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Relationship between Segmental Relaxation of Polystyrene Films and Stick−Slip Behavior during Dynamic Wetting of Liquid Droplets on Their Surfaces Biao Zuo, Xumiao He, Yuping Wang, Jianquan Xu, Juping Yang, and Xinping Wang* Department of Chemistry, Key Laboratory of Advanced Textile Materials and Manufacturing Technology of Education Ministry, Zhejiang Sci-Tech University, Hangzhou 310018, P. R. China S Supporting Information *

ABSTRACT: A novel method was previously reported for detecting the glass transition of thin polystyrene (PS) films by correlating the relationships between the temperature-dependent viscoelasticity of the PS films and stick−slip behavior on their surfaces during dynamic wetting of liquid droplets. In the present study, the frequency dependence of the stick−slip behavior is investigated. The results show that the stick−slip behavior of liquid dynamic wetting on PS films is dependent on the contact line velocity, which is related to the deformation frequency of the PS surface during the moving liquid front. The stick−slip behavior was revealed to be determined by a dimensionless parameter (ξ), which is the ratio of the PS segmental relaxation time (τα) and the characteristic time (τc) for PS surface deformation near the droplet contact line. When ξ is close to 1 (τα ≈ τc), the Δθ (jumping angle), a scale of the stick−slip behavior, reaches a maximum. This correlation between Δθ and ξ demonstrates that the stick− slip behavior is related to the energy dissipation caused by the PS α-relaxation process, and the peak temperature (or frequency) in Δθ corresponds to the α-relaxation temperature (time) of the polymer. These results strongly demonstrate that the utilization of the stick−slip behavior is a creditable method, similar to dynamic viscoelastic measurement, for probing the glass transition and segmental relaxation of thin polymer films. controversy exists in this field due to apparently conflicting results exhibiting Tg depression,38,39 invariant segmental dynamics,38,39 and even slowed chain diffusion40,41 for thin polymer films supported on nonattractive substrates. To date, it remains unclear as to how the dynamics of polymer thin films differ from those in the bulk. Hence, a different experimental approach based on novel mechanisms is needed and developing robust experimental methods for the study of the glass transition and molecular relaxation of thin polymer films would be an important endeavor. Shanahan and Carré42−46 first demonstrated that the spreading kinetics of a liquid on a solid surface is influenced by the corresponding mechanical properties of the solid. The wetting dynamics of a liquid/fluid on a soft polymer surface are affected by their ability to be deformed under the moderate action of the interfacial forces, thus greatly depending on the polymer viscoelasticity.47−52 The wetting behavior of a liquid on a soft solid was much lower than that of the same droplet on a rigid solid, due to the formation of a wetting ridge in the vicinity of the contact line by the vertical component of the

1. INTRODUCTION Thin and ultrathin polymer films have generated much interest for their potential to solve a wide variety of problems in nanotechnology and in the microelectronics industry.1−3 In this physical confinement, the dimensions and surface fields can strongly influence the corresponding dynamics of the polymers. Molecular mobility in thin polymer films is remarkably different from the intrinsic bulk behavior, due in part to finite-size and surface/interface effects.4−10 These effects should be crucial factors affecting the segmental dynamics of thin polymer films. Measurements of the polymer glass transition and segmental relaxation in thin films in situ are challenging, given the nanoscale volumes being probed. Important information can be obtained from the measurement of the viscoelasticity of polymers regarding the polymer chain relaxation and the rate of the configurational rearrangement. Study of the viscoelasticity of thin polymer films is an effective way to deduce the chain relaxation and glass transition of thin films. Many heuristic studies have been undertaken to develop new methods for studying the viscoelastic response of thin films, including the observation of rupture of films from a dewetted substrate,11−17 evolution of small-scale surface deformation,18−23 nanoparticle imbedding,24−30 nanobubble formation,31−33 and capillary leveling of thin films.34−37 However, © 2015 American Chemical Society

Received: June 24, 2015 Revised: August 21, 2015 Published: August 25, 2015 12325

DOI: 10.1021/acs.jpcb.5b06078 J. Phys. Chem. B 2015, 119, 12325−12335

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The Journal of Physical Chemistry B

Figure 1. Evolutions of contact angle and contact diameter of glycerol drop on PS film at temperatures of 379 and 404 K, as liquid is continuously added with time. Thickness of PS film: 602 nm. Stick−slip of the three-phase line and abrupt changes in the drop radius by increases in the volume are evident. The definition of jumping angle is also shown: when a higher contact angle limit of θ1 is obtained, the triple line “jumps” from θ1 to θ2 (θ1 − θ2 = Δθ, jumping angle) with increase in drop volume. The insets show the enlarged views of the stick−slip pattern within the first 100 s period and also present the schematic illustration of the experimental set up.

frequency-dependent during the dynamic wetting of droplets on the surface of thin polymer films. In this article, the frequency dependence of the stick−slip behavior is investigated, in order to unveil the inherent relationships between stick−slip behavior and PS segmental relaxation, further clarifying the underlying physics of this method for probing the Tg and relaxation of thin films. Our results demonstrate that the stick−slip behavior of liquid is determined essentially by the segmental relaxation of polymers and that the maximum in the Δθ corresponds to the αrelaxation process related to the energy dissipation caused by the segmental rearrangement. At the same time, the segmental dynamics of polymer films can be estimated by measuring the stick−slip behavior of the liquid.

surface tension of the liquid. The stick−slip patterns occurring during water drop spreading were previously reported to be dependent on the modulus of polystyrene-b-polyisoprene-bpolystyrene elastomer film.53 Recently, Severtson54−56 and Limat57 have shown that the wetting dynamics of water on a viscoelastic polymer surface are also related to the deformation frequency of the polymer surface during liquid spreading. These experimental results give clear evidence showing that the wetting dynamics of liquids are viscoelasticity-dependent. From a theoretical perspective, Long’s modeling results show that the spreading speed of a liquid is linked with the relaxation of the polymer film and predicts that observing the spreading of liquid droplets on such films may provide an interesting new tool to characterize the relaxation and viscoelastic properties of polymers.58,59 On the basis of the viscoelastic effect on the wetting dynamics, we previously developed a method to detect the dynamic glass transition temperature (Tg) of polystyrene (PS) thin films by investigating the temperature dependence of the wetting dynamics of a liquid on PS film surfaces.60 It was shown that the liquid spreading exhibits stick−slip behavior in the glass−rubber transition region of the PS film, and the peak temperature (Tjm) of the jumping angle (Δθ), which is a scale of the stick−slip behavior, was proven to correspond to the Tg of PS thin films (Tjm ≈ Tg). This method was also employed to probe the film/substrate interfacial effect on the segmental mobility of poly(vinyl acetate) (PVAc) thin films.61 By considering the viscoelastic effect of polymers, one may speculate that the Δθ and Tjm values should also be

2. EXPERIMENTAL SECTION 2.1. Materials. Atactic-polystyrene (PS) (Mw = 1074 kg/ mol, PDI = 1.2) was purchased from Polymer Source Inc. (Canada) and used as received. The Tg of the PS sample was about 376 K (15 K/min), as measured by the differential scanning calorimetry (DSC). Glycerol was purchased from Aldrich Chemical Co. (USA) and used as a test liquid for the dynamic wetting measurements. Silicon (100) wafers, diced into 3.0 × 3.0 cm2 pieces were used as the supporting substrates for the PS films. The silicon wafers were submerged in a piranha solution, i.e., H2SO4/H2O2 (3:1) preheated to 363 K for 30 min, and were then rinsed thoroughly in excessive deionized water and dried with nitrogen. This process removes 12326


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Figure 2. Changes of the jumping angle (Δθ) during advancing contact angle measurement, as liquid is continuously added into the droplet with time.

for times ranging from 15 to 200 s. After that, the PS film was rapidly cooled down to room temperature and then rinsed by ethanol to remove the glycerol drop. Films for measurements were dried with nitrogen gas, to remove the residual ethanol. The three-dimensional profiles of the wetting ridge on the PS film surfaces were accessed by a MultiMode-8 atomic force microscope (AFM) (Bruker Co. Ltd., Germany). 2.5. DMA Measurements. The viscoelastic properties for bulk PS were obtained by temperature (T) scanning measurements using dynamic mechanical analysis (DMA) (Pyrise Diamond DMA, PerkinElmer Co., USA), at various frequencies ( f). The experiments were performed in the tension mode under a 0.05% strain over a temperature range from 313 to 423 K, stepping upward in increments of 0.5 K. At each temperature step, five frequencies of 1, 2, 5, 10, and 20 Hz were tested sequentially. The resulting tan δ−temperature (T) data at various frequencies are displayed in Figure S2. The raw tan δ−T data at various f were first converted to the tan δ−f curve at various temperatures. The tan δ−f data at various temperatures were then shifted horizontally to obtain master curves covering a broad frequency range, based on the time/ temperature-superposition principle with a selected reference temperature (Tref). For each reference temperature (Tref), the segmental relaxation time was calculated as τα = 1/2πf max, where f max is the frequency at which the tan δ value reaches its maximum.70,71

the organic contaminants, leaving the silicon surface with a clean native oxide layer. Since the advancing contact angles were measured at temperatures near the Tg of PS, glycerol with a high boiling point (564 K) and low vapor pressure was chosen as a test liquid for advancing contact angle measurements. The physical parameters of glycerol were outlined in ref 60. The data indicate that glycerol is a very poor solvent for PS, and plasticization of the films is not expected near the Tg of PS. Meanwhile, it was reported that solvent effects on the Tgreduction of PS thin films were negligible due to glycerol immiscibility with PS.15,62,63 2.2. Film Formation. The PS films were prepared by the spin-coating method from toluene solutions onto the clean silicon substrates. The thickness of the PS thin films was set at approximately 600 nm, which was sufficient to avoid substrate and ultrathinning effects.64−66 The samples underwent an annealing process at 403 K for 24 h in vacuum, to remove residual solvent and to reduce the stresses induced by the spincoating procedure. Atomic force microscopy (AFM) analysis showed that the film surfaces were flat and smooth (i.e Rq ≈ 0.3 nm) after thermal annealing (Figure S1). Such extremely low roughness of surface does not influence the wetting behavior of liquid. Films for dynamic mechanical analysis (DMA) tests were prepared using a hot-pressing method, with thickness of about 50 μm. 2.3. Advancing Contact Angle Measurements. The PS films were mounted on a heating stage, which can adjust temperature from 293 to 473 K, with an accuracy of ±1 K. The advancing contact angles of the liquid droplets on PS films were measured in situ using the automated axisymmetric drop shape analysis-profile (ADSA-P) method.67,68 In brief, an initial drop with a diameter of about 1.5 mm is deposited onto the PS surface, ensuring that the drop is axisymmetric. By use of a motor-driven syringe to pump liquid steadily into the sessile drop, a sequence of images of the growing drop is then captured using a DSA 10-MK2 drop shape analysis system (DSA) (Kruss, Germany). The advancing dynamic contact angle behavior was determined by tracing the evolution of the contact angle (θ) using the “tangent method”69 and the diameter of the drop three-phase line with liquid added into the drop. The volume addition velocity (q) used in this study was 0.08 μL of liquid/s. The schematic illustration of experimental set up was shown in the inset of Figure 1. 2.4. Determination of Shape of Wetting Ridge. A glycerol drop was placed on PS film at a temperature of 387 K

3. RESULTS AND DISCUSSION 3.1. Dependence of the Stick−Slip Behavior on the Velocity of Advancing Contact Line. The advancing contact angle of glycerol droplet on polystyrene (PS) film was investigated as liquid was continuously added over time at various temperatures, to access the “kinetics” of the stick−slip behavior. In an automated axisymmetric drop shape analysisprofiling (ADSA-P) method for advanced contact angle measurement, the velocity of the advancing contact line of a liquid droplet (υ) changes with the volume addition velocity (q) of the liquid and the contact radius (R) of the droplet since the advancing contact line velocity (υ) is proportional to q/R2 (υ ≈ q/R2).57 This relation means that a small change in R would lead to large variation of υ, as υ is quadratically related to 1/R when q is a constant value. Accordingly, the relationship between stick−slip behavior and the velocity of an advancing contact line (υ) can be obtained by studying the change in stick−slip behavior with the contact radius (R) of a droplet with time, while q maintains a constant value. 12327


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The Journal of Physical Chemistry B Figure 1 shows the changes of the apparent contact angle and contact diameter of a glycerol droplet with the time of continuous addition of liquid during the advancing contact angle measurements on a 602 nm PS film at 379 and 404 K, respectively. The obvious stick−slip behavior for the droplet contact line motion is clearly observed: as liquid is continuously injected into the drop, the contact angle linearly increases with a constant contact radius of the droplet (contact line “stick”), and the contact line then abruptly slips to a new position, accompanied by a sudden decrease in the contact angle (contact line “slip”). This behavior is repeated as the measurement continues and a sawtooth shaped contact angle vs time curve ultimately emerges (Figure 1). At the same time, it is apparent that the stick−slip behavior on the PS film surface at 379 K is remarkably different from that observed at 404 K. At 379 K, the amplitudes in contact angle vs time curve increase and the jump distances of the contact line become greater, as liquid is continuously added with time (Figure 1). On the contrary, the amplitudes of the stick−slip behavior gradually decrease and the contact line jump distances remain nearly unchanged at 404 K (Figure 1). As reported previously,53,60 the instantaneous jumping angle (Δθ) was proposed as a parameter that could be determined by the difference (Δθ = θ1 − θ2) between the contact angle before (θ1) and after (θ2) slipping during each stick−slip cycle as shown in Figure 1, to scale the contact line stick−slip behavior. The evolution of the Δθ values as liquid is continuously injected into the droplet at 379 and 404 K is shown in Figure 2. It is observed that the Δθ values gradually increase at 379 K and decrease at 404 K with liquid continuously injected into the droplet. During advancing contact angle measurement, the liquid is steadily injected into the droplet at a constant rate and the droplet volume gradually increases. Assuming that the droplet contact line continuously advances with a constant contact angle (θ0), when liquid is added into the drop, the increment in the droplet contact radius reduces the droplet front advancing velocity. The effective advancing velocity of the droplet contact line (υ) at a given droplet contact radius can be deduced from the following equation:57 Vdrop = (2 − 3 cos θ0)π R3/3

Figure 3. Effects of the advancing velocity of droplet contact line (υ) on the jumping angle (Δθ) of PS film (∼600 nm) at various temperatures. The data points have been shifted vertically for clarity.

atures above 387 K, the Δθ value turns to a decrease with the decrement in υ. At 387 K, a peak appears in the Δθ vs υ curve. As reported previously,60 a maximum Δθ value for PS film was located at around 387 K, which was close to the temperature at the peak of the tan δ curve. This is to say, the relationship between the advancing velocity of droplet contact line (υ) and the jumping angle (Δθ) of PS film varied when the temperature of the PS film was above its corresponding Tg. Some reports have indicated that the viscoelastic effects of polymers affect the wetting dynamics of liquids.47−60 In the classic viscoelasticity theory of polymers,73−80 the frequency dependence of dissipation (e.g tan δ−f curve) strongly depends on the temperature in measurement, due to the progressive changes of relaxation time with temperatures. With increasing temperature from below the transition temperature (e.g., Tg) to above Tg, the value of tan δ first decreases with the increment of f, then a peak was exhibited in tan δ−f curve, and whereafter tan δ turn to decrease with increasing in f. We point out that the observed velocity dependence of Δθ is analogical to the behavior of polymer viscoelasticity. Consequently, in this case, each curve in Figure 3 describing the different stick−slip behaviors of the droplet on PS film at various temperatures may reflect the successive changes of segmental relaxation behavior of PS in the viscoelastic state occurring with changing temperature. We then rescaled the abscissa of each curve at various temperatures, along with a small vertical shifting in Figure 3 with a velocity shift factor αT, to produce a master curve using a reference temperature (Tref = 387 K). The curves in Figure 3 were then superimposed onto a master curve, and Figure 4a was obtained. The Δθ−υ master curve describes the dependence of contact line velocity of the glycerol droplet on the stick−slip behavior at 387 K. It may be observed that the stick− slip behavior is less obvious with small Δθ values, when the contact line of the droplet moves either very fast or slow. Only in the intermediate υ value region does the stick−slip phenomenon appear obvious with larger Δθ values. The curve displays a maximum when υ is about 0.009 mm/s (υmax = 0.009 mm/s). The tan δ dependence of PS film on the applied frequency during dynamic mechanical measurement is depicted in Figure 4b. When comparing the Δθ−υ master curve in Figure 4a and the tan δ−frequency curve (Figure 4b), it is obvious that the

(1)

The liquid dosing rate is

q = dVdrop/dt

(2)

and υ is calculated as υ = dR /dt = q/(2 − 3 cos θ0)π R2

(3)

where Vdrop is the total volume of glycerol droplet; q is the liquid dosing (injection) rate; θ0 is the advanced contact angle of glycerol on PS film surface, which is about 78°, the same as a previously reported value,72 and R is the radius of the droplet contact line. The effective contact line velocity (υ) at various values of R during advancing contact angle measurement can be calculated from eq 3. The time evolution of Δθ in the course of liquid injected into the droplet at temperatures from 379 to 404 K with a temperature interval of 4 K (Figures S3 and S4) was converted into the relationships between Δθ and the effective contact line velocity, as displayed in Figure 3. It is obvious from Figure 3 that when the temperature is below 387 K, Δθ increases with decrease of the contact line velocity (υ). However, when the measurements are carried out at temper12328


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Figure 4. (a) Master curve of Δθ−υ relationship obtained by collapsing the curves in Figure 3; (b) master curve of tan δ−f curve from DMA measurements (the reference temperatures are both 387 K).

Figure 5. (a) Semilogarithmic plots of shift factor αT vs T (a) and 1/T − 1/Tref (b). The data in panel a are fitted by the WLF eq eq 4, and the data in panel b are fitted by the Arrhenius equation for elucidating the activation energy.

velocity-dependence of jumping angle (Δθ) is qualitatively similar to the frequency-dependence of tan δ. Meanwhile, it was also shown in our previous work that the temperaturedependent Δθ of PS film was similar to the tan δ−temperature curve obtained by DMA.60 The effect of film thickness are also considered, and it was verified that film thickness does not play a role in the temperature dependence of the stick−slip behavior (detail see Supporting Information). As well, the physical properties of test liquid and specifically the viscosity also have negligible influence on the temperature and velocity (or frequency) dependence of the stick−slip behavior, which has been verified in the former works.60 Therefore, the changes of Δθ value with the variance of temperature or frequency may be solely attributed to the thermal transition or viscoelasticity change of polymers films. These results demonstrate that the stick−slip behavior involves both velocity (or frequency) and temperature-dependence properties, which is analogous to the bulk dissipation behavior for viscoelastic polymers, and also demonstrate the importance of viscoelastic dissipation to the stick−slip behavior. 3.2. Correlations between PS Segmental Relaxation and Stick−Slip Behavior. As shown above, velocity shift factors (αT) could be obtained at each temperature by rescaling the contact line velocity by a constant αT (υ → υ · αT), such that the Δθ values superpose (for detail, see Figures 3 and 4). The change of αT with temperature is depicted in Figure 5a. The shift factors (αT) are observed to decrease with increasing temperature on a log scale. To illustrate the temperature dependence of αT, we attempted to fit the data to a modified Williams−Landel−Ferry (WLF) equation:73

log αT = − C1(T − Tg)/(C2 + T − Tg) + C1(Tref − Tg) /(C2 + Tref − Tg)

(4)

where C1 and C2 are constants. It is observed that the temperature dependence of αT can be suitably fitted using the WLF eq (eq 4), with the fitted values of C1 and C2 being 16.5 and 54.7, respectively. Recalling polymer viscoelasticity theory, the classic WLF equation is a universal rule for describing the temperature dependence of the segmental relaxation process, and the values of C1 and C2 are often quoted as C1 = 17.4 and C2 = 51.6 when the reference temperature is taken as Tg. Herein, a key result is that our fitted C1 and C2 parameters derived from the temperature and velocity dependence of Δθ (C1fitted = 16.5, C2fitted = 54.7) are in general agreement with those values from polymer viscoelasticity studies (C1 = 17.4, C2 = 57.673), which are often obtained from rheological measurements of polymers. This good agreement demonstrates that the stick−slip behavior of glycerol on PS film is mainly controlled by the segmental relaxation of PS and obeys the characteristic time (or frequency)−temperature superposition principle. Thus, the velocity shift factor (αT) used to produce the Δθ−υ master curve may primarily reflect the temperature dependence of the segmental friction coefficient or mobility on which the rates of configurational rearrangements ultimately depend. Additionally, assuming a simple Arrhenius-type temperature dependence of αT, the apparent activation energy (Ea) for stick−slip of the contact line on PS film is estimated to be about 457 kJ/mol (Figure 5b), which is close to the Ea for αrelaxation of PS determined by DMA (426 kJ/mol; Figure S2). 12329


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Figure 6. (left) Representative AFM topographic images showing the presence of a wetting ridge at the contact line of a drop on PS film. The images were measured after placement of the droplet on PS film for 90 s at 387 K. (right) Cross sections of the PS surface ridge profiles formed by placing the glycerol droplets for different placement times (from 15 to 180 s). The distance between the two triangle marks shows the width of the wetting ridge. The cross-section lines have been shifted vertically for clarity.

Figure 7. Schematic illustration of the deformed surface by a sliding tip (a) and the propagation of wetting front on a soft polymer surface as well as the accompanying wetting ridge formation and relaxation process (b).

This coincidence in Ea verifies again that the stick−slip behavior of a droplet on PS film is modulated by the segmental relaxation and viscoelasticity of PS. As evident from previous works,53,60 the observed stick−slip behavior for droplet contact line motion is mainly attributed to the formation of a wetting ridge as temperature approaches the Tg of PS film, resulting in a decrease of its modulus. When a droplet is placed on the soft viscoelastic PS film, a wetting ridge readily forms due to the vertical component of glycerol surface tension pulling up the surface (shown in Figure 6). The surface ridge prevents the movement of the contact line, resulting in pinning of the droplet. When liquid is gradually injected into the droplet, the discontinuous advancing of the droplet contact line is observed. The dependence of Δθ on temperature (see Figure 4a) and υ is reminiscent of the tribological behavior on a viscoelastic polymer surface, in which the friction force depends on both the sliding rate and the temperature.74−78 In tribological experiments, the relationships of the friction force vs sliding velocity or friction force vs temperature also display a maximum.74−78 It is well established that the friction force against sliding is mainly derived from the mechanical dissipation due to polymer viscoelasticity.74−78 When the probe tip slides on a polymer surface, a rim is formed ahead of the tip (see Figure 7a). The mechanical response of the deformed surface rim as the tip moves determines the frictional

behavior of the tip. When the sliding rate is fast or slow, the energy loss due to polymer deformation is negligible; that is, the frictional force is small. Only at an intermediate rate or temperature when the polymer is in a viscoelastic state, the energy required for formation and recovery of the front rim is larger because of the prominent viscoelastic dissipation. Therefore, the magnitude of the frictional force becomes the largest. In tribological experiments, the deformation frequency of a polymer surface is obtained by the scanning velocity divided by the deformation size (i.e., tip−sample contact diameter).79,80 This concept has been successfully applied to correlate tip friction to polymer rheological behavior. As reported previously,60 when PS film changes from glassy to soft viscoelastic states with increasing temperature, the component of liquid surface tension acting perpendicularly to the solid causes a deformation or “wetting ridge” on the film surface. After the wetting front has passed a given zone of the solid as the liquid spreads, the surface is released, and thus for a perfectly elastic substrate, no net work is done and no energy is dissipated. However, for a viscoelastic solid, the strain/ relaxation cycle (i.e., formation and release of the wetting ridge) leads to a certain fraction of the strain energy being dissipated. The viscoelastic dissipation due to wetting ridge relaxation as resistance prevents the spreading of the droplets, as proposed by the “viscoelastic braking” mechanism.42−46,81 The propagation of the wetting front on soft polymer surface as 12330


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Figure 8. (a) Correlation between Δθ and the characteristic time (τc) for PS surface deformation during contact line movement. (b) Relationship between Δθ and the dimensionless ratio of time scales for droplet stick−slip (ξ/ξ = τc/τα).

average width of the wetting ridge at 387 K, about 1.47 μm as obtained from Figure 6, was reasonably used for the L value in eq 5. Thus, the Δθ−υ master curve in Figure 4a can be converted into a Δθ−τc curve as shown in Figure 8a. The Δθ vs τc relationship represents the dependence of the stick−slip behavior of the liquid on the characteristic time (or frequency) of surface deformation on the PS film surface. It is obvious that Δθ reaches a maximum when the characteristic deformation time (and frequency) is about 0.15 s (about 7 Hz). It is worth noting that the frequency at which Δθ reaches the peak value ( fdeformation ≈ 7 Hz) is close to the f max for tan δ of PS (f max ≈ 2 Hz; see Figure 4b). This consistency in peak frequency of both Δθ and tan δ gives a clear demonstration that the velocity dependence of stick−slip behavior of liquid wetting on PS film surface reflects the frequency (or time) dependence of the viscoelastic dissipation of PS. The segmental relaxation time (τα) involved in the αrelaxation of PS at 387 K was determined from the tan δ−f master curve (see Figure 4b) to be τα = 1/2πf max,70,71 and τα = 0.08 s was obtained. In order to clarify the relationship between the stick−slip behavior and polymer segmental relaxation, we compared the time scale associated with the PS segmental relaxation (τα) and the characteristic time of the PS surface deformation (τc) in the course of contact line movement. A dimensionless ratio of time scales is proposed: ξ = τc/τα, to compare the stick−slip kinetics and the segmental relaxation dynamics. The correlation between the jumping angle and the dimensionless ratio of time scales (ξ) is presented in Figure 8b. It is obvious from this Figure that Δθ reaches a maximum when the dimensionless parameter ξ is 1.7, namely, when the PS segmental relaxation (τα) is almost equal to the characteristic time of the PS surface deformation (τc). The Deborah number (De) is a dimensionless number, often used to characterize the viscoelasticity and molecular relaxation process of polymer materials.82−84 The mechanical characteristics are not inherent properties of the material alone, but a relative property that depends on two fundamentally different characteristic times. The Deborah number is defined as a ratio of the relaxation time of a material characterizing the time it takes to adjust to the applied stresses or deformations, and the characteristic time scale of an experiment probing the response of materials.82−84 It is accordingly reasonable to think that the dimensionless parameter (ξ) in the droplet stick−slip behavior has a similar role to that of the Deborah number (De) in rheological measurements. When the velocity of the contact line is about 0.009 mm/s where ξ is close to 1, analogous to the De, the mechanical response of materials is highly viscoelastic and the energy dissipation (hysteresis) is generally at a

well as the accompanying wetting ridge formation and relaxation process are presented in Figure 7b. As schematically illustrated, the mechanical responses of the surface deformation (i.e., wetting ridge for liquid wetting) determine the wetting dynamics. Thus, we may consider the advancing of the contact line of a viscoelastic polymer film resembling the shear process in a viscoelastic substrate, in which the friction resistance is determined by both the temperature and shearing frequencies. The stick−slip behavior of liquid droplets should be related to the deformation rate (or frequency) of a PS surface during the droplet spreading. It is also reasonable that an estimation of the characteristic frequency (or time) of the deformation (fdeformation) observed on the PS surface around the moving contact line at various velocities could be obtained using a similar method with the frictional behavior of an AFM tip. Since the time for contact line slipping to a new position is very short and negligible compared with that of the stage of the contact line sticking in each stick−slip cycle as shown in Figure 1, it is reasonable to assume that the propagation of a wetting front on a soft polymer surface as well as the accompanying wetting ridge formation and relaxation process as shown in the moving velocity of the contact line were mainly determined as shown in Figure 7b. The characteristic frequency of the surface deformation during droplet spreading is thus given by dividing the contact line velocity by the deformed length of the polymer surface by the surface tension of the liquid, which was suitably approximated as the width of the wetting ridge (L), as shown in Figure 7b. As a consequence, the characteristic time for the PS surface deformation (τc) during droplet spreading, which is represented as the inverse of the frequency, can be expressed as τc = 1/fdeformation = L /υ

(5)

where L is the width of wetting ridge and υ is the contact line velocity of the liquid. The width of the wetting ridge (L) on a PS surface was measured by AFM. The AFM profile of the surface wetting ridge (Figure 6) formed by placing a glycerol droplet on a PS surface for 90 s at 387 K shows that the width of the ridge (L) is about 1.49 μm (L = 1.49 μm). It was observed in Figure 1 that the duration time of one stick−slip cycle increased from about 10 to 200 s with increasing time of liquid addition. To assess the change in the surface ridge width at different stick− slip cycles, the surface ridge profiles were measured after the placement of the droplet on the PS surface for times varying from 15 to 180 s (Figure 6), which is close to the duration time for one stick−slip event. The results show that the width of the wetting ridge remained almost unchanged as the liquid droplet was put on the PS film surface from 15 to 180 s. Therefore, the 12331


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Figure 9. (a) Dependence of υmax and wetting ridge width (L) on temperature. (b) Temperature dependence of the segmental relaxation time of PS obtained from DMA (blue open circles) and predicted by the stick−slip behavior (black solid circles). The solid and dashed lines in panel b are VFT eq 6 fits to the experimental points.

maximum during the deformation process. The PS film exhibits the maximum viscoelastic dissipation in the course of the wetting ridge deformation, providing the most significant dissipation resistance to prevent the liquid front advancing. As a result, the glycerol is effectively pinned on the viscoelastic PS film and displays the most obvious stick−slip behavior. Therefore, the dimensionless ratio (ξ = τc/τα) that characterizes the interplay between the rate of surface ridge deformation and the PS segmental rearrangement determines the stick−slip behavior. When the rate of polymer surface deformation near the droplet contact line is much larger or smaller than the segmental relaxation rate (ξ ≪ 1 or ξ ≫1), the polymer is in the glassy or rubbery state with negligible mechanical loss. In these situations, the impedance for liquid spreading is relatively small; thus, the droplet contact line advances with a smaller Δθ value. When the surface ridge deformation rate is close to the polymer segmental relaxation rate (ξ ≈ 1), the polymer was undergoing a glass-to-rubber transition with a significant viscoelastic loss, resulting in the stick−slip behavior with the maximum Δθ value for liquid spreading. Consequently, the Δθ−ξ relation in Figure 8b reveals the correlation between the PS segmental relaxation and the droplet stick−slip behavior. This correlation gives a clear picture of how the segmental relaxation rate affects the stick−slip behavior and also explains the opposite trend of Δθ change with increasing contact line velocity at temperature above and below Tg shown in Figure 3. Based on this mechanism, it may be concluded that the observed peak in the Δθ−υ curve, as well as in the Δθ−T curve in ref 60, is associated with the PS α-relaxation process related to the energy dissipation caused by the segmental rearrangement, which strongly reinforces the idea that Tjm is a suitable measure of the glass transition temperature, and specifically, the α-relaxation temperature of polymer thin films. Additionally, the segmental relaxation time of PS at various temperatures can also be evaluated by reconstructing the Δθ−υ master curve using various reference temperatures, based on the inherent correlation between the υmax and segmental relaxation time (τα) of PS: ξ = τc/τα = L/(υmaxτα) ≈ 1. Figure 9a gives the temperature dependence of the υmax value and the wetting ridge width. The segmental relaxation time of PS is calculated as ταjm ≈ L/υmax from the jumping angle data, and the estimated ταjm is plotted against the temperature, as shown in Figure 9b. Without any adjustment, our simple estimates of the magnitude of ταjm are broadly in agreement with τα values obtained by DMA (ταDMA) with deviations of less than 1 order

of magnitude. This agreement strongly suggests that the stick− slip behavior of the glycerol droplets is controlled by the segmental relaxation of the PS. The empirical Vogel−Fulcher− Tammann (VFT) equation:85,86 τα = τ0 exp[B /(T − Tk)]

(6)

where B and Tk are constants, describes the relaxation dynamics of amorphous materials, which can be fitted well using ταjm obtained by dynamic wetting experiments. By fitting the temperature dependence of ταjm and ταDMA from Figure 9b to eq 6, we obtained B = 1525 and 1504 K and Tk = 325 and 322 K for ταjm and ταDMA, respectively, which are similar to results reported from dielectric relaxation measurement of PS.87,88 The results above suggest that the polymer segmental dynamics could also be suitably indicated by the ταjm value at various temperatures, and it also validates again the feasibility of the proposed approximation model shown in Figure 7 to derive the characteristic time during liquid wetting. Finally, another interesting aspect of our findings is that they may shed new insight into the biological mechanism involved in cellular migration. The contact line friction arising from the viscoelastic dissipation due to the surface deformation of soft materials may be partly responsible for the phenomenon of the directional migration of cells in which cells typically migrate from soft substrates to stiffer ones.89,90

4. CONCLUSIONS In this article, the dependence of the stick−slip behavior of glycerol droplets on the corresponding velocity of the advancing contact line was investigated. It was found that the stick−slip behavior during dynamic wetting of the droplets scaled by the jumping angle (Δθ) depends on both the temperature and advancing velocity of droplet contact line (υ). A Δθ−υ master curve was obtained based on the time/ temperature-superposition principle, which was similar to the frequency-dependent tan δ curve obtained by dynamic mechanical analysis (DMA). The temperature-dependent shift factor (αT) obtained was in good agreement with the Williams−Landel−Ferry (WLF) equation. Since the advancing of the contact line resembles the shear process in a viscoelastic material, the velocity dependence of jumping angle can be converted into the dependence of Δθ on the deformation frequency of the PS surface during liquid spreading. By correlating the frequency dependence of Δθ with the segmental relaxation of PS, we found that the stick−slip behavior of liquid 12332


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wetting was essentially determined by a dimensionless parameter (ξ), which incorporates the PS segmental relaxation time (τα) and the characteristic time (or frequency) for PS surface deformation during liquid spreading (τc). When τα of the PS film is close to τc during liquid front movement, the value of Δθ reaches a peak value, due to the maximal viscoelastic dissipation of the PS film. This correlation between Δθ and segmental relaxation time confirms that the observed peak in the Δθ−υ curve (and Δθ−T curve) is associated with the α-relaxation process of polymers related to the energy dissipation caused by the segmental relaxation, which strongly demonstrates that Tjm (the temperature where Δθ reach maximum in Δθ−T curve) is the α-relaxation temperature of polymer thin films, namely, the glass transition temperature. Based on this proposed mechanism, the segmental relaxation dynamics of PS films could be estimated by simply reconstructing the Δθ−υ master curve using various reference temperatures. The temperature dependence of PS segmental relaxation time deduced from the Δθ−υ master curve is consistent with that derived from DMA analysis and can be fitted with the VFT equation. These results demonstrate that not only Tg but also the segmental relaxation of thin polymer films can be probed as a function of temperature by studying the corresponding stick−slip behavior. Further work is required to systematically explore this possibility.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b06078. Loss factor (tan δ) as a function of temperature at various frequencies; advancing contact angle of glycerol on PS film surface at various temperatures; evidence of the negligible influence of film thickness on the temperature and frequency dependence of the stick− slip behavior (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] or [email protected]. Tel: +86-571-8684-3600. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are thankful for support from the National Natural Science Foundation of China (No. 21174134, 21374104, 21504081), the Natural Science Foundation of Zhejiang Province (No. LY13B040005), and Science Foundation of Zhejiang Sci-Tech University (ZSTU) (No. 15062020-Y).

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