Tightly Bound PMMA on Silica Has Reduced Heat Capacities | Langmuir

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Tightly-Bound PMMA on Silica Has Reduced Heat Capacities Bal Kumari Khatiwada, and Frank D. Blum Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.9b01847 • Publication Date (Web): 13 Aug 2019 Downloaded from pubs.acs.org on August 14, 2019

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Tightly-Bound PMMA on Silica Has Reduced Heat Capacities Bal K. Khatiwada1,2 and Frank D. Blum1,* 1. Department of Chemistry, Oklahoma State University, Stillwater, OK, 74078, United States 2. Current Address: School of Arts and Sciences, Abraham Baldwin Agricultural College, Tifton, GA 31793 * Corresponding author ([email protected]) Abstract The heat capacities of very small adsorbed amounts of poly(methyl methacrylate) on high surface-area silica (Cab-O-Sil) were measured using temperature-modulated differential scanning calorimetry (TMDSC) using a quasi-isothermal method and interpreted via different models. The composition-dependent heat capacities of the adsorbed samples were measurably less than those predicted with a simple mixture model. A two-state model, comprised of tightlyand loosely-bound polymer, fit the data better with heat capacities of the tightly-bound polymer found to be 70-80% (glassy region) and 70-94% (rubbery region) of that of the bulk polymer at the same temperatures. The amount of tightly-bound polymer was estimated to be about 1.2 mg/m2 (about 1 nm thickness) in both the glassy and rubbery regions, consistent with heat flow measurements. The data sets were also extensive enough to model them with a more detailed layered gradient model, including a non-zero heat capacity for the polymer at zero adsorbed amount, which increased based on an exponential growth function to bulk polymer value of the

Khatiwada and Blum

Heat Capacities of Tightly-Bound PMMA on Silica ACS Paragon Plus Environment

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heat capacity away from the surface. More importantly, this gradient model mimicked the experimental dependence on adsorbed amounts in the tightly-bound adsorbed amount region (approximately 1 mg/m2). This model provided, for the first time, an experimental estimate of the heat capacity of the polymer adsorbed closest to the surface. The fractional heat capacity of the adsorbed polymer closest to the silica surface, relative to bulk polymer, increased with temperature from 0.3 (well below) to 0.8 (well above the bulk Tg). It was also possible to estimate the exponential growth parameter of the development from the initial heat capacities to the bulk heat capacity as 0.4 to 0.6 mg/m2, identifying a distance scale (0.3 to 0.5 nm) consistent with the notion of a transition from tightly-bound to loosely-bound polymer.

Keywords: Differential scanning calorimetry (DSC), adsorbed poly(methyl methacrylate), quasiisothermal heat capacity, glass transition temperature (Tg), tightly-bound polymer.

Introduction When two or more than two different types of materials are brought together, the properties of the resulting mixtures can be additive or be very different from the weighted sum of their properties. Additive properties imply "ideal" mixtures where neither component significantly affects the properties of the other. Mixtures of materials often result in changed properties of one or both of the components, especially when moderate to strong interactions exist, such as polar interactions, H-bonding, or ionic interactions. Such interactions are crucial in a variety of applications, especially when those applications are based on interfacial properties.1

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Many studies have been conducted with the aim of understanding the properties of polymers near a solid surface.1-5 The increased interest in solids with nanoscale dimensions is often because of the dramatic improvements in properties due to their inherent large specific surface areas. The resulting polymers near the interface, for example, will likely have properties that are different than those of bulk polymers. A number of diverse techniques have been used to probe the properties of interfacial polymers including: ellipsometry,6 x-ray reflectivity,7 back scattering,8 mechanical,9,10 solvent diffusion,11 thermal analysis,12-16 plus spectroscopic analysis of dielectric,17-20 fluorescence,21-23 infrared,24-29 NMR,30-32 and simulations.33-35 These are a smattering of the studies that have helped shed light on this important region. Of interest to many has been how the glass transition of the polymer responds to an interface. It has been found that the glass transition of the absorbed polymers could decrease, increase, or not change compared to the bulk polymer. In addition, different experiments are sensitive to different distance scales.36 Sometimes these experimental results are not definitive regarding the dynamics of polymer chains near the interface. Many experimental results have led to suggestions that for polymers with attractive interactions with a solid substrate, there are restrictions of mobility caused by the interactions at the interface. These restrictions do not affect the entire material, but are confined to a few nanometers from the surface.9 The existence of such an interfacial layer, or interphase, has been shown by many techniques.9,37-39 In some cases, the interfacial layer was reported to be more or less totally immobilized,14,38,40,41 while in others, a second or broader glass transition, or at least a shoulder at a higher temperature in calorimetric measurements, was observed.13,31-34,42-44

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Given the many experiments on adsorbed polymers, few experiments have focused primarily on the behavior of the heat capacities in these systems. Sargsyan et al.14 reported heat capacity measurements on PMMA nanocomposites with silica nanoparticles. Their results were interpreted in terms of a rigid amorphous fraction (RAF) of polymer45 (which we call tightlybound polymer, vide infra) with a thickness scale of about 2 nm from the silica surface. In this paper, we also report heat capacities of PMMA on silica; however, our measurements are from samples with much smaller adsorbed amounts of polymer than Sargsyan et al.14 Accurate modelling of an extensive data set with varying adsorbed amounts of polymer has allowed us to interpret these results in terms of adsorbed polymer mobility, i.e., a graded interphase. Based on a layered model with an exponential increase in the heat capacity of the layer with added polymer, we were able to experimentally estimate, for the first time, the heat capacities of PMMA in the tightly-bound regime (< 1.2 mg PMMA/m2 silica) and the heat capacity of the polymer closest to the silica surface.

Experimental High molecular mass PMMA with a Mw of 4.5×105 g/mol (Aldrich Chemical Co., Milwaukee, WI) was used as received. Its polydispersity index was 2.6 from gel permeation chromatography with a Dawn EOS laser light- scattering instrument (LLS) and an Optilab refractive index detector (both from Wyatt Technology, Santa Barbara, CA). The PMMA tacticity was analyzed using 1H-NMR (Varian Unity 400, Varian Instruments, Palo Alto, CA), and the fractions of triads were found to be mm: 0.10, rm: 0.36, and rr: 0.54. Cab-O-Sil M-5P (Cabot Corporation, Tuscola, IL) silica with specific surface area of 200 m2/g was dried at 100 °C for 24 h before use. Cab-O-Sil is fumed silica with fused aggregates of spherical non-porous Khatiwada and Blum


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10 nm diameter particles. M5-P has a specific surface area of 200 m2/g (verified by surface area measurements). Samples were prepared from solutions of differing amounts of PMMA (from 30 to 300 mg) dissolved in 7 ml of toluene in test tubes. Silica (Cab-O-Sil, 300 mg) was wetted with 3 ml of toluene and then added to the polymer solutions. The adsorption of the polymer was achieved by shaking the mixtures in sample tubes on a mechanical shaker for 2 d. The samples were then dried by bubbling air through the tip of a Pasteur pipette at the bottom of the tube. The air-dried samples were put under vacuum at 60 °C for 2 days to remove any residual solvent. Portions of samples from different positions in the dried materials were then collected. Samples dried in this way were found to vary in composition by less than 4% between the top, middle and lower portions for larger adsorbed amounts (for samples with more than 3 mg polymer/m2 silica) and less than 2% for smaller adsorbed amounts (less than 3 mg polymer/m2 silica). At small polymer concentrations, each polymer molecule would be expected to have some segments with direct attachment to the silica. A full "monolayer" coverage of PMMA in toluene on silica was previously determined to be on the order of 1 mg/m2.13 At higher concentrations, not all of the polymer molecules would have direct attachment to the silica. The compositions (amount of adsorbed polymer on surface) were determined using a TA Instruments (New Castle DE, USA) Model 2950 Thermogravimetric Analysis (TGA) instrument. The samples were heated from 40 – 600 °C at a heating rate of 10 °C/min. Air was used as a purge gas with flow rate of 50 mL/min. The accuracy and the validity of the method were verified with degradation of bulk PMMA, bulk silica, and PMMA/silica mixtures. After heating, the residual material contained only silica and the adsorbed amounts of polymer on silica were calculated based on the masses of PMMA and silica, and the specific surface area of the silica.

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The heat capacities of the polymer, silica, and the surface samples were measured using the quasi-isothermal temperature modulated differential scanning calorimetry (TMDSC) technique with a Q2000 DSC (TA Instruments). The samples were first annealed at 140 °C for 20 min, then cooled to 40 °C with a ramp rate of 20 °C/min to ensure that the samples had similar thermal histories. After TMDSC runs, the samples were re-weighed to determine the mass of any solvent remaining in the sample. Typically, around 0.5 to 1 % mass loss was found after annealing. Samples used for heat capacity measurements were later subjected to additional TGA analysis for accurate determination of the composition of each sample. The heat capacities were measured every 10 K with the system kept isothermal for 10 min before each heat capacity measurement. A sinusoidal modulation of amplitude 1 K with a period of 120 s was used to measure the heat capacities of all of the samples. The sample pans were referenced against an empty pan. A baseline calibration was performed through the heating of empty cells. Temperature and heat capacity calibrations were performed with indium and sapphire, respectively. Since the silica particles, including many of those with adsorbed polymers, were very light, fluffy, and did not have good thermal conductivity, their heat capacities were measured after pressing the sample into pellets in an FTIR pellet press. FTIR measurements were made on the pellets to test if compressing the samples caused any apparent deformation of the polymer on surface. The resulting FTIR spectra in the carbonyl and surface hydroxyl regions looked very similar to the measurements made with salt plates (sample was put in between two NaCl salt plates) even though there was a small amount of light scattered from the pellets. The pressure applied to make the DSC pellets (less than 70000 kPa or 10000 PSI) was much less than that normally used for making FTIR pellets (more than 350,000 kPa or 50,000 PSI).

Modeling of Heat Capacities of Interfacial Materials Khatiwada and Blum


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The heat capacity data was interpreted in terms of different models to extract the relevant properties of the adsorbed polymers. Three models outlined here are the mixture model, twostate model, and the layered gradient model. Additional information on some aspects of the modeling and a couple other models considered are given for comparison in the Supporting Information. This section also includes a more extensive data set, model summary, and glossary of terms. It is implicitly assumed in the equations that the relevant heat capacities depend on the temperature and the composition of the samples. Mixture Model. For adsorbed polymers, the heat capacities measured were a function of the amount and nature of each component. Perhaps the simplest model is a mixture model, where the heat capacity of the adsorbed sample is a simple mass-weighted superposition of the heat capacities of polymer and silica. The hypothesis in this model is effectively an assumption that polymer and silica behave independently when the polymer is adsorbed. The predicted heat capacity for the sample is given by: 𝐶"($%&'%()*+) = 𝑀" 𝐶"" + 𝑀1 𝐶"1

(1a)

where Cp implies the specific heat capacities at constant pressure in J/(g K), with CPP and CPS representing the Cp of the bulk polymer (Cpp) and silica (CPS), and M's are their mass fractions. It is reasonable to assume that the heat capacity of the silica did not vary with added polymer. This "ideal" model does not account for any effects of the silica on the polymer. Subtraction of the known contribution from the silica, for this model, yields the heat capacity of the polymer, Cp(polymer) alone or: (𝐶"($%&'%()*+) − 𝑀1 𝐶"1 ) 3𝑀 = 𝐶"" = 𝐶"('%45&+6) "

(1b)

For the mixture model, the Cp(polymer) is then the same as that of the bulk polymer, Cpp.

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Two-State Model. The adsorption of a polymer on a silica surface should result in a restriction of the mobility of some of the segments at the polymer-silica interface if an attractive interaction occurred. In this respect, adsorbed polymers can be considered to be similar to semicrystalline polymers, where the crystalline domains reduce the mobility of neighboring amorphous segments. Chen and Cebe45 applied a three-state model in which the heat capacity of a semi-crystalline polymer, just above the glass transition temperature, was given by the heat capacity of solid crystal, rigid amorphous polymer and rubbery polymer. The two-state model, with tightly-bound and loosely-bound polymer, has been used to quantify the amounts of these different components from the changes in ∆Cp in the glass transition region.13,15 These two components are used with the tightly-bound polymer having a constant reduced heat capacity compared to the bulk polymer. The loosely-bound polymer has a heat capacity similar to the bulk polymer and is taken as equal to that of the bulk polymer (CPP). It has been noted that in some systems, the glass transition of the loosely-bound polymer is shifted to a temperature slightly higher than that of the bulk polymer.34,46 Therefore, looselybound is perhaps a better descriptor than bulk-like. Since the tightly-bound polymer is associated with the silica surface, some modification to account for the surface area of the substrate should be made. An appropriate way to do this is to consider the behavior of the polymers to scale based on the adsorbed amount, A (in mg polymer/m2 surface). Given that the density of the surface polymer is the same as the bulk polymer, 1 mg/m2 corresponds to a thickness of 1 nm. In effect, there is a certain amount of adsorbed polymer, 𝑚8" (in mg polymer/m2 surface) which is significantly altered by the substrate interface, i.e., tightly bound. Its reduced heat capacity is represented as a fraction, f (a constant), of the bulk heat capacity or C'pp = f CPP. When the adsorbed amount, A, is greater than the amount of tightly-bound polymer, 𝑚8" ', (A > 𝑚8" ), the

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heat capacity of the composite is given by the sum of the contributions of the loosely-bound (bulk-like, first term) polymer, tightly-bound polymer (second term) and silica (third term), or: 𝐶"($%&'%()*+) = 𝑀" 𝐶""

" (: ; &< )

:

+ 𝑓𝑀" 𝐶""

" &<

:

+ 𝑀1 𝐶"1 (for A ≥ 𝑚8" )

(2a)

or for the polymer alone: 𝐶"('%45&+6) =

" >> (𝐶"($%&'%()*+) − 𝑀1 𝐶"1 ) 3𝑀 = 𝐶"" (: ; &< ) + 𝑓𝐶'' &< (for A ≥ 𝑚8" ) (2b) : : "

In this model, 𝑚8" and f are parameters, which can be used to fit the data. When the amount of polymer is less than the full amount of tightly-bound polymer, A ≤ 𝑚8" , equation 2a and 2b become: 𝐶"($%&'%()*+) = 𝑓𝑀" 𝐶"" + 𝑀1 𝐶"1 (for A ≤ 𝑚8" )

(3a)

or for the polymer alone: 𝐶"('%45&+6) =

(𝐶"($%&'%()*+) − 𝑀1 𝐶"1 ) 3𝑀 = 𝑓𝐶"" (for A ≤ 𝑚8" ) "

(3b)

where the Cp(polymer) is understood to be both a function of temperature and normalized per mass of polymer in the composite. Layered Gradient Model. For the adsorbed polymer, a monomorphic model for the tightlybound polymer is conceptually simple, but polymer segments closer to the silica (smaller adsorbed amounts) should behave differently than those further away from it. The layered gradient model is a layered model, where the heat capacity of the polymer, CP(polymer), transitions from an initial value of fCPP (for the smallest amount of polymer adsorbed or that closest to the silica) to the value for the bulk polymer, CPP, with a simple dependence, exponential in this case. For this model, the CP(polymer) is given by: ?

:

E>

𝐶"('%45&+6) = (:) ∫K A𝑓𝐶"" + (1 − 𝑓)𝐶"" C1 − 𝑒 ; F GH 𝑑𝐴′

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E

OO = 𝐶"" + L (? ; M) N P𝑒 ; F − 1Q :

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(4)

where CPP, the bulk value for the heat capacity of the polymer, and a describes the exponential growth scale of the transition of the polymer as its heat capacity becomes bulk-like. The fitted parameters in this model are f and a. The integral represents the superposition of different layers. At any given adsorbed amount, A, the Cp(polymer) is the superposition (integral) of the Cp's of different "layers" whose heat capacities are described by exponentially growth function approaching the bulk polymer. A distinction is to be made between the layered (integral) model and a simple exponential model for the total heat capacity. The layered (integral) model represents the superposition of layers of polymer with different heat capacities. The simple exponential fit to the heat capacity data represents one heat capacity for the whole layer at a given adsorbed amount. The layered (integral) model fitted the data somewhat better, but result in different values of fitted parameters resulting, in different implications. More information on variations of this model considered can be found in the Supporting Information. Fitting with Models. The best fits of the heat capacity data to the models were made by iteration in which the sum of the squares of residuals (differences between the models and data points) were minimized by changing the parameters using statistical analysis system (SAS) software (SAS Institute Inc., Cary, NC, USA). The uncertainties in the parameters were estimated by varying each parameter independently from the set of best-fit values until the best fit data points are increased or decreased by 1.96×S.D., which represents a 95% confidence interval. The S.D. corresponds to the standard deviation of the residuals. The uncertainties in the parameters were determined by using SAS software.

Results and Discussion

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The mass losses of polymer adsorbed from the different samples were determined using TGA measurements as shown in Figure 1. Over the temperature range studied (40 – 700 °C), all of the PMMA degraded, while silica had very little mass loss (less than 0.5%), mainly from adsorbed water. From the derivative mode curves (Fig. 1b), two-step degradation was easily observed for the bulk PMMA, at around Tmax of 280 and 320 °C, while adsorbed samples had a single-step degradation. Thermal degradation studies by McNeill47 on PMMA synthesized with different techniques has reported that polymer synthesized by free radical methods showed a two-step degradation, while only a one step transition at high temperature was observed for polymer synthesized using ionic methods. Sazanov et al. obtained similar results for PMMA synthesized by ionic techniques.48 Tacticity also plays a role in the degradation of PMMA.49 The lower temperature degradation in the two-step degradation is believed to be due to the presence of weak linkages. For example, a head-to-head linkage between the free radicals or a double bond at the end of the chain from disproportionation is the cause for the first major degradation in this polymer.47,50

1.1

a)

100

Silica 0.59 0.90 1.12 2.34 3.02 3.96 4.48 5.66 Bulk

80 60 40 20 0 0

100 200 300 400 500 600 700 Temperature (°C)

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Derivative Mass Loss (%/ °C)

120

Mass (%)

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b)

Bulk PMMA 3.02 2.34 1.12 0.90 0.59 Bulk Silica

0.9 0.7 0.5 0.3 0.1 -0.1 0

200

400

600

800

Temperature ( °C)


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Figure 1. Mass losses of silica, PMMA on silica, and PMMA as a function of temperature and the adsorbed amount of polymer plotted in a) mass-loss mode and b) derivative mode. The curves are in the order as shown in the legends and the adsorbed amounts are in mg/m2.

The major degradation for adsorbed samples occurred at higher temperatures, from around 360 to 400 °C with the highest temperatures for the polymers with the smallest adsorbed amounts. It has been shown that adsorbed PMMA degrades at higher temperatures than bulk PMMA.51 Madathingal and Wunder52 showed that particle structure and silanol density play roles in the degradation of adsorbed PMMA. Clearly, the H-bonding of polymers with surface silanols causes much of this increase. Isotactic and syndiotactic PMMA on silica also exhibited degradation temperatures dependent on the amount of adsorbed polymer; larger adsorbed amounts had lower Tmax than bulk for both polymer types.49 While smaller adsorbed amounts had Tmaxs similar to bulk for syndiotactic PMMA, the isotactic polymer had rather complex thermal degradation. This difference is likely due differences in the stereo-regularity of the PMMAs used, and hence, the different pathways for degradation. The specific heat capacities for the bulk polymer, silica, and adsorbed samples (represented by symbols) are shown in Figure 2. In the figure, only some of the measurements made are shown for the sake of clarity. These measurements, where they overlapped, were in good agreement with those reported by Sargsyan et al.14 However, it should be noted that the smallest polymer amount reported by Sargsyan was 27%, which for their particles, equates to an adsorbed amount of 3.3 mg/m2.53 Therefore, their sample with the smallest amount of polymer corresponds to our sample with 3.43 mg/m2. From this figure, it is obvious that our samples were prepared in a regime with much smaller adsorbed amounts than their samples.

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Due to the larger heat capacity of PMMA compared to silica, the curves for the adsorbed samples had larger heat capacities with added polymer. For the sample with the smallest amount of adsorbed polymer, 0.60 mg/m2, the heat capacity increased with an increase in temperature with only a very small jump in heat capacity and the slope of the curve changed just above the bulk Tg, suggesting a very broad and weak glass transition. This behavior is in contrast to that of samples with more adsorbed polymer. With increased adsorbed amount of polymer (greater than 1.49 mg/m2), more bulk-like glass transition behavior was observed with an intensity increasing with additional adsorbed polymer. 2.3 Specific Heat Capacity (J/g °C)

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Bulk 5.66 3.96 3.43 2.57 2.56 1.49 1.30 0.90 0.60 Silica

2.1 1.9 1.7 1.5 1.3 1.1 0.9 0.7 0.5 40

60

80

100

120

140

160

180

200

220

240

Temperature (°C) Figure 2. Specific heat capacities of bulk PMMA, silica, and composites as a function of temperature. The curves drawn are to aid the eye and are in the order given in the legend and the adsorbed amounts given in mg/m2.

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In order to understand the behavior of the heat capacities at these small adsorbed amounts, it was instructive to observe the measurements at different temperatures as a function of the mass fraction of polymer. Shown in Figure 3 is one example of the CP's in the PMMA/silica system at 120 °C. This figure shows several general features seen at other temperatures. The dependence of the heat capacity is roughly linear with temperature and the changes in the heat capacities of the two bulk components and their sum, the mixture model, are also shown. It is clear from the figure that the main variation was due to changing the relative amount (mass fraction) of silica (smaller heat capacity) for PMMA (larger heat capacity). The mixture model captures the nature of the variation with composition, but it clearly overestimates the heat capacity of the composite material. This difference occurred because the heat capacity of the adsorbed polymer is less than that of the bulk polymer. 1.8 Specific Heat Capacity (J/g °C)

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120 °C

1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0

0.1 0.2 0.3 0.4 0.5 Mass Fraction of Polymer

0.6

Figure 3. An example of the heat capacity variation of PMMA/silica at 120 °C as a function of the mass fraction of polymer. The figure also shows the prediction from the simple mixture model (top, blue dot-dashed line) and is shown along with the mixture model contributions

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expected from the silica (solid green line, decreasing with mass fraction of polymer) and polymer (dotted brown line, increasing with mass fraction of polymer).

Given that the changes in heat capacities of the adsorbed samples were dominated by the changes in composition and that the heat capacity of the silica was unlikely to change with composition, it is instructive to examine the heat capacity of the adsorbed polymer alone. This can be accomplished by subtracting the contribution of the silica. The heat capacities of the polymer alone, thus calculated, were fitted with three different models to clarify the behavior of adsorbed polymer on the surface, as shown in Figure 4. It was also most useful to plot the behavior as a function of the adsorbed amount of polymer at a given temperature. The mixture model contribution for the polymer was simply the heat capacity of the bulk polymer, which overestimates the CP for the adsorbed polymer. Assuming that the polymer did not affect the heat capacity of the silica, the adsorption of polymer resulted in reduced polymer heat capacity. The two-state model (equation 3), in which the adsorbed polymer was divided into two types, tightlyand loosely-bound polymer, fit the experimental data well except at very small adsorbed amounts where the model had a constant prediction since all of the polymer would be tightly-bound polymer below adsorbed amounts of 𝑚8" . The layered gradient model (Equation 4) fit the data very well in the whole range. The layered gradient model fit the data statistically better than the two-state model, but more importantly, it had the proper shape at very small adsorbed amounts. This distinction was not possible to observe in the work of Sargsyan et al.14 because their measurements were made at much larger adsorbed amounts.

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1.6 Specific Heat Capacity (J/g °C)

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40 °C

1.4 1.2 1.0 Mixture model

0.8

Two-state model

0.6

Gradient model

0.4 0.2 0.0 0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

Adsorbed Amount (mg/m2) Figure 4. Specific heat capacities of the adsorbed polymer alone (calculated by subtracting the specific heat capacity of the silica from composite specific heat capacity) adsorbed on surface at different adsorbed amounts (in mg PMMA/m2 of silica surface) showing the prediction from the mixture, two-state, and layered gradient models at 40 ° C.

The fitting of the heat capacities for the adsorbed polymer alone on the surface with the mixture model, two-state model, and layered gradient model in three different regions; below, around, and above the bulk Tg are shown in Figure 5. The fittings at other temperatures are provided in the Supporting Information. The curves at different temperatures have similar shapes, although the dip in the heat capacity data at small adsorbed amounts is less pronounced as the temperature is increased. The adsorbed polymer is less affected by the interaction with the surface at higher temperatures.

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From the fitting of the heat capacity data with the two-state model, it was observed that the amount of tightly-bound polymer varied with temperature as shown in Figure 6a. Well above and well below the bulk Tg, the amount of tightly-bound polymer was found to be around 1.20 mg/m2. The variation of the fractional heat capacities of the initial polymer on the surface, f, obtained from intercepts, range from 0.7 to just above 0.9 at the higher temperatures. Thus, well above Tg , the heat capacities of the tightly bound polymer approach those of the bulk polymer at

2.5

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Figure 5. Heat capacities of adsorbed polymer alone at different adsorbed amounts showing the predictions from two-state model (red dash) and layered gradient model (black curve) for a) 50 °C, below; b) 120 °C, near; and c) 200 °C, above the bulk Tg. The blue dot-dashed line on the top represents the heat capacity of bulk polymer at the temperatures noted. Full data sets are shown in the Supporting Information.

The parameters from the fits to the layered gradient model are shown in Figure 6b. The values for the exponential growth parameter (a) as a function of temperature increased slightly with increasing temperature well above and below the glass transition. These values were in the range of 0.4 to 0.8 mg/m2. This parameter is the exponential growth parameter for the heat capacity of a given layer approaching bulk-like behavior. The fractional heat capacity from the layered gradient model increased with temperature from around 0.3 well below Tg(bulk) to 0.8 well above Tg(bulk). It was slightly decreasing around Tg(bulk) (vide infra).

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Temperature (°C)

Figure 6. Plots for a) tightly-bound amount, 𝑚8" , and its fractional heat capacity, f, for the twostate model, and b) the exponential growth parameter, a, and intercept, f, for layered gradient

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model at different temperatures. The gray areas represent the region where the models are unreliable due to changes of the behavior around the Tg for bulk-like polymer (see text.)

The behavior of the heat capacities in the vicinity of the glass transitions, especially around Tg(bulk) are difficult to interpret in terms of the models because they are fitted relative to the heat capacity of the bulk polymer (Cpp). For example, the Cpp changes dramatically near the Tg(bulk) while there is no step change (until higher temperatures) for the polymers at small adsorbed amounts. For this reason, the gray areas of Figure 6 were drawn and the values of the parameters from this region not deemed particularly useful. The fits well above and below the Tg(bulk) were quite useful. The focus of this work is on determining the heat capacity of tightly-bound polymer. This term is consistent with the literature originating with filled rubbers (bound rubber) and its properties reviewed by Blow,54 then refined to tightly-bound rubber.55 Others have used the term rigid amorphous fraction (RAF), to describe the region of no or limited mobility in semicrystalline polymers45,56 or silica nano-composites.14 We prefer the former term as it implies limited mobility consistent with some binding, but not complete polymer rigidity and a thermal signature. Previous studies on adsorbed polymers on surfaces have reported that the Tg was increased when there was an attractive interaction between polymer and surface.12,13,23,29,33,34 It has previously been reported that two different, but overlapping, transitions were observed in the MDSC thermograms for adsorbed PMMA on silica. These transitions correspond to loosely- and tightly-bound polymer, with Tg's similar to and higher than that of the bulk polymer,

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respectively.13,15 Similar glass transition behavior for the adsorbed polymer was confirmed using other techniques.12,14,23,29,57,58 For very small amounts of adsorbed PMMA (about 1.1 mg/m2), no loosely-bound polymer was found, with the tightly-bound PMMA having a Tg centered around 45° higher than bulk, allowing the amounts of tightly-bound polymer to be estimated.13,15,34 The two-state model, where polymer segments close to the surface are tightly-bound, and those far from the surface are loosely-bound is depicted in Figure 7. This kind of heterogeneous behavior is expected when there is an attractive interaction such as H-bonding or ionic interactions between the polymer and the surface. The presence of segmental heterogeneity in adsorbed polymers has been demonstrated using deuterium NMR studies of adsorbed poly(vinyl acetate)31 and poly(methyl acrylate) on silica surfaces.32,59-62 These studies revealed a motional gradient in the adsorbed polymer. Molecular dynamics simulation studies also revealed the presence of segmental heterogeneity when the polymer was adsorbed on surface.33,34,63

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Figure 7. Schematic representation of adsorbed PMMA on Cab-O-Sil silica showing the two components of the two-state model (left) comprised of loosely-bound (red), and tightly-bound (blue) polymer segments. Also shown is the layered gradient model (right) comprised of continuously changing segments in terms of mobility from tightly-bound (blue) to loosely-bound (red) segments.

The use of the two-state model allows comparison with a number of other studies where data is insufficient to model the interfacial polymer with a more detailed model. Interestingly, for PMMA on silica, the two-state model results showed that the amount of tightly-bound polymer to be fairly constant well below and above the bulk Tg. In these two ranges, the average amounts of tightly-bound polymer (𝑚8" ) were found to be 1.17 ± 0.04 (1 S.D.) mg/m2 and 1.21 ± 0.05 (1 S.D.) mg/m2, respectively. These values, shown in Table 1, were only slightly lower (around 9%, but within experimental error) of previous measurements from heat-flow curves, using a less sensitive instrument,13 and similar to the measurements done by Khatiwada et al.15 The amount of tightly-bound polymer, based on a bulk density of 1.2 g/cm3, corresponds to a polymer thickness of 1 nm, if the polymer layer was flat and uniform. Again, around the bulk glass transition, the amount of tightly-bound polymer was artificially large as mentioned above. As the temperature increased well above the bulk Tg, more segments became rubbery leaving only small amounts of motionally restricted polymer on surface.

Table 1. Tightly bound amounts (𝑚8" ) and exponential parameter (a) from the two-state model and layered gradient model below, around, and above the Tg(bulk), respectively, from heat capacity data. The uncertainties are from the standard deviation and represent the 95%

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confidence interval. The values of f from the layered gradient model are not shown because they increase with temperature, so the reader is referred to Figure 6. Parameter (model) " 𝑚8 (mg/m2) (two-state)

Belowa (40 -90 °C) 1.17 +/- 0.08

Abovea (150 -200 °C) 1.21 +/- 0.10

Reference

1.30 +/- 0.34b

Blum et al.13

1.21 + /- 0.42c

Khatiwada et al.15

This work

a (mg/m2) 0.55 +/- 0.22 0.56 +/- 0.11 This work (gradient) a relative to Tg(bulk) b,c from heat flow curves obtained from TMDSC measurements.

The heat capacities of tightly-bound polymer from the two-state model, were estimated to be around 70 – 80% of those of the bulk polymer at, below, and through the bulk Tg. The reduction in heat capacity of tightly-bound polymer was due to the reduction in mobility of the polymer adsorbed on surface. Previously, NMR studies on similar systems such as poly(methyl acrylate) and poly(vinyl acetate) also reported the presence of heterogeneous mobility of polymer segments at the interface.57,60,62 Studies on glass transition behavior of adsorbed polymers on surfaces have reported that polymers that were tightly-bound on a surface showed weaker than bulk glass transition behavior at higher temperatures.12,13,29 The estimation of the step change in heat capacity (ΔCP) for tightly-bound polymer also reported the reduction of heat capacity when polymer was bound on the surface.13 The heat capacity of tightly-bound polymer increased with increased temperature, approaching the bulk value well above the Tg(bulk). This result suggests that tightly-bound polymer relaxes more slowly than bulk over a wide temperature range and only approaches bulk-like behavior well above bulk Tg, which is before it undergoes degradation. Studies on devitrification (relaxation) of rigid amorphous fraction (RAF) in semi-crystalline

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materials also suggested that RAF relaxes step-by-step before the melting temperature of the crystal is reached.45,64 In this context, crystals could be considered similar to surfaces in semicrystalline material. The TMDSC measurements on adsorbed polymers also suggested that the tightly-bound polymer relaxes at higher temperature;12,13 however, some studies on adsorbed polymers on surface systems have reported that the tightly-bound (RAF) polymer does not relax before the degradation temperature is reached.14 This work demonstrates that polymers are more complicated than two layers with different heat capacities. Immobilizing one part of the polymer chain through H-bonding at the interface affects the mobility of neighboring segments and so on. Randomly adsorbed polymers tend to have coiled configurations on surfaces.36,65 Computer simulation studies of adsorbed polymers on surfaces have suggested that the polymers retain more random coil configurations when adsorbed from theta or poor solvents.66 However, this phenomenon is highly dependent on polymer surface interaction parameter, the density of the polymer adsorbed and molecular mass. The effect of immobilization decreases as the polymer segments are further away from the surface and eventually attain bulk-like mobility where there is a fairly negligible effect of the surface on the polymer segments. Hence, the heat capacity of the polymer (adsorbed on surface) can be better described with the application of a model in which the heat capacity increases with distance from the surface. The data in Figure 4 for 40 °C (and the other temperatures as well) have heat capacities that show a gradient in Cp(polymer) with adsorbed amount with the shape of an exponential growth function. A gradient model could be formulated in a variety of ways. The heat capacity data as a function of adsorbed amount could be modeled with a simple exponential growth function or the integral of that function, i.e., a layered model. The intercept could be non-zero or zero. All of

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these variations can fit the data and additional information on the fits are given in the Supporting Information. We have chosen to use the layered gradient model based on the exponential growth of the heat capacity (integral layered model) with a non-zero intercept. The non-zero intercept is consistent with an isolated polymer on the surface having some non-zero heat capacity, found by extrapolation. The integral gradient model is built on the layers of fixed heat capacity added together. The concept that a given layer has a fixed heat capacity at a given distance from the surface has merit, especially in the range of tightly-bound polymer. For example, in the MDSC traces of adsorbed PMMA,15 the higher temperature transitions for the tightly-bound polymer are somewhat distinct, can be followed, and are evident in the samples with larger adsorbed amounts. The tightly-bound polymer is tightly bound to the surface; plasticizer could not penetrate tightly-bound PVAc67 and so it seems unlikely added polymer will change the properties of this material. In addition, the fitted parameters seem reasonable. Thus, there is some good support for the layered model. From the heat capacity data interpreted with the layered gradient model at different temperatures, it was observed that the fractional heat capacity of the polymer closest to the surface was much smaller than that of the bulk polymer at all temperatures, as shown in Figure 6b. The reduction in heat capacity was due to the reduction in mobility of polymer chains that are bound to the surface, as mentioned above. The exponential growth parameter a, which indicated the rate of increase in the heat capacity of adsorbed polymer towards its bulk value, was smaller on either side of the Tg(bulk), as shown in Figure 6b. Values of a = 0.4 to 0.5 mg/m2 correspond to 1.2 to 1.5 mg/m2 (or around 1 nm) for obtaining 95% of the bulk heat capacity. This estimate is consistent with that from heat flow curves (1.2 mg/m2) of CP data.

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In the present study, the usefulness of heat capacity measurements to probe the behavior of PMMA adsorbed on silica has been demonstrated. TGA and MDSC techniques showed the presence of tightly-bound polymer at the polymer-silica interface. The heat capacity of bound polymer was found to be smaller than that of the bulk polymer. The mixture model clearly showed that much of the CP variation of the whole sample with composition was due to the simple change in composition, but the interaction of the polymer with the silica was not "ideal" in terms of a mixture. The two-state model was used to estimate the amount of tightly-bound polymer and its heat capacity on surface. This model, which divided the polymer material into two layers, was a modest oversimplification; the bound polymer segments reduce the mobility of polymer segments next to them. Nevertheless, this model provided an estimate of the amount of tightly bound polymer, in this case about 1.2 mg/m2 (roughly a 1 nm thickness), which was similar to that estimated from heat flow curves.13,15 This model and estimate can be quite useful when limited and less detailed measurements are available or made. A more realistic model, especially at smaller adsorbed amounts, referred to as the layered gradient model, was used to probe the heat capacity of polymer alone on the surface. It was a layered model with the heart capacity of each layer given by an exponential growth function. Interpretation of the data with this model provides two significant parameters with new insight. The fractional heat capacity, f, of the polymer initially bound to the surface was estimated to have a heat capacity from 0.3 to 0.8 of that of the bulk polymer (away from the bulk Tg), increasing monotonically with temperature. We believe that this is the first time that this value has been experimentally determined. The heat capacity of the polymer that is bound on the surface was shown to transition to the bulk heat capacity with additional adsorbed polymer. For temperatures above and below the bulk Tg, the heat capacity increases exponentially with a

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distance parameter, a, of 0.4 to 0.5 mg/m2 (corresponding to about 0.3 to 0. 4 nm thickness) providing a first estimate of distance scale for the effect of the surface. Interestingly, three times the distance parameter, a, is about 0.9 to 1.2 mg/m2 (about 1 nm), was the same as the amount of tightly bound polymer found for PMMA on silica from other experiments.

Acknowledgements. The authors acknowledge the financial support of the National Science Foundation (USA) under Grant No. DMR-1005606 and the Oklahoma State University. ORCID Frank D. Blum: 0000-0002-7884-3134 Bal K. Khatiwada: 0000-0001-6335-4787

Supporting Information. More details on the modeling used and a glossary of symbols used. All of the data plots at the different temperatures studied.

References and Notes (1) Alcoutlabi, M.; McKenna, G. B. Effects of Confinement on Material Behaviour at the Nanometre Size Scale. J. Phys.: Condens. Matter 2005, 17, R461-R524. (2) Paul, D. R.; Robeson, L. M. Polymer Nanotechnology: Nanocomposites. Polymer 2008, 49, 3187-3204. (3) Winey, K. I.; Vaia, R. A. Polymer Nanocomposites. MRS Bull. 2007, 32, 314-319. (4) Moniruzzaman, M.; Winey, K. I. Polymer Nanocomposites Containing Carbon Nanotubes. Macromolecules 2006, 39, 5194-5205. (5) Song, Y. H.; Zheng, Q. Concepts and Conflicts in Nanoparticles Reinforcement to Polymers Beyond Hydrodynamics. Prog Mater Sci 2016, 84, 1-58.

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(27) Kulkeratiyut, S.; Kulkeratiyut, S.; Blum, F. D. Bound Carbonyls in Pmma Adsorbed on Silica Using Transmission Ftir. J. Polym. Sci. A.; Polym. Phys. 2006, 44, 2071-2078. (28) Krisanangkura, P.; Packard, A. M.; Burgher, J.; Blum, F. D. Bound Fractions of Methacrylate Polymers Adsorbed on Silica Using Ftir. J. Polym. Sci. A.; Polym. Phys. 2010, 48, 1911-1918. (29) Madathingal, R. R.; Wunder, S. L. Effect of Particle Structure and Surface Chemistry on Pmma Adsorption to Silica Nanoparticles. Langmuir 2010, 26, 5077-5087. (30) McBrierty, V.; Packer, K., Nuclear Magnetic Resonance in Solid Polymers. Cambridge University Press: Cambridge, 1993. (31) Blum, F. D.; Xu, G.; Liang, M.; Wade, C. G. Dynamics of Poly(Vinyl Acetate) in Bulk and on Silica. Macromolecules 1996, 29, 8740-8745. (32) Lin, W.-Y.; Blum, F. D. Segmental Dynamics of Bulk and Adsorbed Poly(Methyl Acrylate)-D3 by Deuterium Nmr: Effect of Adsorbed Amount. Macromolecules 1997, 30, 5331-5338. (33) Mortazavian, H.; Fennell, C. J.; Blum, F. D. Structure of the Interfacial Region in Adsorbed Poly(Vinyl Acetate) on Silica. Macromolecules 2016, 49, 298-307. (34) Mortazavian, H.; Fennell, C. J.; Blum, F. D. Surface Bonding Is Stronger for Poly(Methyl Methacrylate) Than for Poly(Vinyl Acetate). Macromolecules 2016, 49, 4211-4219. (35) Merling, W. L.; Mileski, J. B.; Douglas, J. F.; Simmons, D. S. The Glass Transition of a Single Macromolecule. Macromolecules 2016, 49, 7597-7604. (36) Fleer, G. J.; Cohen-Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B., Polymers at Interfaces. Chapman & Hall: London, 1993. (37) Kirst, K. U.; Kremer, F.; Litvinov, V. M. Broad-Band Dielectric-Spectroscopy on the Molecular-Dynamics of Bulk and Adsorbed Poly(Dimethylsiloxane). Macromolecules 1993, 26, 975-980. (38) Miwa, Y.; Drews, A. R.; Schlick, S. Detection of the Direct Effect of Clay on Polymer Dynamics: The Case of Spin-Labeled Poly(Methyl Acrylate)/Clay Nanocomposites Studied by Esr, Xrd, and Dsc. Macromolecules 2006, 39, 3304-3311. (39) Mammeri, F.; Rozes, L.; Le Bourhis, E.; Sanchez, C. Elaboration and Mechanical Characterization of Nanocomposites Thin Films - Part Ii. Correlation between Structure and Mechanical Properties of Sio2Pmma Hybrid Materials. J. Europ. Ceram. Soc. 2006, 26, 267-272. (40) Lee, D. C.; Jang, L. W. Preparation and Characterization of Pmma-Clay Hybrid Composite by Emulsion Polymerization. J. Appl. Polym. Sci. 1996, 61, 1117-1122. (41) Vieweg, S.; Unger, R.; Hempel, E.; Donth, E. Kinetic Structure of Glass Transition in Polymer Interfaces between Filler and Sbr Matrix. J. Non-Crystal. Solids 1998, 235, 470-475. (42) Tsagaropoulos, G.; Eisenberg, A. Dynamic-Mechanical Study of the Factors Affecting the 2 GlassTransition Behavior of Filled Polymers - Similarities and Differences with Random Ionomers. Macromolecules 1995, 28, 6067-6077. (43) Fryer, D. S.; Peters, R. D.; Kim, E. J.; Tomaszewski, J. E.; de Pablo, J. J.; Nealey, P. F.; White, C. C.; Wu, W. L. Dependence of the Glass Transition Temperature of Polymer Films on Interfacial Energy and Thickness. Macromolecules 2001, 34, 5627-5634. (44) Hartmann, L.; Gorbatschow, W.; Hauwede, J.; Kremer, F. Molecular Dynamics in Thin Films of Isotactic Poly(Methyl Methacrylate). Eur. Phys. J. E 2002, 8, 145-154. (45) Chen, H. P.; Cebe, P. Vitrification and Devitrification of Rigid Amorphous Fraction of Pet During QuasiIsothermal Cooling and Heating. Macromolecules 2009, 42, 288-292. (46) Kabomo, M. T.; Blum, F. D.; Kulkeratiyut, S.; Kulkeratiyut, S.; Krisanangkura, P. Effects of Molecular Mass and Surface Treatment on Adsorbed Poly(Methyl Methacrylate) on Silica. J. Polym. Sci. A.; Polym. Phys. 2008, 46, 649-658. (47) McNeill, I. C. A Study of the Thermal Degradation of Methyl Methacrylate Polymers and Copolymers by Thermal Volatilization Analysis. Eur. Polym. J. 1968, 4, 21-30.

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(48) Sazanov, Y. N.; Skvortsewich, E. P.; Milovskaya, E. B. Thermal Decomposition of Polymethylmethacrylate Synthesized with Anionic Catalysts. J. Therm. Anal. Calorim. 1974, 6, 53-58. (49) Zhang, B.; Blum, F. D. Thermogravimetric Study of Ultrathin Pmma Films on Silica: Effect of Tacticity. Thermochim Acta 2003, 396, 211-217. (50) Grassie, N.; Farish, E. The Thermal Degradation of Copolymers of Styrene and Methyl Methacrylate. Europ. Polym. J. 1967, 3, 305-315. (51) Aruchamy, A.; Blackmore, K. A.; Zelinski, B. J. J.; Uhlmann, D. R.; Booth, C. A Study of the Thermolysis Behavior of Pmma in Polymer/Silica-Lead(Ii) Oxide-Boron Oxide Glass Powder Mixtures. Mater. Res. Soc. Symp. Proc. 1992, 249, 353-361. (52) Madathingal, R. R.; Wunder, S. L. Thermal Degradation of Poly(Methyl Methacrylate) on Sio2 Nanoparticles as a Function of Sio2 Size and Silanol Density. Thermochim Acta 2011, 526, 83-89. (53) Note: This Calculation Is Based on Their Reported Particles Averaging a Dimeter of 10 Nm with Silica Pmma Densities of 2.65 and 1.18, Respectively. (54) Blow, C. M. Polymer-Particulate Filler Interaction - Bound Rubber Phenomena. Polymer 1973, 14, 309323. (55) Kenny, J. C.; McBrierty, V. J.; Rigbi, Z.; Douglass, D. C. Carbon Black Filled Natural Rubber. 1. Structural Investigations Macromolecules 1991, 24, 436-443. (56) Wunderlich, B. Reversible Crystallization and the Rigid-Amorphous Phase in Semicrystalline Macromolecules. Prog. Polym. Sci. 2003, 28, 383-450. (57) Blum, F. D.; Krisanangkura, P. Comparison of Differential Scanning Calorimetry, Ftir, and Nmr to Measurements of Adsorbed Polymers. Thermochim. Acta 2009, 492, 55-60. (58) Harton, S. E.; Kumar, S. K.; Yang, H.; Koga, T.; Hicks, K.; Lee, H.; Mijovic, J.; Liu, M.; Vallery, R. S.; Gidley, D. W. Immobilized Polymer Layers on Spherical Nanoparticles. Macromolecules 2010, 43, 3415-3421. (59) Lin, W.-Y.; Blum, F. D. Segmental Dynamics of Bulk and Silica-Adsorbed Poly(Methyl Acrylate)-D3 by Deuterium Nmr: The Effect of Molecular Weight. Macromolecules 1998, 31, 4135-4142. (60) Metin, B.; Blum, F. D. Segmental Dynamics in Poly(Methyl Acrylate) on Silica: Molecular-Mass Effects. J. Chem. Phys. 2006, 125, 054707. (61) Lin, W.-Y.; Blum, F. D. Segmental Dynamics of Interfacial Poly(Methyl Acrylate)-D3 in Composites by Deuterium Nmr Spectroscopy. J. Am. Chem. Soc. 2001, 123, 2032-2037. (62) Metin, B.; Blum, F. D. Segmental Dynamics in Poly(Methyl Acrylate) on Silica: Effect of Surface Treatment. Langmuir 2010, 26, 5226-5231. (63) Smith, G. D.; Bedrov, D.; Borodin, O. Structural Relaxation and Dynamic Heterogeneity in a Polymer Melt at Attractive Surfaces. Phys. Rev. Lett. 2003, 90, 226103. (64) Huo, P. T.; Cebe, P. Temperature-Dependent Relaxation of the Crystal Amorphous Interphase in Poly(Ether Ether Ketone). Macromolecules 1992, 25, 902-909. (65) Hiemenz, P. C., Polymer Chemistry, the Basic Concepts. Marcel Dekker, Inc.: Madison Avenue, New York, 1984. (66) Chremos, A.; Glynos, E.; Koutsos, V.; Camp, P. J. Adsorption and Self-Assembly of Linear Polymers on Surfaces: A Computer Simulation Study. Soft Matter 2009, 5, 637-645. (67) Hetayothin, B.; Cabaniss, R. A.; Blum, F. D. Does Plasticizer Penetrate Tightly Bound Polymer in Adsorbed Poly(Vinyl Acetate) on Silica? Macromolecules 2017, 50, 2092-2102.

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Tightly Bound PMMA on Silica Has Reduced Heat Capacities | Langmuir

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