Mechanical Stability of Porous Copolymers by Positron Annihilation

May 1, 2015 - A set of porous copolymer samples (VP-TRIM, VP-DVB, and VP-DMN) under mechanical stress up to 1.3 GPa was studied in situ using positron...
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Mechanical Stability of Porous Copolymers by Positron Annihilation Lifetime Spectroscopy Radosław Zaleski,*,† Małgorzata Maciejewska,‡ and Michał Puzio† †

Institute of Physics, Department of Nuclear Methods, Maria Curie-Skłodowska University, pl. M. Curie-Skłodowskej 1, 20-031 Lublin, Poland ‡ Faculty of Chemistry, Department of Polymer Chemistry, Maria Curie-Skłodowska University, ul. Gliniana 33, 20-614 Lublin, Poland S Supporting Information *

ABSTRACT: A set of porous copolymer samples (VP-TRIM, VP-DVB, and VP-DMN) under mechanical stress up to 1.3 GPa was studied in situ using positron annihilation lifetime spectroscopy. A few stages of porosity evolution dissimilar in changes of the pore size distribution (PSD) were observed. At low pressure, the maximum of PSD and the pore volume decreased, indicating pore shrinkage. Simultaneously, the fast decrease in the width of PSD shows that the size of the largest pores is mostly reduced. In copolymers in which the number of relatively weak ester bonds is significant, an additional stage exists at 40−70 MPa. In this range, the trend of the changes in the width of PSD versus pressure is reversed, indicating pore reorganization (probably, they connect with each other). Above a certain pressure (0.2−0.5 GPa), both the maximum and the width of PSD stabilize at minimal values, ca. 1−2 nm. These values as well as the stabilization pressure are specific for each polymer. Pore collapse is observed in a high-pressure range, where only the pore volume decreases. The pores are completely closed at 0.8−1.3 GPa (depending on the polymer), but their porosity is greatly recovered after pressure release. The size and volume of the pores after porous polymer squeezing depend on the maximal exerted pressure.

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sample11 or using the dynamic mechanical analysis.12 The small number of methods used for mechanical stability studies are determined by the limitations of the most common techniques used for characterization of porous materials. A study of porous polymers under high pressure by the most common adsorption analysis as well as small-angle X-ray scattering or neutron scattering techniques is practically impossible. However, such measurements are feasible using positron annihilation lifetime spectroscopy (PALS). The probe in this method is the bound state of a positron and an electron (i.e., positronium, Ps). This pseudoatom is formed in a majority of nonconductive materials when positrons are implanted into their bulk. The positron source is usually a radioactive nuclide enclosed in a durable envelope and surrounded by a sample. The PALS measurement consists of detection of high-energy γ quanta, which can penetrate through typically thick walls of a pressure chamber. Therefore, it is possible to perform PALS measurements in situ even under very high pressure applied to a sample. The stress applied to a material mostly influences its internal empty spaces (i.e., pores, but also free spaces in the bulk material), which change because of reorganization of molecules. Therefore, the possibility of estimating the concentration and

INTRODUCTION A variety of applications of porous polymers1,2 creates a need for thorough examination of their properties. A significant number of the applications requires certain mechanical properties of the materials. Porous polymers are often expected to withstand pressure of the order of tens or even hundreds of bars without a significant change in their structure. Studies of materials suitable for such applications have been performed in the field of gas storage,3,4 proteomic analysis,5 and microfiltration.6 Even higher pressures are exerted when a porous polymer serves as a column filler in high-pressure liquid chromatography.7,8 Numerous applications of macroporous polymers make them an object of mercury porosimetry studies. However, for many years, there have been doubts about the reliability of results obtained by this method operating at the pressure of thousands of bars.9 Particularly in polymers, whose structure is usually flexible, one can obtain confusing results if their porosity changes temporarily during measurement and is restored afterward. Finally, some of the highest requirements are imposed on porous polymers that are designed to repair bones.10 Also in this case, their behavior in situ (i.e., under stress) is the most important. Although knowledge of the microstructure of porous polymers under mechanical stress is highly desirable for the applications presented above, there are no such studies. The mechanical stability is usually examined in macroscopic terms by determining the compression modulus of a stressed © 2015 American Chemical Society

Received: February 20, 2015 Revised: April 24, 2015 Published: May 1, 2015 11636

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(TRIM, Sigma-Aldrich, Steinheim, Germany) monomers were washed with 5% aqueous sodium hydroxide. 1,4-di(methacryloyloxymethyl)naphthalene was obtained according to the procedure described by Matynia and Gawdzik.16 No purification was applied to poly(vinyl alcohol) (PVP) and α,α′azoisobutyronitrile (AIBN) purchased from Fluka. Toluene, ndodecane, acetone, and methanol, were from POCh (Gliwice, Poland). The porous copolymers VP-DVB, VP-TRIM, and VP-DMN (Figure 1) were obtained by suspension copolymerization.

the size of free spaces is very advantageous for studying the mechanical properties of materials on a microscopic scale. This indicates that PALS, whose main ability is to characterize free spaces, is a suitable method for testing mechanical stability. Moreover, the range of free space sizes that can be detected by PALS exceeds the capabilities of most other experimental techniques. This is possible because of the properties of the long-lived triplet state of positronium (ortho-positronium, oPs). In vacuum, an o-Ps, which is composed of two particles with parallel spins, annihilates with a relatively long lifetime (142 ns). However, when o-Ps is trapped in a free space within a solid, its lifetime is significantly shortened because of the pickoff annihilation. The pick-off consists of annihilation of the positron bound in positronium with an electron, which have the opposite spin. Such electrons can be found by the positron in the walls of the free space; therefore, pick-off probability depends on the size of the free space. The PALS method is based on measurement of the time between the detection of two γ quanta: the first photon indicates positron formation and the second positron annihilation. A positron lifetime spectrum contains the results of several million time measurements. Each spectrum is a sum of exponential decays (i.e., components) convoluted with a spectrometer resolution function. A component is characterized by two parameters, the lifetime and the intensity, which are related to the average size of the free spaces where the positron annihilates and their concentration, respectively. The components with a lifetime above approximately 1 ns are typically ascribed to the o-Ps pick-off annihilation. In this case, the relation between the lifetime and the free space size is described by the extended Tao-Eldrup (ETE) model.13 In turn, the relative concentration of free spaces of a given size can be estimated from the intensity of the appropriate component. To achieve this, a calculation scheme,14 which takes into account the probability that a thermalized positron passes through the free space of a given size, is used. A bell-shaped pore size distribution often exists in porous materials. This is the case in most of the porous polymers, where the pore size distribution is wide and the component related to the pores cannot be satisfactorily approximated by a single exponential decay. The distribution of o-Ps lifetimes is present in such materials. To include the distribution in the analysis, an additional parameter, i.e., dispersion, is introduced. The dispersion describes the width of the log−normal lifetime distribution in the component. The pore size distribution in a porous material investigated by PALS can be reproduced based on the methods described previously. We present how the observation of the size of various free spaces (i.e., from mesopores through micropores to spaces between polymer chains) can provide comprehensive insight into changes in the microscopic structure of porous polymers under stress. For this study, three statistical polymers (VPTRIM, VP-DVB, and VP-DMN) with different structures and properties but comparable pore sizes were chosen.15 Our goal is to prove the PALS ability to estimate the sizes of the free spaces present in the polymers under high pressure (up to 1.3 GPa) and after releasing it. We also show differences in the structure changes between the particular polymers.

Figure 1. Chemical structures of the VP, DVB, TRIM, and DMN monomers used.

During the synthesis, VP was used as a functional monomer, whereas DVB, TRIM, and DMN served as cross-linkers responsible for the mechanical properties of the resulting polymeric matrix. The molar ratio of the functional monomer to the cross-linker was 1:1. Copolymerization was performed in an aqueous suspension medium. Initially, 195 mL of distilled water and 6.5 g of poly(vinyl alcohol) were stirred for 6 h at 80 °C in a three-necked flask fitted with a stirrer, water condenser, and thermometer. Then, the solution containing 15 g of monomers and 0.075 g of α,α′-azoisobisbutyronitrile in 22.5 mL of diluents (toluene and n-dodecane) was prepared and added to the aqueous medium under stirring. The copolymerization was performed for 20 h at 80 °C. Porous beads formed in this process were filtered off, and an extensive cleaning procedure was applied to remove the diluent, unreacted monomers, and physically adsorbed stabilizer. The cleaning process was as follows: The microspheres were separated from the aqueous phase by filtration of the polymerization mixture through 5 μm filter paper. The microspheres were first washed with water, and polymeric aggregates were removed by sieving. The microspheres were dispersed in water, and the dispersion was sonificated for 0.5 h in an ultrasonic bath. Then they were extracted in a Soxhlet

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EXPERIMENTAL SECTION Materials. To remove inhibitors, 1-vinyl-2-pyrrolidone (VP, Fluka AG, Buchs, Switzerland), divinylbenzene (DVB, Merck, Darmstadt, Germany), and trimethylolpropane trimethacrylate 11637

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omitted in the case of VP-DMN because dispersion uncertainty was larger than 50% in the whole range of pressures. The lifetime distributions obtained by the LT program, if a log−normal distribution was assumed, were transformed to pore size distributions using the calculation scheme mentioned previously. The relation between the lifetime and the free space size was found according to the ETE model. The pores of irregular shape present in the studied polymers were approximated by infinite cylinders in the model calculations. This standard assumption for open porosity may become inappropriate if the pore entrances are closed under pressure. Therefore, the results may be underestimated by up to 20% at the highest pressure, when a spherical approximation could become valid. The value of the empirical parameter Δ = 0.15 nm was assumed based on estimation thereof from the lifetime temperature dependences for porous polymers.18−20 The model calculations were done using the EELViS program.21

apparatus with acetone, toluene, and methanol. The purified beads were separated into fractions by sieving. Methods. The mechanical stability of the copolymer samples was tested by exerting mechanical pressure during the PALS measurement. For this purpose, a 20 mm layer of a powdered sample was placed in a chamber constructed of a cylinder closed by two movable pistons sealed with double orings. A 22Na positron source enclosed in an 8 μm thick Kapton envelope was placed in the middle of the sample layer. The 20 mm thick sample layer was sufficient to ensure that, even after sample compression, positrons did not annihilate outside the studied material. Before closing the cylinder with the sample inside, the air was pumped out of the chamber to the pressure of about 1 Pa. This prevented ortho−para conversion of positronium on paramagnetic oxygen molecules and adsorption of air molecules on the sample surface. Finally, the sample was sealed in the chamber and placed in a manual hydraulic press with the maximum load of 15 tons. Two piston sizes were used to close the appropriate cylinders with diameters of 12 and 40 mm. They were able to exert a maximum pressure of about 1.3 GPa (high-pressure range) and 150 MPa (low-pressure range), respectively. The applied pressure was uniaxial. Because of the limited precision of the press control, the load was changed in 1 ton steps. All PALS measurements were carried out at room temperature. The delayed coincidence spectrometer used to collect the positron annihilation lifetime spectra was a combined fast−fast (start signal branch) and fast−slow (stop signal branch) setup. Such a setup allowed us to obtain good linearity (flat background) in the whole 2 μs lifetime range. This is required in measurement of positron lifetimes longer than 100 ns, which are observed in porous materials. High-efficiency detection of annihilation radiation was ensured by scintillation detectors equipped with BaF2 crystals. The stop energy window covered a large part of the low-energy spectrum, which originated in great part from the three γ annihilation events. It prevented underestimation of the intensity for the long-lived o-Ps components. In consequence of the latter two settings, a high count rate (4 × 106 per hour) was achieved using a moderate activity (0.5 MBq) of the 22Na positron source. To minimize the influence of the long-term instabilities expected during pressurizing the sample, the measurements lasted usually 4 h at a given pressure, which resulted in 0.9−1.2 × 107 counts per spectrum. During the analysis performed by the LT 9.2 program,17 the spectrometer resolution function had to be approximated by two Gaussian functions with the 280 and 450 ps average full width at half-maximum (fwhm) and the 80% and 20% intensity, respectively. Therefore, the lifetime of the short-lived component, which originates from the para-positronium (pPs) intrinsic annihilation, was fixed at its known vacuum value of 125 ps to minimize the statistical dispersion of the results. A reasonable intensity of the p-Ps component (15−25% depending on the sample) and a lifetime of the next short-lived free positron component equal to 350−380 ps were found. The lifetime of the free positron component agrees with the values observed in the nonporous polymers of the same composition. Besides the p-Ps and e+ components, three o-Ps components were required in the whole range of pressures to obtain an acceptable fit (χ2 < 1.05). If the initial intensity of the longestlived component was large enough (20% in VP-TRIM and 28% in VP-DVB), the log−normal distribution of the lifetimes in this component was assumed. The log−normal distribution was

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RESULTS AND DISCUSSION Lifetimes, Intensities, and Dispersion. The pressure dependences of the lifetimes, intensities, and dispersion of the o-Ps components for VP-TRIM, VP-DVB, and VP-DMN are presented in Figures 2, 4, and 5, respectively. The lifetimes of the corresponding components, τSC = 2.2−2.5 ns (the shortlived component, SC), τMC = 9−11 ns (the medium-lived component, MC), and τLC = 110−120 ns (the long-lived component, LC), are similar in all samples before exerting pressure. The dispersion of ca. 30 ns was found for the longestlived component in both VP-TRIM and VP-DVB. Because of the low LC intensity, it was not possible to determine the dispersion in the VP-DMN spectra with reasonable accuracy, but even without it, the fit was comparable to that of other polymers. The intensities (I) of the corresponding components differ among the samples more than the lifetimes, but the relation ILC > ISC > IMC is preserved in all the samples. Our previous studies of VP-DVB18,22 and other porous polymers23,24 show that the SC and MC components originate from spaces between polymer chains and micropores, respectively. A majority of the micropores is most likely formed during removal of porogen remnants left after material synthesis.14 This is confirmed by their much smaller contribution in the nonporous polymer.18 The analysis of high-statistics PALS spectra usually reveals three components in this lifetime region, but it is highly probable that it is also an approximation. A single wide size distribution with a tail on the side of large sizes is expected for random disordered free spaces between polymer chains and micropores. Nevertheless, two components in this region instead of three give a sufficient approximation of the spectra. The benefits of the two-component approximation are the reasonably small uncertainties of the component parameters. This is particularly important during relatively short measurements, which are required when high pressure is applied. The LC component originates from the mesopores with a wide size distribution, which is indicated by the large dispersion parameter. During PALS measurements, porous materials are usually kept under vacuum to avoid ortho−para positronium conversion and contamination of the pore surface. Continuous pumping is essentially impossible during high-pressure measurements. Therefore, the air was evacuated from the sample, and then the sample chamber was sealed before the beginning of the pressure experiment. However, the risk of a leakage is high because the piston seals must be installed in a 11638

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which is most likely a result of a change in the sample structure (discussed later), but there is no change in τLC, which was supposed to shorten itself with time. It is possible that accidentally the same structure change that is responsible for the ILC decrease compensated the τLC shortening. However, the τLC changes after the pressure release do not resemble continuation of the decreasing run observed without pressure. Despite the large uncertainties, one may notice some wavy τLC time dependence. Its origin seems to be different than before applying pressure; probably it is a result of the slow relaxation of the sample structure. Although the evidence is not conclusive, we suspect that the application of the external pressure suppressed the evaporation observed before squeezing the sample. The discussed effect makes the correction of the time instability of the results questionable. Therefore, we present data without any correction, but one should keep in mind that the τLC and ILC values might have been underestimated. The influence of instabilities on the LC parameters can be evaluated by comparison of the measurements in the low- and high-pressure ranges. The measurement in the highpressure range started without waiting 24 h before applying the pressure, and the result at 86 MPa (second circle point in Figures 2, 4, and 5) was collected about 56 h earlier (according to the sample encapsulation) than during the measurement in the low-pressure range (crosses).

way that allows their movement along the cylinder. Moreover, the seals can be damaged if sample fragments get between the cylinder and the piston. To verify whether our results were distorted because of a leakage, we performed tightness tests. Prior to the measurement in the lower-pressure range, each sample was kept for approximately 1 day in an evacuated and sealed chamber without applying external pressure. During this time, PALS spectra were collected every 4 h. The results for VP-TRIM (Figure 3, crosses) reveal that both LC lifetime and intensity decrease with time, while the parameters of the other components do not change significantly. The same effect is observed for other samples, but the rate of the changes is different in each sample. Assuming that the lifetime and intensity change is linear, the rates relative to the value of the particular parameter at t = 0 were estimated for each sample (Table 1). The changes observed in VP-TRIM and VP-DMN Table 1. Decrease Rate (Relative to the Value at t = 0) of the Lifetime and the Intensity of the Longest-Lived Component Kept in the Evacuated Chamber without Applying Any External Mechanical Pressure to the Studied Samples Δτ (%/h) ΔI (%/h)

VP-TRIM

VP-DVB

VP-DMN

0.67(6) 0.33(8)

0.12(1) 0.15(5)

0.71(9) 0.47(7)

have similar, disturbingly high rates. The ILC change is about two times slower than the τLC change in both these samples. In turn, in VP-DVB, the changes in the LC parameters with time are significantly slower than in VP-TRIM and VP-DMN. Another difference between VP-DVB and the other two samples is that the ILC changes at least at the same rate as the lifetime does in this sample. It could be suspected that the result of the sealing test depends on random quality of the sealing, but the results are reproducible (Figure 3, circles). The second measurement of the VP-TRIM spectra lasted longer than 24 h, which showed that the LC parameters did not change linearly, but they tended toward a certain saturation value. At the saturation, the lifetime decreased by 21% and the intensity by 13% of their initial values. It should be noticed that these changes are significant but much smaller than the differences between the parameters before and after pressurizing the sample, which are described later. Assuming that the τLC shortening is a result of the Ps quenching by the air that has penetrated through the sealing, the ultimate air pressure can be estimated. Taking the air quenching rate of 4.0−4.7 μs−1 MPa−1,25−27 the air pressure in the sample would be 410−570 hPa, i.e., circa half of atmospheric pressure. It is highly improbable to get a relatively fast leak, which disappears far from the external pressure and which is reproducible for the same sample but different for various samples. On the other hand, it is possible that there are differences in the air solubility for particular materials, which can influence the rate of changes. However, the differences in the decrease rate differ several times. Such differences in the air solubility in quite similar materials are unlikely. Therefore, we conclude that the τLC shortening and the ILC decrease was caused by the vapors of the synthesis remnants (e.g., porogen) rather than an air leak. The comparison between the long lasting, continuous measurement (circles in Figure 3) and the continuation of the measurement, which was interrupted for the measurement at elevated pressure (crosses in Figure 3) and then resumed, gives an unexpected result. There is a distinct change in ILC,

Figure 2. Lifetimes (τ), intensities (I), and dispersion (σ) of o-Ps components in VP-TRIM as a function of (a) pressure in the lowpressure range (crosses) and the high-pressure range (circles). The large symbols represent the values measured after the release of the maximal pressure.

The dependence of the LC parameters (Figure 2) reveals two pressure regions where the character of the changes occurring in VP-TRIM is different. The initial fast decrease in τLC and σLC observed at the lowest pressures slows at ca. 40 MPa; then both parameters smoothly start to increase. The dependence of the parameters on the pressure abruptly changes at 70 MPa, and again a decrease is observed until LC eventually disappears (ILC ≈ 0) at 0.8 GPa, which indicates that all mesopores are closed. Simultaneously with the τLC and σLC changes, ILC preserves the decreasing dependence on the pressure, but a small change in its slope is observed at 70 MPa. The behavior of the SC and MC parameters does not differ in the ranges below and above 70 MPa. Their lifetimes, τSC and τMC, decrease slowly in the whole range of pressure, indicating a 11639

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Figure 5. Lifetimes (τ) and the intensities (I) of the o-Ps components in VP-DMN as a function of pressure in the low-pressure range (crosses) and the high-pressure range (circles). The large symbols represent the values measured after the release of the maximal pressure.

Figure 3. Lifetimes (τ), intensities (I), and dispersion (σ) of o-Ps components in VP-TRIM as a function of time when no pressure is applied. The black lines represent fitted exponential functions; the arrow denoted with 0 → 150 → 0 MPa indicates the time taken by the measurement in the low-pressure range presented in Figure 2.

The two other polymers, VP-DVB and VP-DMN, generally show behavior similar to that of VP-TRIM at the elevated pressure, but some differences are clearly visible (Figures 4 and 5). Unlike in VP-TRIM, both τLC or σLC exhibit monotonic dependence on pressure in VP-DVB. Still, the change in the slope of the τLC pressure dependence instead of inflection is visible at 70 MPa. In turn, almost no mark out can be found in the intensities around this pressure. The ISC increase is almost linear until it reaches 0.5 GPa. However, above this pressure, ISC starts to decrease like the other intensities instead of reaching saturation. This indicates a reduced probability of Ps formation in the polymer bulk structure, which is getting denser at the high pressure. The most distinct difference between VPTRIM and VP-DVB is the value of the pressure required for complete pore closing, which is 1.5 times higher for the second polymer. The parameters of all components in VP-DMN depend on the pressure in a way that is more similar to VP-TRIM than to VP-DVB. The nonmonotonic τLC dependence on pressure is visible, and the pores close at relatively low pressure, slightly above 0.9 GPa. Only ISC decreases above approximately 0.5 GPa, as in VP-DVB. However, the ISC change with the pressure is smaller than in VP-DVB. Moreover, the IMC decrease with the pressure is clearly visible, in contrast to that in the other polymers. Both these differences are a consequence of the small initial value of the LC intensity. The ILC decrease with the pressure is approximately two times slower than that in the other polymers. Therefore, the increase in the Ps formation probability in the smaller free spaces (i.e., Ps giving contribution to SC and MC) is reduced in comparison to VP-TRIM and VP-DMN. Pore Size Distributions. The desired information about the change in the size and concentration of mesopores under pressure cannot be read directly from the parameters of the PALS spectra presented in Figures 2−5. Therefore, pore size distributions at selected pressures were calculated for VP-TRIM and VP-DVB, for which dispersion was determined. The distributions for the whole range of pressure are best visible as dV/dlog D in a logarithmic scale (Figures 6a and 7a). However, it is difficult to estimate quantitative differences between them (e.g., surface areas under the distribution are preserved, but

Figure 4. Lifetimes (τ), intensities (I), and dispersion (σ) of o-Ps components in VP-DVB as a function of pressure in the low-pressure range (crosses) and the high-pressure range (circles). The large symbols represent the values measured after the release of the maximal pressure.

monotonous decrease in the sizes of the free spaces between polymer chains and micropores. Unlike other parameters, ISC increases until it eventually reaches saturation. This is a consequence of the relative nature of intensities. Two or more kinds of free spaces often compete in Ps formation. In this case, these are intrachain spaces (SC) and mesopores (LC). If the concentration of both types of free spaces decreases at different rates, the Ps intensity will increase for these free spaces whose concentration decreases slower. Therefore, the increase in ISC in VP-TRIM is probably caused by the slower decrease in the concentration of intrachain spaces than of mesopores. The approximately constant IMC value is most likely a consequence of the summation of two similar but opposite contributions. The reduction of the size and concentration of micropores causes the IMC decrease (like in mesopores) simultaneously, and the Ps formation probability increases because of the ILC decrease (like in free spaces between polymer chains). 11640

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Figure 6. (a) Pore size distribution calculated from the PALS spectra collected at 0, 40, 70, 350, and 780 MPa in VP-TRIM. The direction of the pressure increase is indicated by the arrows. (b) The diameter at the maximum of the pore size distribution (Dmax), the fwhm of the distribution (Dfwhm), and the pore volume (the area under the distribution) (V) as a function of the pressure applied to VP-TRIM.

Figure 7. (a) Pore size distribution calculated from the PALS spectra collected at 0, 40, 70, 350, 780, and 1130 MPa in VP-DVB. The direction of the pressure increase is indicated by the arrows. (b) The diameter at the maximum of the pore size distribution (Dmax), the fwhm of the distribution (Dfwhm), and the pore volume (the area under the distribution) (V) as a function of the pressure applied to VP-DVB.

maxima are shifted toward larger pore diameters). Therefore, the pressure dependences of the parameters describing the shape of the pore size distributions (i.e., the diameter at maximum (Dmax), the width at half of the maximum (Dfwhm), and the area under the distribution (V)) are also presented in Figures 6b and 7b. The average pore diameter (D) and the pore

volume (V) are presented in Figure 8. The comparison of the evolution of the pore size distributions with the pressure increase allows understanding the cause of the differences in the response of each sample to squeezing. 11641

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changes consist mostly of a pore volume decrease without a significant change in the shape of the pore size distribution. This suggests that pore collapse is the major process in this pressure range. Before applying the pressure to VP-DVB, the pore size distribution is shifted toward large pore sizes (Dmax is ca. 4.2 nm) and is wider in comparison to that of VP-TRIM (Figure 7). Taking into account the relatively large uncertainties of these values, we regard this result as similar to the case of VPTRIM. However, the changes of the pore size distributions during the compression are clearly different in both polymers. Even though Dmax, Dfwhm, and V decrease in VP-DVB in a manner similar to that of VP-TRIM below 40 MPa, there is no indication of pore connection between 40 and 70 MPa. Moreover, Dfwhm practically stabilizes at as low as 70 MPa. Also in the high-pressure range, the pore size distribution in VP-DVB changes slightly differently in comparison to that of VP-TRIM. The almost linear decrease in Dmax is observed in VP-DVB until the pressure reaches 0.6 GPa, which is a three times greater value than in VP-TRIM. At this pressure, approximately half of the initial pore volume is still open, but their Dmax drops to 1.3−1.5 nm, which is lower than in VPTRIM. Further changes are most likely a result of pore collapse. The lack of information about the width of the pore size distribution in VP-DMN makes it impossible to perform analyses similar to the ones presented for the other polymers. However, we can compare the character of the changes and the pressures of the inflection points with the other samples. The nonmonotonic dependence of the average pore size (D) on the pressure in VP-DMN (Figure 8) is definitely of the same origin as in VP-TRIM (i.e., pore connection). The high-pressure region shows behavior intermediate between VP-TRIM and VP-DMN. The average pore diameter stabilizes above 0.5 GPa. The D value cannot be directly compared to Dmax without the knowledge of the distribution width, but we can certainly conclude that above this stabilization pressure no change in either Dmax or Dfwhm occurs. The pores close completely at approximately 1 GPa. Porosity Restoration after Pressure Release. As already pointed out, the porosity is at least partially restored after releasing the pressure. The most distinct indicator of this fact is an increase in the mesopore related intensity (ILC) from almost zero at the maximal pressure to over half of its initial value after pressure release in all the polymers (Figures 2−5). The flexibility of the polymers manifests itself also at lower pressure, e.g., after the pressure release from 150 MPa. Figure 9 shows that Dmax and Dfwhm return to values intermediate between the

Figure 8. Average pore diameter (D) and pore volume (V) as a function of the pressure applied to VP-DMN.

The initial pore size distribution in VP-TRIM is wide and asymmetric with the maximum around 3.3 nm (Figure 6). The maximum shifts toward smaller sizes when the pressure increases to 40 MPa. Simultaneously, the distribution narrows, which causes an increase in the peak height, even though the area under it decreases. The pore size decrease is an expected effect. The reason why the pores are getting more uniform in size is less obvious. This indicates higher susceptibility to the compression of the largest pores. In the range of 40−70 MPa, where the nonmonotonic dependency of τLC and σLC is observed, V and, unexpectedly, also Dmax continue decreasing. The only increasing parameter is Dfwhm. This is possible because τLC is the average lifetime value in the distribution (not the value at the maximum, like Dmax) and it shifts with the change in the distribution width alone in the case of an asymmetric distribution. The Dfwhm change can be attributed to a substantial reconfiguration of the pore walls, which results in pore connection. Above 70 MPa, the pores continue to shrink until Dmax drops slightly below 2 nm at ca. 0.2 GPa. Further

Figure 9. Pore size distribution in (a) VP-TRIM and (b) VP-DVB before applying the pressure (solid line), at 150 MPa (dashed line), and after the pressure release (dotted line). 11642

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of a free space by a sphere and taking into account only the ground state of a Ps in a potential well. The only exception from the classic model was the assumption of Δ = 0.15 nm, as in the case of the ETE calculations, instead of the usual Δ = 0.166 nm. The plots of R as a function of pressure are very similar for all three polymers (Figure 10). They can be approximated by

initial and the pressurized values in both VP-TRIM and VPDVB. Nevertheless, the degree of the pore size change as well as the total pore volume change seems to be different in each polymer. The quantitative data (Table 2) confirm this Table 2. Diameter at Maximum (Dmax), Width at Half of the Maximum (Dfwhm), and Area (V) under the Pore Size Distribution in VP-TRIM, VP-DVB, and VP-DMN before Applying the Pressure, under Pressure, and after Pressurizinga p (MPa) 0 150 0 (after 150 MPa) 0 (after 0.78 GPa) 0 150 0 (after 150 MPa) 0 (after 1.3 GPa) 0 150 0 (after 150 MPa) 0 (after 0.95 GPa)

Dmax (nm) VP-TRIM 3.25(12) 2.35(4) 2.72(6) 2.30(3) VP-DVB 4.33(31) 2.26(2) 3.02(8) 2.42(2) VP-DMN 6.23(11) 4.06(8) 6.01(1) 4.42(5)

− − − −

Dfwhm (nm)

V (a.u.)

2.78(4) 1.58(1) 2.28(1) 1.65(3)

1.55(4) 0.62(1) 1.08(2) 1.02(1)

4.34(14) 1.22(6) 2.18(1) 1.45(2)

2.12(8) 1.23(1) 2.04(2) 1.89(1) 1.94(6) 1.14(6) 1.49(6) 1.24(4)

Figure 10. Radius of a sphere that approximates the mean free spaces between polymer chains in VP-TRIM (circles), VP-DVB (crosses), and VP-DMN (stars) as a function of pressure. The solid lines represent fitted exponential functions. The large symbols represent the values measured after the release of the maximal pressure.

a

For VP-DMN, the average diameter, D, is presented in the Dmax column.

observation. The relative change in Dmax in VP-TRIM (ca. 30% after maximum pressure) is much smaller than that in VPDVB (∼45%). The same tendency is found for Dfwhm, but in this case, the changes are even greater (∼40% and ∼70% respectively). On the other hand, the pressure-induced change in the total pore volume, V, shows the opposite tendency. The relative volume decrease in VP-TRIM (∼35%) is greater than that in VP-DVB (∼10%). The different method for spectra analysis used in the case of VP-DMN makes the reliability of the results for this sample uncertain. Nevertheless, the changes in Dmax and V are similar to those in VP-TRIM. The only difference is the slightly lower susceptibility of VP-DMN to the pressure-induced changes, i.e., the relative change in the parameters after pressure release from 150 MPa in VP-DMN is smaller than that in VP-TRIM, while practically the same relative change after pressure release is observed in both samples if VP-DMN was pressurized to almost 20% higher pressure. The results obtained after applying and then releasing pressure at which all pores are closed (Table 2) do not show porosity degradation either. On the contrary, the increase in V followed by a further decrease in Dmax and Dfwhm are observed. The increase may seem suspicious because an LC intensity decrease was presented previously (Figures 2 and 4). However, it should be noted that after pressurizing the pore sizes are shifted toward the small pores range (∼2 nm), where the same o-Ps intensity corresponds to a ca. 2 times larger volume than that for the large pores (3−4 nm).23 Intrachain Spaces. The short-lived component (SC) provides interesting information about the bulk of the polymers. The radii (R) of the free spaces between polymer chains were calculated from τSC using the Tao−Eldrup model28,29 with the classic assumptions, i.e., the approximation

exponential decays with the decay rate λp ≈ 2 GPa−1 and the saturation value Rp→∞ ≈ 0.17 nm. The similar polymer compressibility suggests that the major cause of the different behaviors under pressure are not differences in the polymer network structure (e.g., a cross-linking) but the arrangement of pores (e.g., their connectivity or shape) and/or the pore wall flexibility. After the pressure release, the size of the free spaces practically returns to the initial values in all the polymers.

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CONCLUSIONS The PALS measurements of porous materials under mechanical pressure require sealing the sample in an air-evacuated chamber. Such measurement in static vacuum does not ensure stability of the results in time. However, the instability is low enough to facilitate observation of much larger changes in the lifetimes and the intensities of the o-Ps components. The qualitative estimation of the pore size and their volume in the particular materials provides reasonable results. However, it has to be kept in mind that the values obtained can be underestimated, especially near the end of a measurement series. The analysis of the time drift of the results in the various samples leads to the conclusion that the drift is more likely caused by vapors from the sample than an air leak. The dependence of three o-Ps components on the pressure is consistent with identification thereof as spaces between polymer chains, micropores, and mesopores. The lifetime and intensity of the longest-lived o-Ps component change significantly with pressure in all the studied porous polymers. This indicates a large change in the size and, especially, the concentration of pores. The mesopores eventually disappear under pressure of the order of 1 GPa. The highest pressure 11643

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required for the complete pore collapse is observed in VP-DVB; the lowest such pressure is observed in VP-TRIM. Such an order cannot be related either to the initial pore size or to the pore concentration. Similarly, the changes in the shortest-lived o-Ps component, which originates from the free spaces between polymer chains, do not indicate significantly greater compressibility of any of the polymers studied. Only the ratio between the intensity after pressure release and the initial one shows a correlation with the pressure required for the pore collapse. This suggests that the smaller the susceptibility to permanent changes the higher the pressure required for pore collapse. This relation is slightly deviated for VP-DMN in the case of the calculated total volumes. However, this can be attributed to neglecting the lifetime dispersion in the VP-DMN spectra, which renders the results for this sample not fully comparable to those in which dispersion was taken into account. The above observations correlate with the rigidity predicted based on the composition of the materials. The most resistant is VP-DVB, where the concentration of carbon rings is the highest. The ester bonds in VP-TRIM are much more flexible in comparison to the aromatic rings. The properties of VP-DMN can be regarded as an outcome of the presence of both the aromatic rings and the ester bonds in the polymer network. The pressure regions, where the particular processes of pore transformation (e.g., pore connection or collapse) dominate, can hardly be recognized in VP-DVB. This may indicate greater rigidity of the VP-DVB bulk or else a different pore structure (e.g., less interconnected) in comparison to the other polymers, which results in greater resistance to deformation. The effect interpreted as the pore connection occurs at the same pressure in both VP-TRIM and VP-DMN. This is somewhat surprising because each polymer has a different composition, pore size, and pore concentration. The difference in the composition of the pore walls is not reflected in any way in the pressure dependences of the short-lived o-Ps component related to the spaces between polymer chains. The mean volume of the single free space in the polymer bulk decreases to about 25% of its value without the pressure (65% of the sphere radius) at about 1 GPa in each polymer. Then, in all the materials, it restores completely to 0.1 nm3 after the pressure release. All the observations described previously support the supposition that a property undetectable by PALS, such as the pore structure, determines the behavior of porous polymers under the pressure. Unfortunately, it is difficult to verify the differences in the pore structure by the standard methods like electron microscopy because electron energies required to obtain magnifications sufficient to observe mesopores are high enough to melt a polymer. The partial recovery of the porosity after the pressure release in the studied materials can be used as a novel method for pore size and volume tailoring. The application of various pressures allows easy acquisition of porous polymers with different porosities from the same initial material.

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Article

AUTHOR INFORMATION

Corresponding Author

*Phone: +48 81 537 61 45. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

MATLAB script for calculation of pore size distributions, the extended Tao−Eldrup model data required by the script, results of the PALS spectra analysis, pore size distributions, shape parameters of the pore size distributions, AFM micrographs, and SEM micrographs. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b01722. 11644

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