Degradation of Polymer Films on Surfaces: A Model Study with Poly(sebacic anhydride)

Abstract

There is compelling evidence that the degradation kinetics of thin polymer films differ significantly from those of bulk materials, as interfacial effects become dominant. Therefore, it is crucial to investigate these kinetics separately. Qualitative analytics of thin film degradation exist, e.g. by scanning electron microscopy or atomic force microscopy (AFM), but a quantitative study is so far missing. In this work, poly(sebacic anhydride) (PSA), an aliphatic polyanhydride, is used as a model system for a quantitative degradation study. PSA was spin-coated onto silicon or gold substrates. The degradation of these PSA films was monitored by ellipsometry, surface-plasmon resonance spectroscopy (SPR), and Fourier transform infrared spectroscopy (FTIR). Two kinetic regimes were observed when plotting the relative layer thickness determined by FTIR and SPR against the degradation time. The data obtained by FTIR showed a single process for the rate of ester bond cleavage. Overall, the degradation rate constants of PSA determined by the different methods were consistent. The degradation rate constants of PSA film up to 378 nm thickness were constant. Several thicker free-standing samples studied gravimetrically had a degradation rate constant that was one order of magnitude slower, thus confirming thickness-dependent degradation rate constants.

1. Introduction

Degradable polymers have gained much attention in the biomedical field in the past decades, particularly as drug delivery systems, scaffolds for tissue regeneration, and resorbable implants.^[1] Polyesters and polyanhydrides are two important classes of degradable polymers that decompose by hydrolysis.^[2] In the medical field, the FDA-approved copolyesters of lactic acid and glycolic acid (PLGA) are used, e.g. for degradable sutures,^[3] and copolyanhydrides of 1,3-bis(p-carboxyphenoxy)propane and sebacic acid (P(CPP-SA)) are applied as delivery system for the antitumor drug carmustine (bis-chloroethylnitroso urea, Gliadel^® Wafers).^[4] The processing, physiochemical and mechanical properties, degradation and drug release kinetics, and the biocompatibility of both polyesters and polyanhydrides have been intensively studied.^[5] When considering the 'degradation' of these materials, i.e. their molecular and structural breakdown, two processes need to be distinguished. One is polymer chain degradation, i.e. the cleavage of covalent polymer main chain bonds (typically by hydrolysis). This causes a molar mass reduction of the polymer.^[6] Second, polymer erosion, i.e. mass loss of the macroscopic material, is observed.^[6–7] In solution, the kinetics of polymer chain degradation can be studied quite easily, e.g. by HPLC or UV-VIS spectrometry, as it is the only degradation process present. In polymeric bulk materials, chemical bond degradation and material erosion are interrelated and often do not occur homogeneously throughout the sample volume, which makes these processes multifactorial, and their analytics complicated.^[7]

When looking more closely at erosion, it is found that polymers erode either throughout the material volume (bulk erosion), or only at the interface of the material with the surrounding medium (surface erosion).^[7–8] Polymers that degrade via surface erosion decrease in their dimensions during the process;^[8] in bulk erosion, samples maintain their geometry but become more porous throughout the sample volume until they final break down mechanically.^[8–9] Which kind of erosion prevails depends on the relative rate of water diffusion through the material compared to the rate of backbone hydrolysis.^[8] The main factors affecting these rates are the polymer hydrophobicity, crystallinity, and molecular weight.^[9b] For example, PLGA undergoes bulk erosion, which means that water diffusion through the whole sample volume is fast compared to the hydrolysis rate of the ester linkages.^[5c] P(CPP-SA) on the other hand undergoes surface erosion, meaning that the hydrolysis of the anhydride groups at the polymer-water interface is fast compared to water molecules diffusion through the material.^[7]

Polyanhydride degradation under simulated physiological conditions has been studied in some detail. In most cases, for example for poly(sebacic anhydride) (PSA), surface erosion was observed.^[10] Depending on the exact structure of the polyanhydride studied, different degradation/erosion kinetics were observed. P(CPP-SA)^[7] and poly(1,6-bis-(p-carboxyphenoxy hexane)-co-(sebacic anhydride) (disk-shaped samples with 8 mm radius and 1 mm thickness)^[11] showed a linear mass loss profile indicating a zeroth-order degradation/erosion kinetics. On the other hand, the copolymer poly(ethylene glycol-b-sebacic anhydride) degraded with first-order kinetics.^[12] Unusually, an amphiphilic crosslinked polyanhydride-based hydrogel (disk-shaped samples with 5 mm radius and 2 mm thickness) degraded by bulk erosion,^[13] probably because its high hydrophilicity enabled faster water diffusion. In many of these studies, the degradation products of the macroscopic samples were tracked by HPLC,^[14] the sample mass loss was monitored gravimetrically,^{[11, 15]} and the decrease of polymer molecular mass was measured by gel permeation chromatography (GPC).^[16] The sample types used in these studies were macroscopic polymer slabs (molded or compressed polymer disks or cylinders), or microspheres with a diameter of 25 μm.^[17]

The parameter that quantifies whether a material preferentially undergoes surface erosion or bulk erosion is the critical length (L_critical).^{[7] [9b]} It can be obtained experimentally by monitoring the erosion front movement and the sample weight loss, or modelled by Monte Carlo techniques.^{[7, 9a, 16a]} The mere existence of such a length-dependent parameter already is an indication that sample dimensions will have a profound effect on the degradation kinetics and mechanism. For samples in which all three dimensions are larger than L_critical of the given polymer, predominantly surface erosion takes place. For samples where one dimension is small compared to L_critical, bulk erosion dominates. For the class of polyanhydrides, L_critical was estimated ≈ 75 μm (based on literature data for the degradation rate of the anhydride bonds and diffusion theory); in practice this value depends on the exact repeat unit composition,^[18] the nature of the polymer end groups,^[19] and other effects.^[8] Thus, L_critical gives an impression how susceptible a polymer is against hydrolysis and provides a point of orientation where to expect the transition range of bulk to surface erosion.

In the context of polymer films made from degradable polymers, it is clear that one sample dimension, i.e. the film thickness, is significantly smaller than the other two. This aspect may drastically change the degradation kinetics and mechanism of the film compared to macroscopic samples. Thus, for films made from polyanhydrides, if the film thickness is lower than the 75 μm assumed as L_critical, it is no longer safe to assume that the material degrades via surface erosion only. Also, because of the very different surface to volume ratio of thin films compared to macroscopic samples, interfacial or transport effects have an additional influence on the degradation and erosion kinetics. This is already hinted at in the literature.^[20] Therefore, to get a general idea how much the degradation rates of macroscopic polymer samples and polymer films differ, it is necessary to study the erosion and degradation process in both sample types.

So far, there is only a very limited amount literature on polymer film degradation, and virtually none on thinner films. For example, solution cast or melt-crystallized PSA films were studied by in-situ atomic force microscopy (AFM) under alkaline conditions.^[21] The degradation process was monitored by following changes of the film morphology and the sample volume using AFM,^[21b] and by simultaneous AFM-surface plasmon resonance spectroscopy measurements.^[22] By these methods, the relative erosion rates of different materials could be compared, yet quantitative rate constants were not obtained. The preferential degradation of amorphous polymer regions previous observed in scanning electron microscopy (SEM) degradation studies were also confirmed by these studies.^[23] In another study, the surface properties of PSA - poly(lactic acid) blends during alkaline degradation were monitored by secondary ion mass spectroscopy, X-ray photoelectron spectroscopy and AFM and compared to the parent homopolymers films.^[24] The degradation of films made from PLGA-poly(ethyleneoxide)-PLGA triblock copolymers (film thickness: 300 μm) was studied gravimetrically, and the apparent rate of mass loss of these films was k_app = 0.09 d^-1 under simulated physiological conditions.^[16b] Very recently, the degradation of poly(methacrylic anhydride-co-methacrylic acid) films (film thickness: 1 μm) at different pH values was monitored by Fourier transform infrared spectroscopy (FTIR).^[25] The degradation rate of these polymer films was faster in neutral and alkaline solution, which could be attributed to deprotonation of the methacrylic acid units enhancing the dissolution rate of the polymer. To the best of our knowledge, further quantitative information on polymer film degradation or methods to study such degradation processes are not available.

Thus, the aim of this work was a) to develop methods for a quantitative study of polymer film erosion, and b) to find out whether the degradation rate constant of such films was thickness dependent, and how it compared to the rate constant of bulk material degradation. The films investigated were surface-mounted, with a thickness of 450 nm down to 52 nm, and were compared to free standing thicker samples (190 to 670 μm thickness, i.e. above L_critical). We established three analytical procedures based on ellipsometry, surface-plasmon resonance spectroscopy (SPR), and FTIR to quantify the rate constants of degradation and erosion. Poly(sebacic anhydride) (PSA, Figure 1) was used as a model system for method development. It can be synthesized easily and in large amounts by melt polycondensation.^[26] The erosion and degradation rate constants obtained from the different methods and the degradation profile obtained from the different sample types were then compared and correlated to structural features of the materials.

Figure 1.

Synthesis of poly(sebacic anhydride). The sebacic acid was activated with acetic anhydride and then melt-polymerized to give poly(sebacic anhydride).

2. Experimental Section

General information on chemicals sources and instrumentation used is given in the Supporting Information.

2.1. Synthesis of Poly(sebacic anhydride)

PSA was synthesized according to literature procedures.^[26] After recrystallizing from methanol twice, sebacic acid (8.3 g) was heated in acetic anhydride (excess, 1/10 m/v) under reflux for 60 minutes. Excess anhydride was removed under high vacuum at 50°C. The resulting pre-polymer was dissolved in dichloromethane and precipitated into diethyl ether. The precipitate was filtered after 12 hours and dried under vacuum. Pre-polymer (590 mg) was put into a Schlenk tube, which was placed into an oil bath that had been pre-heated to 180°C. The flask was kept at that temperature throughout the reaction. After the pre-polymer had melted, vacuum was applied and the mixture was left to react until its viscosity remained constant. It was then allowed to cool to room temperature and solidify. The thus obtained solid was dissolved in dichloromethane and added drop-by-drop into hexane while stirring. The polymer precipitated in white flakes, was recovered by filtration using a filter funnel (por. 3), and dried under vacuum (yield: 75%). The structural integrity of the polymer was confirmed by ¹H-NMR spectroscopy (Figure S1 in the Supporting Information), which was also used to calculate the average molecular mass M_n of the polymer. M_n,NMR was 11,100 g·mol^-1; the molecular mass determined by gel permeation chromatography in CHCl₃ was M_n,GPC = 13000 g·mol^-1 (Figure S2, M_w,GPC = 30,000 g·mol^-1, PDI = 2.3). Since PSA has a short shelf-life,^[26] it was carefully stored (under nitrogen, - 24°C) and used timely before a loss of molecular mass was observed.

2.2. Preparation of Thin Poly(sebacic anhydride) Films by Spin-coating

Single side-polished silicon wafer pieces were used for the ellipsometry measurements, and double side-polished silicon wafer were used for measuring the infrared spectra. Poly(sebacic anhydride) (5 mg to 38 mg depending on the targeted layer thickness, e.g. 5 mg for a layer thickness on silicon of about 52 nm) was dissolved in chloroform (1 mL). The resulting solution was filtered before use using a syringe filter (pore size 0.2 μm). Silicon wafers were cut into pieces with an area of about 1.5 cm × 1.5 cm and were cleaned by washing with dichloromethane and isopropyl alcohol. The polymer solution was then spin-coated (3000 rpm, 1000 rpm·s^-1, 30 sec) onto these substrates.

Gold substrates were used for surface plasmon resonance spectroscopy measurements. Gold-coated LaSFN9 substrates were prepared as described previously.^[27] A poly(sebacic anhydride) solution (e.g. with a concentration of 5 mg mL^-1 for a layer thickness on gold of about 50 nm) was prepared as described above. The gold substrates were washed and spin-coated with that solution as described above.

2.3. Preparation of Thicker Poly(sebacic anhydride) Films by Doctor-blading

Double side polished-silicon wafer pieces were treated with 4-[(3-triethoxylsilyl)propoxy-benzophenone] (3-EBP) to increase their hydrophobicity.^[28] The exact procedure for this silanization step is given in Section 4 of the Supporting Information. An increase in the static contact angle from 32° to 72° confirmed that the silanization was successful (Table S1 in the Supporting Information). A highly concentrated polymer solution (550 mg mL^-1) was then applied onto the substrate and a doctor blade (nominal height 15 μm) was driven with a speed of 10 mm·sec^-1 over the polymer droplet under ambient condition. After solvent evaporation under nitrogen overnight, a sample thickness of about 450 nm on substrate was thus obtained.

2.4. Preparation of Free-standing Samples

Poly(sebacic anhydride) was frozen with liquid nitrogen and ground to powder. The molecular weight after grinding was determined to be 7000-9000 g·mol^-1 and the polydispersity had increased to 3-4. The GPC elugram of one ground sample is shown in Figure S3 in the Supporting Information as an example. Free-standing samples were prepared by compression-molding using a hydraulic press with an inner diameter of 13 mm at room temperature. The pressure of ten tons was applied onto the sample for five minutes and then the pressure was slowly released over one minute. The obtained samples were store at - 24°C before the degradation studies.

2.5. Degradation Studies

The degradation studies were continued until the limit of instrumental accuracy of the methods used was reached. Depending on the method and sample type, the last measurement was after 48, 60, 72, 96 or 144 hours. For degradation, the samples were immersed into a 50 mM triethanolamine hydrochloride buffer solution (pH 7.4) at 37°C. The buffer volume (10 mL for each sample) was not changed during the experiment. In order to avoid shear force in the system, the degradation was performed without stirring. In general, the samples were placed into the preheated buffer and retrieved at defined time points, dried and measured. For the samples on substrates, two samples of each type were prepared and studied. From the thus obtained data, the experimental error (standard deviation) for each data point was calculated. For the free-standing samples, only one sample was measured at every single time point due to the limited amounts of PSA from the same batch. At each time point, the buffer was carefully removed, and the remaining sample was frozen at −24°C until the last sample of that series had been removed from buffer. The vials with the samples were then brought to room temperature and dried under high vacuum for 12 hours. Inaccuracies due to weighing errors and the residues of buffer salts were estimated and given as the error of each measured value.

For the SPR measurements, PSA films on gold substrates were mounted in the SPR setup, and changes in the sample were monitored in situ by measuring full angular reflectivity curves. More details on the measurement are given in the Supporting Information, Section 7.

3. Results and Discussion

3.1. Sample Preparation and Degradation Conditions

To compare the degradation and erosion kinetics of thin films and free-standing macroscopic samples made from poly(sebacic anhydride) (PSA), two sample sets with different thickness ranges were prepared: Samples with a thickness much lower than the L_critical for polyanhydrides were obtained by spin-coating and doctor blading. Using the same spin-coating parameters, the layer thickness could be varied between 52 to 378 nm by using different concentrations of PSA in chloroform. Using a doctor-blade, a layer thickness of about 450 nm (based on AFM measurements) was obtained. The thicker samples (190 to 670 μm) were prepared using a hydraulic press. The initial layer thickness of the PSA samples was determined by ellipsometry and SPR (thin samples), AFM and surface profilometry (medium thick samples) or calipers (thicker samples). For the degradation studies, thus prepared samples were immersed into triethanolamine buffer at 37°C, pH 7.4, and an ionic strength of ca. 100 mM (simulated physiological conditions). Under these conditions, the labile anhydride linkages of PSA were hydrolyzed, resulting in a continuous reduction of the molecular mass of the polymer, and formation of acid end-groups at each chain end. At a given time point, the samples were removed from the buffer, dried, and analyzed.

3.2. Method Selection and Development.

The methods used to quantitatively follow the degradation and erosion of these PSA samples were gravimetry, Fourier-transform infrared spectroscopy (FTIR), surface plasmon resonance spectroscopy (SPR), and ellipsometry. A sample list and a summary of the methods suitable for each sample is shown in Table 1.

Table 1. Overview of the samples with different thicknesses obtained from spin-coating, doctor-blading or compression-molding and their tracking methods.

Thickness	Solution Concentration or Polymer Mass used	Methods
52 nm	7 mg mL-1	Ellipsometry, IR, SPR
88 nm	10 mg mL-1	Ellipsometry, IR, SPR
125 nm	12 mg mL-1	Ellipsometry, IR, SPR
166 nm	18 mg mL-1	Ellipsometry, IR, SPR
378 nm	38 mg mL-1	Ellipsometry, IR
450 nma)	550 mg mL-1	IR
190 μm	25 mg/pellet	gravimetry
370 μm	50 mg/pellet	gravimetry
670 μm	100 mg/pellet	gravimetry

^a)on 3-EBP treated substrate

3.2.1. Gravimetry

Gravimetry was used to quantify the mass loss of the thicker samples, simply by recording the change of the sample mass over time. This was possible for the free-standing disks, with a sample weight in the range of 25 to 100 mg, yet it was too imprecise for studying thin films. For the thick samples, the sample mass m_t recorded at each time point was normalized to the initial mass m₀ of the sample, and the resulting relative mass of the remaining sample (= m_t / m₀) was plotted versus time to determine the degradation/erosion kinetics.

3.2.2. Ellipsometry

Ellipsometry was used to monitor the change in layer thickness of the thinner samples. We assumed that the thickness loss of the degraded sample after drying would be proportional to the mass loss of the sample. To obtain sufficiently precise data, the layer thickness of each sample was measured on six points each on two different samples. This worked well for the initially smooth surfaces but became increasingly difficult during continued degradation and increasing sample roughness. With our sample set, the method worked well up to a layer thickness of 378 nm. For the thicker samples, this method failed as the samples were either not sufficiently transparent (free-standing samples), or the erosion process increased the surface roughness so much that the measurement was disturbed by interference effects. To determine the degradation kinetics from the ellipsometry data set, the sample thickness d_t recorded at the different time points was normalized to the initial thickness d ₀, and the resulting relative thickness of the remaining sample (= d_t/d ₀) was plotted versus time.

3.2.3. Surface Plasmon Resonance Spectroscopy (SPR)

Surface Plasmon Resonance Spectroscopy was chosen as a second method for tracking changes in the layer thickness of the degrading samples. Unlike the ellipsometry measurements, which were performed on different sample spots at each time point, these measurements were performed in situ and on a single sample. Again, the measured thickness changes were assumed to be proportional to mass loss of the sample. The general set-up of an SPR measurement is shown in Figure 2 and explained in the figure caption. The method is based on the excitation of surface plasmons in the gold substrate, whose properties are affected by the dielectric properties of the sample on that substrate,^[29] i.e. the degrading PSA layer. By measuring the reflected light intensity (reflectivity) as a function of angle of incidence (which gives information about the energy of the excited plasmons), the thickness and dielectric properties of the polymer film on the substrate can be calculated.^[30] There are two important limitations for the use of this method to monitor polymer degradation. Experimentally, the index-matching oil used to prevent undesired reflections at the prism-substrate interface (Figure 2) evaporates over time. After about 60 h measurement time, this leads to inaccuracies in the reflectivity measurement and thus limits the maximal experiment time. From a theoretical perspective, the vertical expansion of the evanescent wave that forms when the plasmons are excited (Figure 2) is finite. (The penetration depth of an evanescent wave is on the order of half the wavelength of the incident light,^[29] which means in our case, it is ca. 300 nm). Thus, surface processes on thicker samples cannot be accurately monitored as they are outside the measurement range. In our sample set, we found that SPR was useful for thin samples up to 166 nm thickness. To determine the degradation kinetics by SPR, the sample thickness d_t was calculated from fits to the angular reflectivity curves recorded at different time points. This thickness was then normalized to the initial thickness d ₀. The resulting relative thickness (= d_t/d ₀) of the remaining sample was plotted versus time.

Figure 2.

SPR set-up: Polarized light is coupled through a prism (via an index-matching oil layer, a LaSFN9 glass slide, and chromium adhesion layer) into a gold layer (orange). The gold substrate is covered by the sample (blue). An evanescent wave (yellow) is formed as surface plasmons are excited within the gold layer. The vertical distance describes the decay length of the evanescent field. The reflected light is detected to measure the energy of the surface plasmons, which is affected by the dielectric properties of the sample on the gold layer. The layers are not drawn to scale.

3.2.4. Fourier Transform Infrared Spectroscopy (FTIR)

Fourier Transform Infrared Spectroscopy could be used for all thin films on substrates. While ellipsometry and SPR monitor changes in the film thickness, FTIR can be used to measure changes in the chemical composition of the samples. Thus, it is sensitive to the kinetics of the degradation process rather than to overall erosion, as anhydride degradation leads to a decrease of the anhydride adsorption band of the polymer, and an increase in the adsorption band of the degradation products, the acids. Saturated aliphatic anhydrides have characteristic double peaks at 1850-1800 cm^-1 and at 1790-1740 cm^-1 (asymmetric and symmetric stretching vibrations of the two carbonyl groups).^[31] In the PSA samples, the peak area of the anhydride peak at 1810 cm^-1 (which did not overlap with other peaks) was used and compared to the emerging peak at about 1740-1700 cm^-1 caused by the carbonyl groups of the degradation products (sebacic acid and oligomers). In our sample set, the method could be used for the thinner samples, but failed for the thicker free standing samples as they were not sufficiently IR transparent. To determine the degradation kinetics by FTIR, the peak intensity of the anhydride band at 1810 cm^-1 for each time point was normalized to the peak intensity of the same band at t₀to give the relative peak area. This data was then plotted versus time.

3.3. Degradation/Erosion Kinetics of Polymer Films with 52-166 nm Thickness

A typical data set obtained by the above described methods using a PSA film with an initial thickness of 166 nm (determined by ellipsometry) is shown in Figure 3. (The data sets obtained from the other polymer films are given in Figures S4 to S9 of the Supporting Information in Section 8, 9 and 10.). In the first line of Figure 3, a plot of the data versus time is shown for each method (Figure 3a - ellipsometry, Figure 3b - SPR, Figure 3c - FTIR). These data sets were fitted with a single exponential function (y_t = y ₀ — A · e^{k_app · t}, where y_i is the normalized data at different time points (layer thickness or FTIR peak area, respectively), A is a fitting constant, and k_app is the apparent erosion/degradation rate constant). The data sets obtained by ellipsometry (Figure 3a) and FTIR (Figure 3c) were well-fitted with this function, whereas fit to the dataset obtained by SPR (Figure 3b) showed a systematic deviation starting at around t = 40 hours. In particular, the measured data after 40 hours were underestimated by the exponential function.

Figure 3.

Degradation/erosion of a PSA film with d ₀ = 166 nm monitored by ellipsometry, SPR and FTIR. The data points at time t were normalized to t ₀. First line: normalized data (thickness or peak area, respectively) versus time with exponential fit; second line: linear fit to the logarithmic plots of the same data. The inset in (b) is shows the angular reflectivity curve at t = 14 h obtained by SPR, from which the data at that time point was obtained, as an example. The inset in (c) shows the FTIR spectra at t = 6 h (green) and 24 h (violett), respectively, with carbonyl bands at 1810 cm^-1 and 1749 cm^-1.

The same data was also plotted logarithmically versus time for each method (second line of Figure 3) to check whether the single exponential used, which assumes first order degradation kinetics, was really appropriate to fit the data. While the thus obtained FTIR data could be fitted with an uninterrupted linear fit (Figure 3c, second line), there was a pronounced change in gradient in the linearized data obtained from the other two data sets (Figure 3a and 3b, second line). This is an indication for two different kinetic regimes during the degradation/erosion process: a fast process followed by a slower process. These two processes were fitted by two separate linear functions (z_t = a ₁ — k_fast · t and z_t = a ₂ — k_slow · t, respectively, where the a_i are fitting parameters and the k_i are the apparent degradation/erosion rate constants).

From these fits, the rate constant k_fast = 0.039 ± 0.004 h^-1 and k_slow = 0.011 ± 0.002 h^-1 were obtained (Figure 3a). For the SPR data (Figure 3b), k_fast = 0.058 ± 0.007 h^-1 was for the fast process, and k_slow = 0.011 ± 0.0003 h^-1 for the slow process. In the literature, preferential degradation of the amorphous polymer areas was reported for semicrystalline polymers. This was, for example, observed for different polyesters and the degradation of poly(sebacic anhydride) under alkaline conditions.^{[5b, 9a, 24]} This would be consistent with the observed two degradation rate constants.

In contrast to the two-regime kinetics observed by ellipsometry and SPR (Figure 3a and b), the linearized fit to the FTIR data (Figure 3c) had a single slope, corresponding to only one kinetic process (Figure 3c). It could be fitted by a single linear function, giving an apparent degradation rate constant R₀ = 0.07 ± 0.01 h^-1. This difference is observed because the thickness decrease detected by SPR and ellipsometry measures the erosion kinetics, whereas FTIR detects the kinetics of the anhydride bond hydrolysis. Thus, the anhydride bond hydrolysis proceeds with a constant rate constant throughout the experiment, whereas the erosion process changes its rate over time. Similar effects were observed in the data sets obtained for the other samples with a thickness between 52-378 nm (Figures S4 to S9), thus the results obtained from the three methods for this sample set are consistent.

3.4. Morphological Studies

AFM measurements were used to observe changes in the roughness and morphology of the PSA surfaces during the degradation/erosion process under simulated physiological conditions. In Figure 4, representative AFM height images of a PSA film (thickness: 166 nm) on silicon surfaces at four different time points are shown, together with the measured root-mean-square averaged surface roughness (R _q). The AFM height image of the PSA film at t = 0 (Figure 4a) revealed the typical morphology of a semi-crystalline polymer: tightly packed spherulites with crystalline lamellae radiating from the central nucleating cores were observed, and grain boundaries between the spherulites were detected. After two hours degradation (Figure 4b), the spherulites seemed to have finer features. The morphology was altered but did not indicate degradation of the crystalline domains. After 24 h (Figure 4c), vacancies within the crystalline lamellae formed, and the distinct spherulite shape observed earlier was lost, indicating the crystalline domains start to disintegrate. After 48 h (Figure 4d), substantial hole formation was observed. R_q (ranging from 11 nm to 13 nm) did not change much during the first 48 hours.

Figure 4.

AFM height images of PSA thin films on silicon wafers after different degradation times (sample thickness at 0 h: 166 nm). Scale bars: 1 μm. Roughness values R_q are given underneath the images. Left to right: (a) at 0 h, (b) 2 h, (c) 24 h, and (d) 48 h.

Further AFM images or this series (from t = 0 - 96 h) are shown in Figure S10. The AFM images are qualitatively consistent with the data from ellipsometry and SPR and indicate that there is indeed a preferential removal of amorphous polymer before substantial erosion of the crystalline spherulites is observed. Previously, PSA degradation was semi-quantitatively studied by AFM under non-physiological conditions (e.g. pH 12.5).^[21] Expectedly, this process was faster than the here described kinetics under physiological conditions, yet the qualitative observations were comparable.

3.5. Degradation/Erosion Kinetics of Polymer Films with 378-450 nm Thickness

The thickest thin film sample obtained by spin-coating had a layer thickness of 378 nm. It could not be studied by SPR for the reasons discussed in Section 3.2. Consequently, the sample was investigated by ellipsometry (Figure 5a) and FTIR (Figure 5b) only. Interestingly, the logarithmic plot of the data indicated that the FTIR data could also be fitted with two linear functions.

Figure 5.

Degradation/erosion of the 378 nm thick PSA film monitored by ellipsometry (a) and FTIR (b), and degradation/erosion of the 450 nm thick film monitored by FTIR (c). The data points at time t were normalized to t₀. First line: Normalized data (thickness or peak area, respectively) versus time and exponential fit; second line: linear fits to the logarithmic plots of the same data.

The reason for this deviation is unclear at this stage. The degradation of one further sample with a film thickness of 450 nm (obtained by doctor blading) was studied by FTIR spectroscopy only (Figure 5c), since its surface was too rough for consistent ellipsometry measurements. Only a limited amount of data points was obtained from this sample, yet it seems like the FTIR data involves only one kinetic processes. All kinetic constants obtained by the different methods are summarized in Table 2.

Table 2. Rate constants obtained by from the exponential and linearized fits to the ellipsometry, SPR, FTIR and gravimetry data.

sample thickness	method	kapp from exponential fit [h-1]	kapp from linearized fit (one process) [h-1]	kfast and kslow from linearized fit (two processes) [h-1]
52 nm (Si) 50 nm (Au)	Ellipsometry	0.09 ± 0.01		Fast: 0.039 ± 0.004 Slow: 0.002 ± 0.001
	SPR	0.01 ± 0.003		Fast: 0.011 ± 0.002 Slow: 0.006 ± 0.0001
	FTIR	0.13 ± 0.03	0.11 ± 0.01
88 nm (Si) 97 nm (Au)	Ellipsometry	0.11 ± 0.028		Fast: 0.06 ± 0.011 Slow: not enough data
	SPR	0.05 ± 0.005		Fast: 0.031 ± 0.003 Slow: 0.007 ± 0.0003
	FTIR	0.07 ± 0.007	0.07 ± 0.01
125 nm (Si) 119 nm (Au)	Ellipsometry	0.09 ± 0.005		Fast: 0.046 ± 0.002 Slow: 0.004 ± 0.0004
	SPR	0.14 ± 0.016		Fast: 0.046 ± 0.006 Slow: 0.005 ± 0.0003
	FTIR	0.14 ± 0.02	0.15 ± 0.01
166 nm (Si) 162 nm (Au)	Ellipsometry	0.06 ± 0.01		Fast: 0.035 ± 0.003 Slow: 0.006 ± 0.002
	SPR	0.10 ± 0.01		Fast:0.058 ± 0.007 Slow: 0.011 ± 0.0003
	FTIR	0.09 ± 0.02	0.07 ± 0.01
378 nm (Si)	Ellipsometry	0.09 ± 0.03		Fast: 0.03 ± 0.002 Slow: 0.0026 ± 0.0003
	FTIR	0.13 ± 0.02		Fast: 0.06 ± 0.002 Slow 0.0033 ± 0.0013
450 nm	FTIR	0.04 ± 0.01	0.04 ± 0.01
190 μm	gravimetry	0.029 ±0.008a)	0.009 ± 0.002b)
370 μm	gravimetry	0.016 ±0.005a)	0.007 ± 0.001b)
670 μm	gravimetry	0.010 ±0.004a)	0.03 ± 0.0003b)

^a)k_app for degradation until 150 h

^b)k_app for degradation until 72 h

4. Degradation Kinetics of Free-standing Samples with a Thickness of 190 to 670 μm

In order to compare the erosion/degradation kinetics of the substrate-borne thin films described above with macroscopic samples having a thickness above L_critical, the degradation kinetics of free-standing PSA samples with a thickness from 190 to 670 μm under simulated physiological conditions were investigated gravimetrically. This situation is not completely identical to the degradation of thin films on substrates, where the substrate is an impermeable water barrier, yet it is the best possible approximation and potentially less error-prone than alternatives like, e.g. gluing the free-standing samples onto a substrate.

The initial layer thickness of the free-standing materials was determined using a caliper with a resolution limit of 10 μm, and ranged from 190 μm to 670 μm. Thus, even considering that water can permeate from two surfaces in this case, this is above twice L_critical for polyanhydrides. After degradation in buffer for a defined time, the mass loss of the dried samples was determined and plotted versus time (Figure 6). In all plots, the second data point was slightly higher than the first one due to water uptake. This indicated that the anhydride hydrolysis reaction was slower than the water uptake, which pointed towards bulk erosion.^[32] As can be seen both from the linear and the exponential fit, the data scattering and error bars were large, so that it is difficult to ascertain the reaction order. Thus, a single process was assumed, and from the exponential fit to the data up to t = 150 h, the degradation rate constants 0.029 ±0.008 h^-1, 0.016 ±0.005 h^-1 and 0.010 ±0.004 h^-1, respectively, were determined for the three samples investigated (Table 2). Compared to the degradation rate constants of the thinner, surface-mounted samples, the degradation rate constant of the free-standing samples was slower by roughly one order of magnitude (Table 2). Moreover, within this range, the degradation rate constant became thickness-dependent. Apparently, the degradation rate constant decreased when the sample thickness increased.

Figure 6.

Degradation/erosion of the free-standing samples with a thickness of 190 μm (a), 370 μm (b), and 670 μm (c) monitored gravimetrically. The data acquired was fitted by a single exponential function (first row). From the logarithmic plot, it is unclear whether one or two kinetic processes are found. The degradation rate constants obtained from these fits (based on degradation times from 0 h to 72 h) are given in Table 2.

5. Dependency of the DegradationZErosion Rates on the Sample Thickness

The degradation rate constants determined by the various methods as described above were summarized in Table 2 and in Figure 7. A plot of the rate constants k_app from the single exponential fits to the ellipsometry, FTIR and gravimetry data (Figures 3 and 6) against the initial layer thickness are shown in Figure 7a. This plot indicates that the methods used to monitor thin film degradation gave qualitatively and quantitatively consistent results, although the error bars obtained were somewhat large (Figure 7a). The latter is a result of the small film dimensions, which are much more susceptible to measurement errors than thicker films. Notably though, the rate constants for the films differed only by a factor of 2.3. The average value for PSA degradation thus obtained using a single exponential fit was 0.10 ± 0.02 h^-1. Additionally, there was no apparent correlation between the degradation/erosion rate constant and layer thickness in the range from 52 nm to 378 nm. This indicates that water diffusion through these thin samples was not a rate-determining step, and that the degradation mechanism was bulk erosion. In the light of the significantly higher average L_critical value of polyanhydrides,^[8] this is a plausible result.

Figure 7.

(a) Plot of log (Initial layer thickness in nm) vs. apparent degradation rate constants k_app (obtaind by fitting the data with a single exponential function). Literature data from reference ^[10] was also included. (b) Plot of Initial Layer thickness vs. fast and slow process degradation rate constants k_fast and k_slow.

As pointed out before, logarithmic plots to the SPR and ellipsometry data of the thin films (Figure 3) indicated that there were two kinetic regimes, a fast process and a slow process. A summary of the rate constants obtained from these plots is shown in Figure 7b. In the absence of clear correlations between rate constant and film thickness in this range, the average of each rate constant was calculated. Thus, for the fast process, k_fast was determined as 0.04 ± 0.004 h^-1. For that process, the data obtained by ellipsometry scattered less than the data obtained by SPR. This is most likely because the SPR study was performed under flow conditions, which introduced shear to the system and could have affect the erosion process. For the slow process, k_slow was determined as 0.0055 ± 0.007 h^-1, and the data sets obtained for both methods was quite consistent.

The data obtained for the free-standing films via gravimetric methods is also included in that plot in Figure 7a. It is clear from that data that the degradation rate constant is thickness-dependent when considering film thickness differences of several orders of magnitude, yet it is not possible to judge from that data set what kind of correlation exists between the sample thickness and the degradation rate constants. In literature, degradation of PSA pellets with a thickness of 0.6 to 1.8 mm were also studied using gravimetric methods.^[10] The degradation rate constants of the theses samples were fitted based on zeroth order kinetics, although some deviation from a zeroth order rate law was observed.^[10] The rate constants thus obtained were 0.0056 h^-1 for 0.6 mm, 0.0033 h^-1 for 1.2 mm and 0.0022 h^-1 for 1.8 mm thickness after 168 h.^[10] These data points have also been included in Figure 7a, even though these zero-order rate constants are not directly comparable to our first order rate constants. Nevertheless, the rate constants were found on the same order of magnitude, and a similar trend (increasing rate constant with decreasing sample thickness) was observed both for the literature data and our gravimetry-based rate constants. The line included in Figure 7a is a guide to the eye only, not an actual fit of the data, and was drawn to illustrate a possible trend how these rate constants might be film-thickness dependent. Based on the data sets shown in Figure 7, with significantly altered degradation kinetics for the free-standing samples, we would predict a thickness dependent rate constant up to a certain threshold, after which the rate constants becomes independent of layer thickness, as shown for the thin film samples. This would also be consistent with the notion of a mechanistic change from surface erosion to bulk erosion.

Polymer erosion and degradation is a complex process. Not only has it been previously demonstrated that the amorphous and crystalline parts of a polymer have different degradation rates;^[9a] other more subtle events have also been observed, such as different degradation rate constants of crystallites with different sizes, and the crystallization of degradation products.^[9a] Thus, a single exponential fit to degradation data most likely cannot capture all the physically significant events happening during degradation and erosion. Nevertheless, comparing apparent rate constants enable the experimentalist to compare these events between different sample types.

6. Conclusions

In this study, we investigated the degradation of poly(sebacic anhydride) (PSA) samples in a thickness range of from 52 nm to 670 μm under simulated physiological condition. One sample set consisted of thin surface-attached films with up to 450 nm thickness, the other sample set were free-standing PSA samples with a thickness from 190 to 670 μm. Importantly, the first sample set had a thickness that was much smaller than the average L_critical of poly(anhydrides) (75 μm), whereas the other sample set was significantly thicker. First, three methods were developed to study thin film degradation. Using ellipsometry and SPR, the whole erosion process was monitored, whereas FTIR was sensitive to the actual bond hydrolysis kinetics. With SPR, an in-situ method for thin film degradation was available. The data sets thus obtained were fitted with one or two exponentials, corresponding to one or two physically observable processes that have a rate-determining effect on degradation and erosion. Particularly for the thin film samples, two-regime degradation was observed, probably corresponding to degradation of the amorphous and crystalline areas of PSA, respectively. AFM measurements of the degraded samples showed that this assumption was plausible.

For the free-standing samples with a thickness above L_critical, the data scattering was so large that it was not possible to decide whether the degradation and erosion was a one-regime or two-regime process. Nevertheless, it was possible to observe that the overall degradation rate constant for these samples was one order of magnitude lower than the apparent degradation rate constant obtained from the thin film samples. That data also matched literature values. For the thin polymer films, the sample thicknesses had no influence on the degradation rate constant, while there was a thickness-dependency for the free-standing samples. This indicates that in that size range, water diffusion starts to become rate-determining, i.e. these thicker samples are in a regime where there is a transition from bulk erosion to surface erosion.

Overall, in this study quantitative methods for studying thin film degradation/erosion were presented and validated. Additionally, the data obtained added further details to the general picture of the degradation/erosion of polyanhydrides. Importantly, it showed that for a sample thickness much below the L_critical, the layer thickness did not affect the degradation/erosion rate. Thus, neither water diffusion nor removal of the degradation products seem to have a rate-determining effect on the overall process. Above the L_critical, a thickness dependency was observed, which could be related to transport-associated effects. From an application point of view, the data indicates that thin films provide a matrix with relatively robust degradation kinetics. This could be of practical relevance, for example in the context of drug release from polymer coated micro- and nanoparticles.