Gieseke, A.; Gebhardt, J. C. M.; Rief, M. The Complex Folding Network of Single Calmodulin Molecules. Science 2011, 334, 512−516. (67) Feng, W.; Wang, Z.; Zhang, W. Effect of Chain Conformation on the Single-Molecule Melting Force in Polymer Single Crystals: Steered Molecular Dynamics Simulations Study. Langmuir 2017, 33, 1826−1833. (68) Song, Y.; Feng, W.; Liu, K.; Yang, P.; Zhang, W. K.; Zhang, X. Exploring the Folding Pattern of a Polymer Chain in a Single Crystal by Combining Single-Molecule Force Spectroscopy and Steered Molecular Dynamics Simulations. Langmuir 2013, 29, 3853−3857. (69) Czerwinski, F.; Richardson, A. C.; Oddershede, L. B. Quantifying Noise in Optical Tweezers by Allan Variance. Opt. Express 2009, 17, 13255−13269. (70) Hansen, C. M. Hansen Solubility Parameters: A User’s Handbook, 2nd ed.; CRC Press: Hoboken, NJ, 2007. (71) Bicerano, J. Prediction of Polymer Properties, 3rd ed.; Marcel Dekker: New York, 2002. (72) Roe, R. J. Surface Tension of Polymer Liquids. J. Phys. Chem. 1968, 72, 2013−2017. (73) Kawakami, M.; Taniguchi, Y.; Hiratsuka, Y.; Shimoike, M.; Smith, D. A. Reduction of the Damping on an AFM Cantilever in Fluid by the Use of Micropillars. Langmuir 2010, 26, 1002−1007. (74) Churnside, A. B.; Sullan, R. M.; Nguyen, D. M.; Case, S. O.; Bull, M. S.; King, G. M.; Perkins, T. T. Routine and Timely SubpicoNewton Force Stability andPrecision for Biological Applications of Atomic Force Microscopy. Nano Lett. 2012, 12, 3557−3561.

I

DOI: 10.1021/acs.macromol.8b01544 Macromolecules XXXX, XXX, XXX−XXX