Surface Dynamics of Polymer Glasses: Sub-Tg Surface

Article pubs.acs.org/Macromolecules

Surface Dynamics of Polymer Glasses: Sub‑Tg Surface Reorganization in End-Functional Polymers Derek Wong,‡,§ Claire A. Jalbert,‡,⊥ Patricia Anne V. O’Rourke-Muisener,‡,∥ and Jeffrey T. Koberstein†,* ‡

Polymer Program, Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06269-3136, United States Department of Chemical Engineering, Columbia University in the City of New York, MC4721, New York, New York 10027, United States

†

ABSTRACT: Dynamic water contact angle analysis is applied to characterize the surface reorganization of glassy polystyrenes (PS), terminated with either a fluorosilane or carboxylic acid end group, upon exposure to an atmosphere of saturated water vapor. Fluorosilane end groups are initially adsorbed preferentially at the surface and diffuse away from the surface when exposed to water vapor. Carboxylic acid end groups are initially depleted from the surface and are drawn to the surface when exposed to water vapor. The time dependence of the surface composition during reorganization, determined by application of Cassie’s equation, scales with the square root of time, consistent with a diffusive process. Angle dependent X-ray photoelectron spectroscopy (ADXPS), applied to characterize the surface concentration depth profiles of the fluorosilane-terminated PS before and after exposure to water vapor, indicates that reorganization in the glassy state involves motions on a length scale of about 2 nm. Modified lattice model calculations, assuming that reorganization can occur only over length scales of this magnitude, are found to provide a reasonable representation of ADXPS surface composition depth profiles, supporting the conclusion that the length scale for surface reorganization of end-functional polymers in the glassy state is of the order of a few nanometers. When this length scale is coupled with the dynamic contact angle data, apparent diffusion coefficients in the range of 10−13 to 10−10 cm2/s are obtained. Analysis of the temperature dependence of the apparent diffusion coefficients, found to be an activated process following Arrhenius behavior, yields activation energies of 137 kJ/mol for fluorosilane-terminated PS and 39 kJ/mol for PS terminated with a carboxylic acid end group, considerably lower than experimental values determined from analysis of either polymer−polymer interdiffusion or free surface dynamics. These activation energies are a closer match to those of the βrelaxation of bulk PS than they are to the α-relaxation of either the PS surface or the PS bulk, suggesting that surface reorganization in glassy PS can occur by virtue of short-range motions characteristic of a surface activated β-relaxation occurring over length scales of a few nanometers.

■

INTRODUCTION The wide applicability of polymer glasses has led to considerable interest in understanding the dynamic properties of their surfaces. Surface mobility has an important influence on properties such as friction and adhesion and also limits the ultimate stable feature size obtainable by lithography or nanopatterning. Methods for controlling surface mobility may therefore have considerable impact on a broad range of applications. Previous studies have documented enhanced mobility at the free surface of a glassy polymer. Enhanced surface mobility was initially investigated through the construct of a surface glass transition (Tg,s), measured on thin films, either free-standing or cast onto various substrates. The original experimental measurements of Tg,s for polystyrene (PS) documented depressions on the order of tens of degrees when the film thickness was reduced below 40 nm.1 Since that time, numerous measurements on the Tg,s of PS using a variety of different techniques, for PS of varying molecular weights, and collected for a variety of experimental conditions have been found to be in general agreement.2 The current consensus is that: the free surface Tg,s is depressed for PS films of thickness © 2012 American Chemical Society

less than about 100 nm; the depression is inversely dependent on thickness and the dependence of Tg,s on thickness found in almost all studies can be represented by a single empirical function. Tg, however, is only an indirect measurement of polymer dynamics. Recent measurements using more direct methods to characterize surface and interfacial dynamics in polymers, have found that the temperature dependence of surface relaxation rates above the apparent Tg,s does not follow the Williams−Landau−Ferry relation characteristic of a polymer melt, but rather corresponds to Arrhenius behavior,3−10 suggesting that surface mobility can be ascribed to polymer motion on the segmental length scale. The elementary unit involved in segmental motion has been postulated to be the Kuhn segment,3 typically several nanometers in length comprising about 8−10 monomers.11 To account for this behavior, the concept of a mobile surface layer was introduced, a liquid-like layer on the surface of polymers at all Received: July 19, 2012 Revised: September 10, 2012 Published: September 28, 2012 7973

dx.doi.org/10.1021/ma301513s | Macromolecules 2012, 45, 7973−7984

Macromolecules

Article

temperatures.1,12,13 Estimates of the thickness of the mobile surface layer fall in the range of 0.1−10 nm.2,3 Surface activation energies for PS, determined from analysis of the Arrhenius temperature dependence of various dynamic surface properties, range from 200 to 360 kJ/mol.3 These values generally fall below the 330−880 kJ/mol reported for the activation energy of the α-relaxation of bulk polystyrene,14 suggesting that the α-relaxation process is activated at the surface. The only direct measurements of surface diffusion coefficients,3 determined from interface healing experiments carried out below the bulk glass transition temperature, yielded values ranging from 10−25 to 10−15 cm2/s. The temperature dependence of these diffusion coefficients was also found to be Arrhenius in nature. The time scales associated with surface mobility are therefore faster than comparable bulk relaxation processes by a factor as large as 109.15 A number of important questions remain, such as whether the overall chain mobility at the polymer surface is greater than that in the bulk and what the exact nature of molecular motion at the surface is. One of the most important consequences of surface mobility at glassy polymer surfaces is the instability of surface properties in multicomponent polymers. In air, these materials typically exhibit surface segregation behavior where the component of lowest surface tension adsorbs preferentially at the surface.16,17 Surface mobility allows the surfaces of these heterogeneous materials to reorganize when subjected to some external stimulus such as contact with water, even in the glassy state.18 Surface reorganization can be advantageous when used as a basis to construct adaptive or responsive materials, or can be detrimental because it compromises the temporal stability of surface properties. The latter effect is important in surface modification strategies that are designed to either increase or decrease the surface tension. For example, oxidative treatments used to promote adhesion or wetting by increasing surface polarity are thermodynamically unstable, subject to rapid recovery of the initial surface properties by diffusion of oxygenated species away from the surface.16 Applications requiring improved release properties call for a reduction in surface tension, usually accomplished by incorporating low energy functional groups such as fluorocarbons into the surface. When placed in hydrophobic environments, these low energy groups move away from the surface, resulting in significant changes in the material surface properties,18 a surface reorganization phenomenon that is particularly important for implantable biomaterials.19 Surface segregation and reorganization occur in virtually all heterogeneous polymers. Numerous studies using a broad range of techniques have documented preferential surface segregation of side chains, chain ends, segments of block and random copolymers as well as entire chains in the case of polymer blends.16,17 The existence of a mobile surface layer on polymers, even below their Tg, makes it virtually impossible to create stable surfaces in these heterogeneous, multicomponent polymers. It is important therefore to understand the dynamics of the surface reorganization process in order to properly design the surface properties of multicomponent polymer systems. To date, however, there have been no comprehensive studies of surface dynamics for multicomponent polymers. Toward that end, we have studied the reorganization of ωfunctional polystyrenes terminated with either fluorosilane or carboxylic acid end groups as model systems for multicomponent polymers. Fluorosilane end groups are initially adsorbed preferentially at the surface and diffuse away from the

surface when the material is exposed to water vapor as a stimulus. Conversely, carboxylic acid end groups are initially depleted from the surface and diffuse to the surface when exposed to water vapor. Surface segregation phenomenon have been widely studied for end-functional polymers, both from the experimental and theoretical viewpoints,18,20 especially for fluoro-terminated PS.21−28 We use dynamic contact angle analysis to show that changes in the surface composition scale with the square root of time during surface reorganization, consistent with a diffusive process. Angle dependent X-ray photoelectron spectroscopy measurements are employed to determine appropriate length scales for surface reorganization, which enable estimation of surface diffusion coefficients when coupled with the contact angle data. We also show that the temperature dependence of sub-Tg surface reorganization follows an Arrhenius process from which we calculate activation energies. These results are compared to the results of previous investigations of the dynamic surface properties of glassy PS and to known relaxation processes in bulk PS.

■

EXPERIMENTAL SECTION

Materials. ω-Functional polystyrenes (PS) terminated with a fluorosilane end group were synthesized by anionic polymerization of styrene in cyclohexane at 60 °C using sec-butyl lithium as initiator. Styrene monomer was distilled over calcium hydride, and cyclohexane solvent was distilled over sulfuric acid. The reaction was terminated with tridecafluoro-1,1,2,2-tetrahydrooctyl-1-dimethylchlorosilane (Huls-America) to provide an end group of structure [−Si(CH3)2− (CH)2(CF2)5−CF3] and with carbon dioxide to incorporate carboxylic acid end groups. The schematic structure of the ω-fluorinated polystyrenes is shown in Scheme 1.

Scheme 1. Chemical Structure of ω-Fluorosilane Polystyrenes

Note that all of the PS samples have one sec-butyl end group that is a remnant of the anionic initiator used in their synthesis. The nonfunctional polystyrene (PSH120), with a number-average molecular weight of 120 000 Da, was purchased from Polysciences and used as received. Sample Characterization. Gel permeation chromatography (GPC) was used to determine the molecular weights and molecular weight distributions of the polymers. The system used was a Waters 150-C consisting of a model 510 pump, model 410 refractometer, model 840 data station, and four Ultrastyragel columns with pore sizes of 1000, 100, 50, and 10 nm. Tetrahydrofuran was the mobile phase, and the system was operated at room temperature. Calibration was performed with seven polystyrene standards (Scientific Polymer Products). Elemental analysis (Galbraith Laboratories) was used to determine the fluorine content (% F) of ω-fluorosilane polystyrenes. The efficiency of ω-end functionalization or functionality, f, is defined as the ratio of fluorine content obtained from elemental analysis to the fluorine content expected from the chemical formula and the measured molecular weight. The efficiency of ω-end group functionalization for the carboxy-terminated PS samples was determined by end group 7974


Macromolecules

Article

Table 1. Characteristics of End-Functional Polystyrenes sample designation

α-end group

ω-end group

Mn, kDa

Mw/Mn

%F

mol of COOH per g

f

Tg, °C

PSF5 PSF10 PSF25 PSCOOH6 PSCOOH10 PSH120

sec-butyl sec-butyl sec-butyl sec-butyl sec-butyl sec-butyl

fluorosilane fluorosilane fluorosilane carboxy carboxy H

5.3 10.9 25.0 6.5 10.0 120

1.04 1.06 1.12 1.06 1.04 n.a.

4.17 1.77 0.84 0 0 0

0 0 0 0.000 144 0.000 097 0

0.84 0.72 0.85 0.94 0.97 0

83 92 102 95 99 n.a.

for 24 h, and the fluorine-to-carbon ratio was measured as a function of time. The fluorine signal decreased with exposure time and, after 6 h of exposure to the X-rays, was reduced by about 10% due to photoelectron damage.30 To minimize fluorine loss, samples were exposed to the X-ray beam for 4 h or less. Data for different takeoff angles were collected in random order to block systematic errors. Measurements on several takeoff angles were repeated for each new sample in order to ensure reproducibility of the data. A typical ADXPS data set as reported in this paper is thus a collection of data from 5 to 6 samples superimposed onto one graph. Although it is difficult to establish absolute errors for XPS data, the limited scatter of data observed in the superimposed composite graphs illustrates that the repeatability of the data is excellent, generally falling within a range defined by 2−3 times the diameter of the symbols shown in the graphs of ADXPS data. Sample Preparation. Polymer films were prepared by spincoating solutions of the polymers onto silicon wafers. Polymers were dissolved in chloroform and filtered through a 0.2 mm Teflon filter prior to spin-coating. The substrates, 3 in. silicon (111) wafers (Motorola, Inc.), were rinsed three times with filtered chloroform before use. The concentration of the polymer solution was 15% (w/v) leading to film thicknesses in the range of 1000−1200 nm. In this range of film thicknesses, the glass transition temperature is not expected to be depressed or to depend on film thickness.13 Spincoated films were annealed in vacuum for 16 h at 165 °C to attain equilibrium. The annealed samples were introduced to the X-ray photoelectron spectrometer chamber within 6 h of being removed from the vacuum chamber. While direct measurements were not made, these conditions are known to produce polymer surfaces with minimal surface roughness.

titration. A 0.1N KOH solution was added until a persistent pink end point was obtained using phenolphthalein as an indicator. Duplicate samples were titrated leading to an estimated error of ±1.5% for these measurements. Characterization results for the polymers used are summarized Table 1. Because of the inefficiencies of termination, the functionality, f, was not unity in all cases. In the nomenclature adopted, PSF is ω-fluorosilane polystyrene, PSH is nonfunctional polystyrene and PSCOOH is carboxy-terminated polystyrene. The number that follows denotes the nominal molecular weight in thousands. The designation PSF10, for example, refers to nominal 10 kDalton ωfluorosilane polystyrene. Because all samples were prepared via anionic polymerization, the α-termini for all polymers studied were sec-butyl groups that were remnants of the initiator. A Perkin-Elmer DSC 7 was used to measure the glass transition temperatures (Table 1) and to determine whether the fluorosilane end groups formed any crystalline or liquid crystalline aggregates. The cell was purged with dry nitrogen, and the temperature was scanned from 30 to 350 at 10 °C/min. No thermal transitions were detected that might be associated with phase transitions of the fluorosilane end groups. Water contact angle measurements (Millipore Milli-Q purified water, 18 MW resistivity, filtered through a 0.2 μm nylon filter to remove any bacterial contamination) were used to follow the timedependent changes in surface energy of the polymers as the environment was changed from air to saturated water vapor. Measurements were made using a sample cell compatible with the pendant drop system for digital analysis developed by our group.29 The cell is capable of maintaining a constant temperature environment within an atmosphere saturated with the vapor of the probe liquid. Contact angles were measured as a function of time in contact with a saturated water vapor atmosphere at temperatures of 30, 40, 55, and 70 °C in advancing mode. Under these conditions all of the polymers are below their glass transition temperatures by at least 13 °C. The stability of temperature control was ±1 °C. All samples were initially equilibrated for 4 h at 30 °C. Drops were formed using 10-μL Drummond positive displacement syringes fitted with disposable glass capillaries. Two measurements on each of two drops were taken, and the contact angles reported are the average of these measurements. Visual inspection after measurement did not reveal any interaction of the liquid drop with the surface. The results reported are the average of all measurements with an accuracy of ±2° (95% confidence interval). Immediately after placing the samples in the cell, the first contact angle was measured (t = 0), after which contact angles were measured at time intervals that depended on the rate of change being observed (more frequent measurements were taken when the contact angle was changing more rapidly). The analysis software for determining contact angle from robust shape comparison analysis of sessile drops was an extension of the algorithm developed previously for pendant drop analysis.29 Surface composition depth profiles were measured using angle dependent X-ray photoelectron spectroscopy (ADXPS). ADXPS provides composition depth profiles of end-groups in the near surface region both before and after exposure to the water vapor environment. All of the samples studied by XPS were measured within 4 h of completion of the contact angle analysis. ADXPS measurements were made with a PHI system 5300 spectrometer equipped with a monochromatic Al Kα source providing 1487 eV X-rays with a line width of 0.85 eV. To determine the chemical stability of the fluorinated end groups, sample PSF10 was exposed to the X-ray beam

■

RESULTS

The surface reorganization of the end-functional polystyrenes was characterized by measuring the time-dependent changes in water contact angles after exposure to a saturated water vapor environment. Polymer films were placed into a sealed chamber with a saturated water vapor atmosphere that served as a hydrophilic stimulus for surface reorganization. After a proscribed period of reorganization time, a sessile water drop was formed on the polymer surface within the same environmental chamber and the contact angle was measured in place. The environmental chamber contained a carousel capable of holding ten separate samples simultaneously so that contact angle measurements could be performed at ten different reorganization times (i.e., on 10 different substrates) without disturbance. The results of these dynamic water contact angle measurements at four different temperatures are presented in Figures 1−4. The initial (i.e., time = 0) contact angles for the PSF materials are all higher than that of PSH120 due to preferential surface segregation of the lower surface tension fluorinated end groups. Initial PSF contact angles decreased with molecular weight in a manner proportional to their fluorine contents (see Table 1). The static contact angles for these materials have already been analyzed in some detail.26 Upon exposure to saturated water vapor, the contact angles for all PSF samples 7975


Macromolecules

Article

Figure 1. Water contact angle, θ, as a function of time exposed to saturated water vapor at 30 °C: PSF5K (filled squares), PSF10 (filled circles), PSF25 (filled triangles), PSCOOH6 (open circles), PSCOOH10 (open squares), and PSH120 (stars).




decreased with time with a rate of change that increased as the temperature was increased. After long exposure times, PSF contact angles approached a value similar to that for PS. These results indicate that the fluorine end groups for PSF samples were initially adsorbed preferentially at the surface, but that they were gradually replaced by PS backbone units when exposed to saturated water vapor. The driving force for surface reorganization is the difference in surface tensions between the lower surface tension fluorinated end groups and the higher surface tension PS backbone.31−33 The exchange of fluorinated end groups with PS backbone segments at the surface during reorganization replaces less favorable interactions between water vapor and the fluorinated end groups with more favorable interactions between water vapor and the polystyrene backbone. The contact angles of the PSCOOH samples exhibited behavior that was essentially opposite to that of the PSF

materials. The initial contact angles at time zero were similar to the contact angle of PSH120. After exposure to saturated water vapor, the PSCOOH contact angles decreased with time, approaching an asymptotic value that was much lower than that of PSH120 at extended times. The asymptotic contact angle was lower for lower molecular weight PSCOOH consistent with its higher carboxylic acid content. These results indicate that for the PSCOOH materials, the higher surface tension carboxylic acid end groups were initially depleted from the surface but migrated to the surface when the material was exposed to water vapor. In this case, the initial interactions between the polystyrene backbone and water were gradually replaced by more favorable interactions between water and carboxylic acid end groups as the latter migrated to the surface. The contact angles for PSH120 show some time dependence as well, decreasing slightly with exposure time to water vapor. 7976


Macromolecules

Article

f E, defined in (2) is a property that follows this relationship, and normalize for the value at zero time, we can rewrite (3) as

We believe this to be an effect of the sec-butyl end group (i.e., α-terminus) on PSH120 that is a remnant of the sec-butyl lithium initiator used in its anionic synthesis. We have shown previously that this end group, with a surface tension below that of the PS backbone, segregates preferentially to the surface.25 With time in contact with water vapor, the secbutyl end group will gradually be replaced by PS backbone segments, leading to a decrease in the contact angle with time. The PSCOOH samples also have a sec-butyl end group in the α position and because this group has the lowest surface tension of any unit in PSCOOH, it will also segregate preferentially to the surface. The zero contact angle data support this interpretation as PSCOOH6, PSCOOH10, and PSH120 have essentially identical initial contact angles that are higher than the asymptotic value found for PSH120 that is characteristic of the polystyrene backbone. The sec-butyl group had an insignificant effect on the contact angles of the PSF samples because the fluorosilane terminus has the lowest surface tension in the PSF samples. In order to interpret these results it is important to consider the heterogeneous nature of end-functional polymers, that is, they comprise two chemically distinct components, the end group and the polymer backbone. The contact angle for a surface that is compositionally heterogeneous is often described by Cassie’s law, which may be written34 cos θ = fE cos θE + (1 − fE ) cos θPS

{cos θ(t ) − cos θPS} = k′D1/2t 1/2 + k″

(4)

where cos θ(t) is the time dependent water contact angle, cos θPS is the water contact angle for pure PS estimated from the long time asymptote of the PSH120 contact angle, k′ = (4/lπ 1/2){cos θ(t = ∞) − cos θPS}

(5)

and k″ = {cos θ(t = 0) − cos θPS}

(6)

If this diffusion model holds, a plot of the factor {cos θ(t) − cos θPS}against t1/2 should be linear with a slope of k′D1/2. Examination of the data in Figures 5−8 shows that a linear

(1)

where θ is the contact angle of the composite surface, θE is the contact angle of the pure end group, θPS is the contact angle of polystyrene and f E is the surface area fraction of end groups. Since the contact angles of PS and of the end group are constant, it is convenient to recast (1) in the form cos θ − cos θPS = (cos θE − cos θPS)fE = kfE

(2) Figure 5. Time dependence of water contact angle data plotted according to the diffusion model represented by (4). The samples were exposed to saturated water vapor at 30 °C: PSF5 (filled squares), PSF10 (filled circles), PSF25 (filled triangles), PSCOOH6 (open circles), PSCOOH10 (open squares), and PSH120 (stars).

where k is a constant. The difference between the cosine of the measured contact angle and the cosine of the contact angle of the PS backbone is therefore directly proportional to the surface composition and can be used to monitor temporal changes in the surface composition during surface reorganization. The value of θPS required in 2 for each temperature was set to the asymptotic contact angle for PSH120 observed at long times at that temperature. The contact angles for the pure end groups are not known. Rigorous modeling of the reorganization kinetics is complicated by the existence of an initial end group surface concentration gradient that depends on polymer molecular weight and the thermodynamic nature of the end group. Previous kinetic studies of dynamic surface processes and surface reorganization,35 as well as molecular dynamics simulations36 and experimental investigations of polymer chain end motion37,38 found that dynamic properties scaled with t1/2, characteristic of a diffusive process. We therefore assumed that the reorganization process could be modeled as sorption into a thick film by Fickian diffusion. In this case, the time dependence of some property, M(t), is expected to follow a relation of the form39 1/2 M (t ) 4 ⎛ Dt ⎞ = ⎜ ⎟ M (t = ∞ ) l⎝π ⎠

relationship of this nature provides an excellent representation of the time dependence of contact angles for all of the materials studied at all four temperatures. The contact angle data support the conclusion that surface reorganization can be modeled as a diffusive process following (4). On the basis of this finding, we were encouraged to determine apparent diffusion coefficients for the surface reorganization process as a function of molecular weight, end group nature and temperature. Several difficulties arise, however, in applying (4) to the data because the factor k′ contains two unknown parameters: the film thickness, l, and cos θ (t = ∞). The film thickness in our case is equivalent to the distance over which an end group can segregate, a distance that is limited by the structure and mobility of the polymer chain. The length scale for segregation is limited on the high side by the radius of gyration of the polymer as the polymer chain and end group are linked by a covalent bond, and on the low side by the smallest unit, that is, the statistical segment length. Both the radius of gyration and statistical segment length are dependent upon temperature and the radius of gyration is also dependent upon the molecular weight.

(3)

where l is the film thickness t is time and D is the diffusion coefficient. If we assume that the surface fraction of end groups, 7977


Macromolecules

Article

Figure 8. Time dependence of water contact angle data plotted according to the diffusion model represented by (4). The samples were exposed to saturated water vapor at 70 °C: PSF5 (filled squares), PSF10 (filled circles), PSF25 (filled triangles), PSCOOH6 (open circles), PSCOOH10 (open squares), and PSH120 (stars).


ADXPS yields an integral concentration depth profile defined by42 I (θ ) ∝

∫0

∞

n(z)e−z cos(θ)/ λ dz

(7)

where I(θ) is the ADXPS signal for a takeoff angle, θ, and n(z) is the true atomic concentration depth profile for a depth, z. Experimental ADXPS data can be modeled by calculating a true atomic concentration depth profile, n(z), from a theoretical model and then computing a theoretical integral concentration depth profile for comparison with experiment by inserting the true atomic concentration depth profile into (7). This procedure was applied previously to model the equilibrium surface structure of the PSF materials.27 The low surface tension fluorosilane end groups adsorb preferentially at the surface and we found that the integral surface concentration depth profiles measured by ADXPS corresponded well with the predictions based on a simple incompressible lattice model.31,33,43 The model has four basic parameters: a reference or lattice site volume, a normalized chain length, a Flory− Huggins bulk interaction parameter, χb, and a surface interaction parameter, χs, related to the difference in surface tensions between the functional end group and the polymer repeat unit. The model derives a reference volume by assuming that an end group occupies one or two lattice sites, that is, the reference volume was set equal to either the end group volume or one-half of the end group volume. The normalized polymer chain length is the volume of the polymer backbone divided by this reference volume. Simultaneous global regression of the lattice model predictions to all of the ADXPS data for PSF5, PSF10, and PSF25 yielded best fit values of χb = 1.59 and χs = −2.18 with one fluorinated end group occupying two lattice sites.27 The surface interaction parameter is related to the difference in surface tensions of the end group and polystyrene backbone, γE and γPS, respectively, according to31


ADXPS integral concentration depth profiles were determined for the PSF materials in order to characterize the length scales inherent to surface reorganization. The fluorine to carbon ratio reflects the surface composition depth profile of the fluorosilane end group.27 The sampling depth of ADXPS can be approximated as 3λ(sin θ), where θ is the photoelectron takeoff angle, that is, the angle between the normal to the sample and the detector, and λ is the electron mean free path, about 2.3 nm for polymers.40,41 The maximum sampling depth is therefore on the order of 7 nm, while the minimum sampling depth, limited by instrumental factors and surface roughness, is about 1.5 nm. ADXPS data therefore provide information on surface concentration gradients over the range of about 1.5−7 nm.

χS = 7978

(γE − γPS) kT

(8) dx.doi.org/10.1021/ma301513s | Macromolecules 2012, 45, 7973−7984

Macromolecules

Article

depth” of less than about 5 nm. Second, the fluorine to carbon ratio decreases upon exposure to water vapor up to an “integral depth” of about 2 nm. Third, this decrease is necessarily compensated for by a slight increase in the fluorine to carbon ratio over the “integral depth” range of about 2−5 nm. Qualitatively, the data indicate that fluorinated end groups initially located in the top nm or so of the material move slightly deeper into the material upon exposure to water vapor, exchanging positions with PS repeat units that relocate to shallower depths. Because ADXPS measures integral depth profiles, the actual depths of changes in surface composition are smaller than the “integral depths” indicated in the ADXPS profiles. A theoretical model for n(z) incorporated into (7) is required to determine the actual changes in the end group concentration depth profile during surface reorganization. A more quantitative understanding of the surface reorganization process and the length scales involved is provided by developing a theoretical model to analyze the ADXPS data after exposure to water vapor and comparing the resultant concentration depth profiles to those predicted before exposure. Lacking a theoretical framework for a rigorous treatment, we developed an approximate method to account for changes in the surface structure upon exposure to water. On the basis of the observation that exposure to water vapor did not change the ADXPS integral depth profiles for values of sin(θ) greater than about 0.7, we adopted a modified lattice model in which compositions in only the first two lattice layers were allowed to reorganize when exposed to water vapor. To simplify the lattice calculations, we allowed the end group to occupy only one lattice site and set the bulk interaction parameter to zero. In this case, the optimal fit of the lattice model to the data before exposure to water vapor, shown as the solid line in Figure 11, was obtained for a value of χs ≈ −4. If we adopt the simplest assumption, that Antonoff’s rule44 can be applied to calculate the interfacial tension between components 1 and 2, γ12, from their surface tensions, γ1 and γ2 (i.e., γ12 ≈ γ1 − γ2), then the surface interaction parameter after exposure to water vapor can be calculated as

Details pertaining to the lattice model calculations can be found in a number of previous publications.31−33 The model predictions agree well with the experimental integral concentration depth profile (i.e., fluorine to carbon ratio) for PSF5 before exposure to water vapor as shown in Figure 9.

Figure 9. ADXPS integral concentration depth profiles for fluorine to carbon ratio of PSF5: experimental data (filled squares); lattice model assuming end group occupies two lattice sites with χb = 1.59 and χs = −2.18 (solid line).

Figure 10 shows how the experimental ADXPS integral concentration depth profiles for PSF10 and PSF25 change upon exposure to water vapor. The agreement between the three different data sets for PSF10 samples after exposure to water vapor indicates that the results are highly reproducible. An interesting feature of these data is the presence of apparent local maxima and minima in the integral depth profiles. The depths at which the local maxima appear were found to be dependent on molecular weight and to scale roughly with the radii of gyration of the polymers, but we were not successful in finding a model that could reproduce this feature of the concentration depth profiles and have no conclusive explanation of its origins. These features fortunately have little effect on our analysis of the surface reorganization process. The ADXPS data sets for PSF10 and PSF 25 exhibit several common features. First, the data for sin(θ) greater than about 0.7 is unchanged upon exposure to water vapor, showing that the effects of surface reorganization are confined to an “integral

χS =

(γE / WATER − γPS / WATER ) kT

≅

(γPS − γE) kT

(9)

where k is the Boltzmann constant, T is temperature, γE/WATER is the interfacial tension between the end group and water and γPS/WATER is the interfacial tension between the PS backbone

Figure 10. ADXPS integral concentration depth profiles for fluorine to carbon ratios: before exposure to water vapor (solid squares) and after exposure to water vapor (open symbols): circles, 10 days at 30 °C; squares, 5 days at 40 °C; triangles, 24 h at 70 °C. The figure on the left is for PSF10 and the figure on the right is for PSF25. 7979


Macromolecules

Article

Figure 12. Experimental ADXPS integral concentration depth profiles for fluorine to carbon ratios of PSF10: before exposure to water vapor (solid squares) and after exposure to water vapor (open symbols): circles, 10 days at 30 °C; squares, 5 days at 40 °C; triangles, 24 h at 70 °C. The solid line is the lattice model prediction for the sample equilibrated in vacuum, and the solid line is the modified lattice model prediction for the sample after exposure to water vapor.

Figure 11. Lattice model calculations of the end group concentration, ϕE, as a function of the depth in terms of number of lattice layers. Each lattice layer adds a depth of approximately 0.75 nm. The dashed line is the lattice model calculation for the sample equilibrated in vacuum with χs = −4 and χb = 0. The solid line is lattice model calculation for the sample after exposure to water vapor with χs = 4 and χb = 0. In the latter calculation, the end group concentration for layer numbers 3 and greater were frozen at the values obtained from the calculation for the sample equilibrated in vacuum.

therefore provides a reasonable explanation for the XPS surface reorganization data, and suggests that the appropriate length scale for estimation of diffusion coefficients by application of (3) may be taken as l ≈ 2 nm. Lattice model calculations where more than two layers were allowed to reorganize did not improve the agreement with experiment. Diffusion coefficients were calculated for all samples from the slopes of the linear regressions to the data in Figures 5−8 according to eqs 4−6 using the value l ≈ 2 nm and setting the factor cos θ(t=∞) equal to longest time value of the cosine of the contact angle for that sample. The diffusion coefficients calculated in this manner increased with temperature as expected, falling within the range of 4 × 10−13 to 8 × 10−10 cm2/s, as shown in Figure 13. The diffusion coefficients for PSH120 are not shown because the errors in the calculation were of the same order of magnitude as the temporal changes. The temperature dependence of the diffusion data can be regressed to the Arrhenius equation in order to calculate the activation energy, Ea.

and water. Comparing (8) and (9), it is apparent that, within the assumptions made, the surface interaction parameters before and after exposure to water vapor will have the same magnitude but will be of opposite sign. A concentration depth profile for the sample after exposure to water vapor was calculated from the lattice model using the following approach: the concentration depth profile for the sample before exposure to water vapor was first calculated from the lattice model using values of χs ≈ −4 and χb = 0; concentrations for depths greater than the second lattice layer were frozen at these values and the concentrations in the top two lattice layers were recalculated from the lattice model using χs ≈ 4 and χb = 0. The composition depth profiles calculated from the lattice model in this manner are shown in Figure 11. The theoretical atomic concentration depth profiles from Figure 11 are inserted into (7) for both the carbon and fluorine signals in order to calculate theoretical fluorine to carbon ratios. The results of the model calculations are compared to the experimental ADXPS integral concentration depth profiles in Figure 12. Each lattice layer adds about 0.75 nm (i.e., the lattice dimension) to the depth because the lattice reference volume was set equal to the volume of the fluorosilane end group (v = 0.42 nm3).27 The lattice dimension, 0.75 nm, is the cube root of the end group volume. The lattice model calculation of the integral concentration depth profile for PSF10 before exposure to water vapor, the solid line in Figure 12, corresponds well with the experimental data (filled squares) for an optimal value of χs = −4. The integral concentration depth profile for PSF10 after exposure to water vapor (i.e., produced by the modified lattice model calculation) is represented by the dashed line in Figure 12. There are no adjustable parameters in this calculation; the value for χs was set to the same magnitude as that found from the optimal fit for the sample equilibrated in vacuum but given a positive value, that is, χs = 4. The prediction does not quantitatively reproduce the experimental data (open symbols), however, the fit does capture the shape of the integral concentration depth profile. The simple model adopted, that reorganization occurs only in the top two lattice layers,

Figure 13. Apparent diffusion coefficients as a function of temperature: PSF5 (filled squares), PSF10 (filled circles), PSF25 (filled triangles), PSCOOH6 (open circles), and PSCOOH10 (open squares). 7980


Macromolecules DApparent = D0 e−Ea / RT

Article

and after reequilibration are presented in Table 2. After 1 month, the contact angles approach their original contact

(10)

Arrhenius plots for all six end-functional polymers are shown in Figure 14. The first observation of note is that, within error,

Table 2. Recovery of Water Contact Angles (deg) material

contact angle before exposure

contact angle after exposure

contact angle after recovery

PSF5 PSF10 PSF25 PSCOOH6 PSCOOH10

99 95 90 88 87

84 90 87 63 76

94 92 89 86 83

angles before exposure to water vapor, but do not recover completely. Incomplete recovery may be attributed to a number of factors: surface oxidation after 1 month storage,45 surface contamination during storage, insufficient time to reequilibrate, or permanent reorganization of the glassy surface due to water penetration. It is perhaps not surprising that complete reversibility is not observed in a glassy material that is never at true equilibrium.

■

Figure 14. Arrhenius plot of the log of the apparent diffusion coefficients ln(D) versus 1/T: PSF5 (filled squares), PSF10 (filled circles), PSF25 (filled triangles), PSCOOH6 (open circles), and PSCOOH10 (open squares). The solid line is the result of linear regression to the fluorosilane-terminated samples and the dashed line is the result of linear regression to the carboxylic acid-terminated samples.

DISCUSSION It is generally accepted that the diffusion of polymer chains is not possible in the glassy state. The results of this study, however, as well as investigations of interfacial healing between glassy polymers46 and nanoparticle embedding9,10 at polymer surfaces document processes that appear diffusive in nature well below the bulk Tg. The development of lap shear strength and fracture toughness at the interface between glassy polymers, for example, has been found some 20−50 °C below the Tg and follow a t1/2 dependence with time, indicative of a diffusive process. This has been attributed in part to the dynamics of chain ends as embodied in the reputation model for chain motion.47,48 Because chain ends immediately escape the tube of configurational constraints, they can move freely in all directions and are predicted to exhibit Fickian diffusion with an expected t1/2 scaling. Molecular dynamics simulations36 and experimental measurements on the relaxation of end-deuterated polymers37,38 have confirmed this time dependence. It has been argued that interfacial interdiffusion between glassy polymers is diffusive in nature due to the formation of a “devitrified” contact zone.3 The presence of this viscoelastic contact zone was attributed to depression of the glass transition at the surface, Tgsurface, compared to the glass transition of the bulk polymer, Tgbulk, a phenomenon that has been observed experimentally and has been predicted by theory.2 The influence of a surface on the Tg, however, remains a controversial subject, and investigators have also demonstrated that the dynamics of the glass transition for thin polymer films with a free surface were unchanged down to a thickness of 10 nm, leading to the conclusion that enhanced mobility effects must be limited to length scales of only a few nanometers.49 The surface dynamics of polymer thin films have frequently been discussed in terms of a layered model that envisions a highly mobile surface layer of thickness, h, on top of a lessmobile bulk-like layer. Experimental estimates for the depth of penetration (equivalent to the thickness of a mobile surface layer) from polymer−polymer interfacial healing studies for glassy polystyrene fell within a range of 0.1−4 nm, with higher values found closer to the Tg.1−3,12,13 Theoretical values of this quantity are higher, either increasing from 1 to 10 nm as Tg is approached, or constant at a value of 10 nm.2 Experimental

the data fall into two classes of behavior: the data sets for the three fluorosilane-terminated samples superimpose and the data sets for the two carboxylic acid-terminated samples superimpose. The diffusion coefficients for reorganization therefore are dependent on the nature of the end group but not on the molecular weight. Since lower molecular weight polymers have higher initial end group concentration gradients, the latter result also indicates that the diffusion coefficients are not concentration dependent. The diffusion coefficients for the fluorosilane-terminated samples are larger than those of the carboxylic acid-terminated samples and show a stronger dependence on temperature. The scatter apparent in the data in Figure 14 arises mainly from the difficulty in determining the factor {cos θ(t=∞) − cos θPS} in (5) that is necessary to calculate apparent diffusion coefficients by applying (4) to the contact angle data. The term cos θ(t=∞) was taken as being equal to the cosine of the contact angle for that sample at the longest measured time. It can be seen from the data that some samples do not present a clear asymptotic value at long times making this estimation difficult. Because of the potential errors in the analysis and the superposition of data, we limited our analyses to two separate regressions of the data to (10): one regression to the combined data for the three fluorosilane-terminated samples and another for the two carboxylic acid-terminated samples. The activation energies determined from the two linear regressions shown in Figure 14 were: 137 kJ/mol (95% confidence limit of 104 kJ/ mol < Ea < 170 kJ/mol) for the fluorosilane-terminated samples and 39 kJ/mol (95% confidence limit of 22 kJ/mol < Ea < 55 kJ/mol) for the carboxylic acid-terminated samples. The reversibility of surface reorganization was studied by taking samples equilibrated in saturated water vapor and allowing them to reequilibrate in air at room temperature for a period of one month. Water contact angles determined before 7981


Macromolecules

Article

groups in polybutadiene melts53 and other groups have also observed dimerization of carboxylic acids in polymer blend systems.54,55 Chain ends that can hydrogen bond have been shown to influence the diffusion behavior for polymer melts,56 but we are not aware of similar studies for polymer glasses. In the present case of surface reorganization in polymer glasses, we speculate that dimerization does not have a large influence for two reasons: experimental surface reorganization rates are not found to be dependent upon molecular weight for either the PSF or PCOOH polymers, and reorganization occurs by short chain motions rather than diffusion of the entire polymer chain. The third difference between the two methods that might account for the higher apparent diffusion coefficients for surface reorganization is the environment used. Because the surface reorganization experiments are performed in a saturated water vapor environment, some water molecules may dissolve in the polymer, thereby plasticizing the polymer surface and increasing its relative mobility. The temperature dependence of surface reorganization does not follow the Williams−Landau−Ferry relation, but instead exhibits Arrhenius behavior, indicating that the process is controlled by local dynamics rather than bulk dynamics characteristic of a polymer above its glass transition. There is no evidence in our experiments that reorganization of our glassy surfaces is related to depression of the so-called “surface” Tg. These observations are consistent with previous investigations of interfacial mobility that have all documented Arrhenius type temperature dependence and have used it to estimate activation energies for thermally activated diffusion. Interface healing experiments yielded activation energies in the range of 240−300 kJ/mol with a weak dependence on molecular weight.57 Analysis of the temperature dependence of interdiffusion for PS glasses, determined by DSIMS and NR experiments, led to activation energies ranging from 240 to 320 kJ/mol.50 These activation energies were also found to correspond well with activation energies reported for diffusion in PS melts above Tg, 250−360 kJ/mol58 and to activation energies associated with the α-relaxation process for the free surface of PS: 210−270 kJ/mol5−7 and 325 kJ/mol.3 Activation energies determined from surface viscosity and surface nanohole recovery measurements were lower, at 1858 and 150 kJ/mol,9 respectively. Surface dynamics measurements on the free surface of PS by lateral force microscopy detected two separate regions of Arrhenius behavior that were attributed to surface α and β relaxations. Activation energies of the surface βtransition were reported as 1006 and 54−200 kJ/mol4 while those for the surface α-transition were reported as 220,7 269,6 and 210−240 kJ/mol.4 Surface β-transitions were only observed in ultrathin films, however; they are not believed to be associated with the β-transition for bulk PS and most likely have little if any relevance to our surface reorganization process. In most cases, the measured surface activation energies are smaller than the activation energies for bulk PS, the latter reported to be in the range of 360−880 kJ/mol for the αrelaxation process and 140−168 for the β-relaxation.59−61 The activation energies determined from our analysis of surface reorganization were 137 kJ/mol for the three PSF polymers and 39 kJ/mol for the two PSCOOH polymers, considerably lower than experimental values determined from analysis of either polymer−polymer interdiffusion or free surface dynamics. A number of differences between surface reorganization and other surface dynamics processes may account for these results. The observation that activation

estimates of h for PS determined from dynamic secondary ion mass spectroscopy (DSIMS) and neutron reflectivity (NR) measurements agree well with the penetration depth values,50 falling in the range of about 2−4 nm near room temperature and increasing to values as large as 10 nm as Tg is approached. A value of h = 2.3 nm or less was determined for PS based upon an analysis of surface viscosity measurements.8 Finally, nanoparticle embedding experiments led to estimates of h that fell in the range of about 1−6 nm, rising as Tg is approached.9,10 These values for the thickness of the mobile surface layer agree well with our own value of about 2 nm estimated from the ADXPS measurements. Experimental measurements of surface mobility are therefore consistent with a model for surface reorganization in polymer glasses where only the top 2−3 lattice layers take part in the reorganization process while the compositions in deeper layers do not change. To our knowledge, there are no other reported diffusion coefficients for the free surface of glassy polymers to compare to our measured values. We know of only one earlier study that reported diffusion coefficients for glassy polystyrene and these were determined for a polymer−polymer interface during healing.3 Analysis of the time dependence of lap shear strength and T-peel fracture energy during polymer−polymer healing provided estimates of the diffusion coefficients for a variety of glassy polymer interfaces that fell within a range of 10−25 to 10−15 cm2/s. Analysis of our dynamic contact angle measurements coupled with the assumption that the diffusion length is 2 nm (a lower limit) led to diffusion coefficients in the range of 10−13 to 10−10 cm2/s. The diffusion coefficients for glassy PS determined from surface reorganization experiments for a polymer−air interface are therefore several orders of magnitude larger than those determined from interfacial healing measurements for a polymer−polymer interface. There are three important differences between the two methods of estimation that account for this difference. First, there is considerable free volume at the free surface between a polymer and air (saturated with water vapor) because the surface density gradient is predicted to change from the density of the polymer to the density of air over a distance on the order of 1 nm.51 In contrast, the initial surface density gradients disappear rapidly during healing of a polymer−polymer interface. Second, surface reorganization in heterogeneous materials is driven by a chemical potential difference associated with lowering the surface free energy (as reflected by the finite magnitude of the surface interaction parameter), whereas the surface interaction parameter is effectively zero for the case of healing of a polymer−polymer interface. The fact that our apparent diffusion coefficients depend on the nature of the end group supports this argument. Group contribution estimates of the Flory interaction parameters between water and PS, between water and the fluorosilane end group and between water and the carboxylic acid end groups are 0.84, 1.25, and 0.62, respectively.52 These values, taken into consideration with (8), suggest that χS, the driving force for surface reorganization, is larger for the PSF materials than for the PSCOOH materials. Indeed, we find that, for the same molecular weight, reorganization is more rapid for PSF polymers compared to PSCOOH polymers, consistent with what would be expected for a diffusion process driven by a difference in chemical potential. A factor that complicates this conclusion, however, is dimerization of the carboxylic acid end groups. We have previously observed the dimerization of carboxylic acid end 7982


Macromolecules

Article

mers Program of the National Science Foundation (DMR-9809687, DMR-02-14363 and DMR-0704054).

energies for surface relaxations are generally smaller than those for bulk relaxations has been in part attributed to the existence of excess free volume at the surface due to the presence of a surface density gradient and to segregation of end groups to the free surface. These effects are exacerbated in the present studies of surface reorganization because we specifically modify the polymer chain ends to either enhance or to inhibit chain end surface segregation. In addition, surface reorganization is driven by a chemical potential difference that may lower the energy required for surface molecular motion. As discussed earlier, the surface segregation experiments are performed in a saturated water vapor environment that may lead to plasticization of the surface by dissolution of water molecules and a subsequent increase in surface mobility. Finally, since no solvent is present, the bulk screening length is equivalent to the statistical segment length and interactions between chemically distinct end groups and the PS backbone are effectively screened over distances approximating a single lattice layer. In principle, surface reorganization can therefore occur by simply exchanging a chain end located in the first lattice layer at the surface with a PS backbone unit in the second lattice layer, or vice versa, as we have envisioned in the modified lattice model calculations. Motion over such short length scales may not require cooperativity such as that involved with the α-relaxation, but may be possible with shorter range kink-type motions as are involved with a β-relaxation. In fact, the activation energies found for surface reorganization are a much closer match to that of the β-relaxation of bulk PS than they are to the αrelaxation of either the PS surface or the PS bulk. A previous surface reorganization study on a poly(vinyl chloride-vinyl acetate) (PVC−PVAc) copolymer molded against gold foil62 reported an activation energy of 43 kJ/mol, falling between the activation energies for the β-relaxations of pure PVAc and pure PVC, 40 and 68 kJ/mol, respectively. The β-relaxation in polymers has been attributed to the motion of a single Kuhn segment, which is estimated to contain 8 styrene monomers. The length of a styrene monomer is about 0.25 nm leading to a Kuhn segment length of about 2 nm for PS, consistent with the diffusion length scale for surface segregation determined by the ADXPS measurements. It is plausible therefore that surface reorganization in glassy PS can occur by virtue of short-range motions characteristic of a surface activated β-relaxation.

■

■

REFERENCES

(1) Keddie, J. L.; Jones, R. A. L.; Cory, R. A. Europhys. Lett. 1994, 27, 59. (2) Kawana, S.; Jones, R. A. L. Phys. Rev. E 2001, 63, 021501. (3) Boiko, Y. M. Colloid Polym. Sci. 2011, 289, 971. (4) Akabori, K.; Tanaka, K.; Kajiyama, T.; Takahara, A. Macromolecules 2003, 36, 4937. (5) Boiko, Y. M.; Lyngaae-Jørgensen, J. Polymer 2005, 46, 6016. (6) Fu, J.; Li, B.; Han, Y. J. Chem. Phys. 2005, 123, 064713. (7) Kajiyama, T.; Tanaka, K.; Satomi, N.; Takahara, A. Macromolecules 1998, 31, 5150. (8) Yang, Z.; Fujii, Y.; Lee, F. K.; Lam, C.-H.; Tsui, O. K. C. Science 2010, 328, 1676. (9) Fakhraai, Z.; Forrest, J. A. Science 2008, 319, 600. (10) Qi, D.; Ilton, M.; Forrest, J. A. Eur. Phys. J. E 2011, 34, 56. (11) Van Krevelen, D. W. Properties of polymers, 3rd ed.; Elsevier: Amsterdam, 1997. (12) Forrest, J. A.; Dalnoki-Veress, K. Adv. Colloid Interface Sci. 2001, 94, 167. (13) Ellison, C. J.; Torkelson, J. M. Nat. Mater. 2003, 2, 695. (14) McCrum, N. G.; Read, B. E. Anelastic and Dielectric Effects in Polymeric Solids; Dover: New York, 1967. (15) Dutcher, J. R.; Ediger, M. D. Science 2008, 319, 577. (16) Wu, S. Polymer Interface and Adhesion; Marcel Dekker: New York, 1982. (17) Jones, R. A. L.; Richards, R. W. Polymers at Surfaces and Interfaces; Cambridge University Press: Cambridge, England, 1999. (18) Koberstein, J. T. J. Polym. Sci., Polym. Phys. Ed. 2004, 42, 2942. (19) Holly, F. J.; Refojo, M. F. In Hydrogels for Medical and Related Applications; Andrade, Ed.; ACS Symposium Series 31; American Chemical Society:Washington, DC, 1976; pp 252−266. (20) Koberstein, J. T. in Polymer Surface, Interfaces and Thin Films; Series on Directions in Condensed Matter Physics; World Scientific Publishing: Singapore, 2000; pp 115−181. (21) Hunt, M. O. J.; Belu, A. M.; Linton, R. Q.; DeSimone, J. M. Macromolecules 1993, 26, 4854. (22) Affrossman, S.; Hartshorne, M.; Tiff, T.; Pethrick, R. A.; Richards, R. W. Macromolecules 1994, 27, 1588. (23) Schaub, T. F.; Kelley, G. J.; Mayes, A. M.; Kulasekere, R.; Ankner, J. F.; Kaiser, H. Macromolecules 1996, 29, 982. (24) Tanaka, K.; Kawaguchi, D.; Yokoe, Y.; Kajiyama, T.; Takahara, A.; Tasaki, S. Polymer 2003, 44, 4171. (25) Elman, J.; Johs, B.; Long, T.; Koberstein, J. T. Macromolecules 1994, 27, 5341. (26) Mason, R.; Jalbert, C. A.; O’Rourke-Muisener, P. A. V.; Koberstein, J. T.; Elman, J. F.; Long, T. E.; Gunesin, B. Z. Adv. Colloid Interface Sci. 2001, 94, 1. (27) O’Rourke-Muisener, P. A. V.; Jalbert, C. A.; Yuan, C.; Baetzold, J. P.; Mason, R.; Wong, D.; Kim, Y. J.; Koberstein, J. T.; Gunesin, B. Macromolecules 2003, 36, 2956. (28) Yuan, C.; Ouyang, M.; Koberstein, J. T. Macromolecules 1999, 32, 2329. (29) Anastasiadis, S. H.; Chen, J.-K.; Koberstein, J. T.; Siegel, A. F.; Sohn, J. E.; Emerson, J. A. J. Colloid Interface Sci. 1987, 119, 55. (30) Graham, R. L.; Baht, C. D.; Hans A. Biebuyck, H. A.; Laibinis, P. E.; Whitesides, G. M. J. Phys. Chem. 1993, 97, 9456. (31) Jalbert, C.; Koberstein, J. T.; Hariharan, A.; Kumar, S. K. Macromolecules 1997, 30, 4481. (32) Jalbert, C.; Yilgor, I.; Gallagher, P.; Krukonis, V.; Koberstein, J. Macromolecules 1993, 26, 3069. (33) O’Rourke-Muisener, P. A. V.; Koberstein, J. T.; Kumar, S. K. Macromolecules 2003, 36, 771. (34) Cassie, A. B. D. Discuss. Faraday Soc. 1948, 3, 11. (35) Jones, R. A. L.; Kramer, E. J. Philos. Mag. 1990, 62, 129. Bogue, R.; Gamet, D.; Schreiber, H. D. J. Adhes. 1986, 20, 15.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Addresses §

BASF, 100 Campus Drive, Florham Park, NJ 07932. E-mail: [email protected] ⊥ 3M Center, 219-1S-01, Saint Paul, MN 55144. E-mail: [email protected] ∥ Department of Chemistry, University of South Florida, 4202 E. Fowler Ave., CHE 205, Tampa, FL 33620. E-mail: [email protected] Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This material is based on work supported by, or in part by, the US Army Research Office (Grants DAAD19-00-1-0104, W911NF-10-01-184, and W911NF-11-01-137) and the Poly7983


Macromolecules

Article

(36) Paul, W.; Binder, K.; Heermann, D. W.; Kremer, K. J. Chem. Phys. 1991, 95, 7726. (37) Lee, A.; Wool, R. P. Macromolecules 1986, 19, 1063. (38) Walcak, W.; Wool, R. P. Macromolecules 1987, 20, 1924. (39) Crank, L.; Park, G. S. Diffusion in Polymers: Academic Press: New York, 1968. (40) Clark, D. T.; Thomas, H. R. J. Polym. Sci., Polym. Chem. Ed. 1977, 15, 2843. (41) Szajman, J.; Liesegang, J.; Jenkin, J. G.; Leckey, R. G. G. J. Electron Spectrosc. Relat. Phenom. 1978, 14, 247. (42) Fadley, C. S. Prog. Surf. Sci. 1984, 16, 275. (43) Wong, D. A.; O’Rourke-Muisener, P. A. V.; Koberstein, J. T. Macromolecules 2007, 40, 1604. (44) Antonoff, G. Ann. Phys. 1939, 36, 86. (45) Wells, R. K.; Badyal, P. S. J. Polym. Sci, Polym. Chem. 1992, 30, 2677. (46) Boiko, Y. M.; Lyngaae-Jørgensen, J. J. Macromol. Sci., Part B: Phys. 2004, 43, 925. (47) De Gennes, P. G. Scaling Concepts in Polymer Physics: Cornell University Press: Ithaca, NY, 1979. (48) Edwards, S. F. Proc. Phys. Soc. London 1967, 92, 9. (49) Serghei, A.; Huth, H.; Schick, C.; Kremer, F. Macromolecules 2008, 41, 3636. (50) Kawaguchi, D.; Tanaka, K.; Kajiyama, T.; Takahara, A.; Tasaki, S. Macromolecules 2003, 36, 1235. (51) Sauer, B. B.; Dee, G. T. J. Colloid Interface Sci. 1992, 152, 85. (52) Jalbert, C. A. Ph.D. Dissertation, University of Connecticut, 1993. (53) Fleischer, C. A.; Morales, A. R.; Koberstein, J. T. Macromolecules 1994, 27, 379. (54) MacKnight, W. J.; McKenna, L. W.; Read, B. E.; Stein, R. S. J. Chem. Phys. 1968, 72, 1122. (55) Landry, C. J. T.; Teegarden, D. M. Macromolecules 1991, 24, 4310. (56) Appel, M.; Fleischer, G. Macromolecules 1993, 26, 5520−5525. (57) Boiko, Y. M. Colloid Polym. Sci. 2011, 289, 1847. (58) Whitlow, S. J.; Wool, R. P. Macromolecules 1991, 24, 5926. (59) McCrum, N. G.; Read, B. E.; Williams, G. Anelastic and Dielectric Effects in Polymeric Solids; Wiley: London, 1967. (60) Santangelo, P. G.; Roland, C. M. Macromolecules 1998, 31, 4581. (61) Molecular Basis of Transitions and Relaxations; Boyer, R. F., Turley, S. G., Eds.; Gordon and Breach Science Publishers: New York, 1978; p 33. (62) Pennings, J. F. M.; Bosman, B. Colloid Polym. Sci. 1979, 256, 720.

7984


Surface Dynamics of Polymer Glasses: Sub-Tg Surface

Recommend Documents