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Mesoscale Polymer Dissolution Probed by Raman Spectroscopy and Molecular Simulations Tsun-Mei Chang,† Sotiris S. Xantheas,*,‡ and Andreas E. Vasdekis*,§,∥ †

University of WisconsinParkside, P.O. Box 2000, Kenosha, Wisconsin 53141, United States Physical Sciences Division, Pacific Northwest National Laboratory, 902 Battelle Boulevard, P.O. Box 999, MS K1-83, Richland, Washington 99352, United States § Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, United States ∥ Department of Physics, University of Idaho, Moscow, Idaho 83844, United States ‡

S Supporting Information *

ABSTRACT: The diffusion of various solvents into a polystyrene (PS) matrix was probed experimentally by monitoring the temporal profiles of the Raman spectra and theoretically from molecular dynamics simulations. The simulation results assist in providing a fundamental, molecular-level connection between the mixing/ dissolution processes and the difference, Δδ = δsolvent − δPS, in the values of the Hildebrand parameter (δ) between the two components of the binary systems: solvents having values of δ similar to those for PS (small Δδ) exhibit fast diffusion into the polymer matrix, whereas the diffusion slows down considerably when the δ’s are different (large Δδ). To this end, the Hildebrand parameter was identified as a useful descriptor that governs the process of mixing in polymer−solvent binary systems. The experiments also provide insight into further refinements of the models specific to non-Fickian diffusion phenomena that need to be used in the simulations.

P

more recently demonstrated Solvent Immersion Imprint Lithography (SIIL), specific to microstructures and microfluidics14 as well as polymer sensors.15 Polymer−solvent interactions controlling processes such as miscibility, swelling, and dissolution are usually discussed in the context of the Hildebrand solubility parameter,16,17 δ, defined as

olymers have made a significant impact in science and everyday life due to their ability to undergo shape changes at a low energy cost in a wide range of stimulants, such as temperature and electrical or electromagnetic fields, as well as solvents.1−4 With regard to the latter, upon contact between a polymer matrix and thermodynamically compatible solvent (vide infra), polymer dissolution takes place, primarily through two transport mechanisms.5,6 The first is solvent diffusion into the polymer, giving rise to polymer plasticization and a gel-like layer proximal to the solvent. The second is the disentanglement of the polymer chains and eventually their separation from the matrix itself. These basic forms of polymer−solvent interactions have found a wide variety of applications, such as in the bottom-up synthesis of asymmetric membranes7 or in drug delivery, where therapeutic agents can be discharged from the host polymer in controlled amounts and with controlled kinetics upon interaction with the solvent.8,9 Finally, polymer dissolution has been of considerable importance in microfabrication, such as in the traditional field of photolithography, in which solvents selectively remove areas of a polymer film exposed (or not) to radiation,10,11 or in more recent ones, such as direct fabrication of polymer nano- and micro-structures. One such approach specific to nanostructures is Solvent Assisted Micromolding (SAMIM), developed by the Whitesides group.12,13 We have © 2016 American Chemical Society

δ=

ΔH v − RT Vm

(1)

where ΔHv is the solvent’s enthalpy of vaporization, Vm is the solvent’s molar volume, T is the temperature, and R is the ideal gas constant. δ measures the square root of the cohesive energy density, that is, the amount of energy required to convert a unit of volume of the material from the condensed to the gaseous phase. The closer the solubility parameters between two materials (polymer vs solvent in the case at hand), the easier it is for them to interact with each other. This parameter was originally developed for hydrocarbon solvents, whereas more recent extensions introduced by Hansen18 have included the Received: June 2, 2016 Revised: September 20, 2016 Published: September 21, 2016 10581

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Figure 1. Temporal profiles of the Raman intensity, obtained via eq 2, for the PS−solvent binary systems for hexane, 1-propanol, and acetonitrile. The dark lines denote the Fickian fits per experimental condition.

Figure 2. Snapshots of the MD simulations of the solvent−PS binary systems at t = 25, 50, 75, and 100 ns. The various solvents are shown in the upper part of the panels in different colors. The difference in the experimental (theoretical) Hildebrand parameter between PS and the various solvents is listed at the top.

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spectra. The temporal profiles, P(t), of the Raman intensity (I) were derived using the following expression20

Table 1. Molecular Properties and Hildebrand Parameters (δ) Obtained Experimentally (at T = 298.2 K) and Calculated (in Parentheses) for PS and the Various Solvents Considered in This Studya compound

ΔHv (kcal/mol)

PSb hexane

(37.54) 7.54 (7.36)

chloroform

7.48 (7.43)

acetone

7.41 (7.09)

acetonitrile

7.93 (7.69)

1-propanol

11.34 (10.11)

ρ (g/cm3) (1.044) 0.661 (0.656) 1.479 (1.470) 0.785 (0.801) 0.780 (0.772) 0.800 (0.795)

Mm (g/mol)

δ (cal/cm3)1/2

432.6 86.18

9.13 (9.44 ± 0.52) 7.30 (7.18 ± 0.53)

119.4

9.23 (9.18 ± 0.67)

58.08

9.60 (9.47 ± 0.73)

41.05

11.79 (11.55 ± 0.81)

60.09

11.96 (11.22 ± 0.59)

profile(t ) =

Isolvent(t ) − Ibackground(t ) Ipolymer(t ) − Ibackground(t )

(2)

Duplicate samples were tested for each condition, and the temporal profiles were averaged. Classical MD simulations were carried out to investigate the dissolution processes between PS consisting of four monomer units and various solvents, including hexane, chloroform, acetone, acetonitrile, and 1-propanol. The energy of the system was decomposed into a sum of Lennard-Jones (LJ), Coulombic, and intramolecular interactions. All intramolecular bonded interactions (harmonic-bond bending, dihedral potentials, and bond stretching) were taken from the AMBER force field.21 All MD simulations used all-atom (AA) pairwise potential models to describe intermolecular interactions that included LJ parameters and point partial charges on AA sites. The charges and LJ parameters were taken from the optimized potential for liquid simulations (OPLS)-AA force fields for the acetone, hexane, 1-propanol, and PS potentials. 22 For acetonitrile, a six-site model developed by Nikitin et al.23 was used, whereas for chloroform, a potential modified from our previous model was employed.24 Standard Lorentz−Berthelot combining rules were used to describe the cross LJ interaction terms between unlike atoms. All MD simulations were carried out using the AMBER simulation package.25 The simulations were performed for systems containing 200 PS molecules and 1000 acetone, 1000 chloroform, 620 hexane, 1200 1-propanol, or 1600 acetonitrile molecules. All MD simulations were carried out using rectangular boxes, in which the lateral dimensions were identical (51.6 Å), whereas the interfacial dimension (z axis) was larger (around 170 Å). The initial configurations of the systems were obtained by joining a polymer slab and a liquid solvent slab, which have been equilibrated separately to produce the correct bulk densities. The total energy of the initial structures was first minimized to remove the excess strain. After energy minimization, we followed the system evolution for 100 ns at a constant volume and temperature (NVT ensemble), with the temperature of the system maintained at T = 300 K using a Langevin dynamics thermostat.26−28 A time step of 2 fs was used to integrate the equations of motion. A molecular cutoff of 10 Å was used for LJ interactions, and the particle mesh Ewald method was employed to handle the long-range Coulombic interations.29,30 During the entire simulation process, periodic boundary conditions were applied in all three spatial directions and all of the bonds involving hydrogen atoms were constrained using the SHAKE algorithm. Molecular configurations were saved every 10 ps during the 100 ns production run for data analysis. To evaluate the Hildebrand solubility parameters of various solvents using eq 1, we carried out additional MD simulations of pure solvents at a constant pressure and temperature (NPT ensemble) and in the vapor phase. The molar enthalpy of vaporization, ΔHv, can then be determined from

The error bars in the computed δ’s are estimated using a ±1 kcal/mol error in ΔHv. ΔHv is the solvent’s enthalpy of vaporization; ρ is the density; Mm is the molar mass; and δ is the Hildebrand parameter. b The calculated values are for a PS with four monomers. a

effects of hydrogen bonding and polar solvents. Both Hildebrand and Hansen solubility parameters have been previously reported for a variety of compounds from molecular dynamics (MD) simulations.19 In this article, we report experimental Raman spectroscopic and theoretical MD results that probe the interactions and subsequent mixing between polystyrene (PS) and various solvents (acetonitrile, 1-propanol, hexane, acetone, and chloroform). Our combined experimental/theoretical effort provides a fundamental, molecular-level connection between the observed phenomena and the difference in the values of the Hildebrand parameter between the two components of the binary system, which was identified as a useful descriptor that governs the process of mixing in polymer−solvent binary systems. The experiments were performed at room temperature for PS−solvent mixtures of the three solvents, namely, hexane, 1propanol, and acetonitrile (all from Sigma-Aldrich, with a purity greater than 99%). A confocal Raman spectrometer (Raman; HORIBA Jobin Yvon) combined with a Nikon Eclipse Ti microscope with an automated stage and an excitation source of 532 nm was used to record the spectra. To carry out the dynamic Raman analysis, the PS sample (1.2 mm thick slabs with a surface area of approximately 6 cm2; Goodfellow, UK) was bonded on a perforated glass Petri dish using NOA 86 UVcurable epoxy (Norland Adhesives). The PS−glass Petri dish combination was placed on the microscope, and the top surface of the PS slab was identified via bright-field transmission microscopy using a 40× magnification objective and the microscope’s charge-coupled device detector. Subsequently, 10 mL of the solvent was dispensed on top of the polymer, and the Petri dish was covered to eliminate solvent evaporation. The Raman spectra were acquired by translating the stage z = 200 μm below the polymer surface. To ensure high signal-tobackground noise, the integration time was, on average, 10 s for all experimental conditions. The confocal aperture was held constant at a diameter of 50 μm, and an optical excitation power of 12 mW was employed in all experiments. The spectra were subsequently analyzed by considering the representative Raman peaks of the PS matrix and each solvent separately, see Figure S1 of the Supporting Information for the annotated peaks and Table S1 for the integration ranges of the Raman

ΔH v = Egas − E liq + RT

where Egas and Eliq are the molecular energies in the gas and liquid phases, respectively. Additionally, the molar volume, Vm, can be determined from the simulated liquid density and the Hildebrand solubility parameter can be evaluated from eq 1. 10583

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Figure 3. Snapshots of the MD simulations of the solvent−PS binary systems, showing the diffusion of PS into the various solvents (not shown) at t = 25, 50, 75, and 100 ns. The difference in the experimental (theoretical) Hildebrand parameters between PS and the various solvents is listed at the top.

Vm) Hildebrand parameters (δ) are listed in Table 1. The experimental ΔHv and Vm values were taken from ref 35 (at T = 25 °C). In Table 1, the error bars associated with the computed δ’s correspond to a ±1 kcal/mol error in the computed ΔHv’s. For PS, the experimental δ = 9.13 (cal/cm3)1/2, whereas the calculated value for a four-monomer unit is 9.44 (cal/cm3)1/2. Overall, the computed Hildebrand parameters are in good agreement with the experimentally obtained ones, albeit the former were always found to underestimate the latter. The signed errors of the computed δ’s, relative to the experimental ones, are −1.7% (hexane), −0.6% (chloroform), −1.3% (acetone), −2.0% (acetonitrile), and −6.2% (1-propanol). Figure 2 shows typical snapshots of the binary PS−solvent systems at 25, 50, 75, and 100 ns simulation times, for hexane, chloroform, acetone, acetonitrile, and 1-propanol. The column panels are ordered from left to right in terms of the increasing signed dif ferences in the Hildebrand parameters between PS and

The temporal profiles of the intensity (I) of the Raman spectra, obtained via eq 2, for various PS−solvent binary systems are shown in Figure 1 for hexane, 1-propanol, and acetonitrile. With the exception of acetonitrile, the solvents exhibit the characteristics of Fickian diffusion,31 with a lower diffusion rate observed for hexane and a higher one for 1propanol. In contrast, acetonitrile exhibited a sigmoidal nonFickian sorption (S-shaped), with a characteristic slow diffusion initially (up to ∼475 s), followed by a faster solvent penetration rate, saturating at approximately 2000 s.32,33 Such a behavior is indicative of the limited sorption kinetics at the polymer interface. This, in turn, leads to the slowing of solvent molecules before diffusing into the polymer matrix.34 To obtain deeper physical insight into and a molecular-level understanding of the observed PS−solvent interactions, we rely on the picture rendered by the results of the MD simulations. The experimentally obtained as well as computed (via ΔHv and 10584

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the respective solvent; the experimental differences are estimated with respect to a value of 9.13 (cal/cm3)1/2 for PS, whereas the differences between the calculated δ’s (in parentheses in Figure 2) are estimated with respect to the computed value of 9.44 (cal/cm3)1/2, cf. Table 1. In this respect, the order based on the experimental differences is hexane, chloroform, acetone, acetonitrile, and 1-propanol, and this order (save the last two) is also reproduced from the theoretically computed differences. It should be noted that for solvents with δ values very close to that of PS (such as for chloroform and acetone in our case), the diffusion of the solvent into the PS matrix is so fast that it cannot be experimentally captured by the temporal profiles of the Raman spectra. Specifically, attempts to perform such experiments not only suffered from limited temporal resolution but also resulted in the solvent either completely dissolving the polymer or substantially modifying the polymer−solvent interface due to swelling. For this reason, only the profiles for hexane, 1-propanol, and acetonitrile are shown in Figure 1. In general, there is good correspondence between the difference in δ’s between PS and the solvent (cf. Table 1 and Figure 2) and the experimentally observed diffusion profiles of Figure 1. Hexane and 1-propanol have comparable, large Δδ’s with respect to PS (Δδ = δsolvent − δPS), and for this reason, they exhibit smaller, comparable diffusion rates. Albeit having a smaller Δδ than 1-propanol with respect to PS, acetonitrile exhibits a delayed diffusion onset, due to the aforementioned interfacial phenomena underlying a sigmoidal diffusion process. For this reason, acetonitrile exhibits a larger diffusion rate into the PS matrix. The above are evident from Figure 3, in which only the PS molecules diffusing into the solvent are shown. It is clear that the dissolution of PS into the solvent is larger for chloroform and acetone (for which the dissolution rate is so high than it cannot be captured by the temporal profiles of the Raman spectra shown in Figure 1), whereas the rate for acetonitrile is larger than that for 1-propanol. We have estimated the diffusion rates from the results of the MD simulations based on Fick’s law. Assuming a steady state, the number of solvent molecules that cross the interface can be related to flux J (amount of material transferred per unit area) via

Figure 4. Density profiles at 1 ns and 100 ns for the various PS− solvent binary mixtures. The density profiles at 1 ns were used to estimate the concentration gradient.

J=D

dz

approximated by the change in concentration across the interfacial width. Flux J can be estimated by obtaining the number of molecules penetrating into PS as a function of time, with the caveats that (1) the statistics are poor because the amount of solvent molecules crossing the interface is small and (2) the fitting of the curve is to a straight line (J is estimated from the slope). The concentration gradient is estimated from the simulation at 1 ns, something that was deemed appropriate given the density profiles for the various solvents at 1 ns, and at 100 ns, shown in Figure 4 (see also Figure S2). The diffusion constant, D, is then estimated as the ratio of flux J over concentration gradient dC .

Table 2. Estimated Diffusion Coefficients for the PS− Solvent Binary System via Equation 3a diffusion constant (cm2/s) solvent

calculated 2.7 2.7 1.8 1.1 4.6

× × × × ×

10−8 10−8 10−8 10−8 10−9

(3)

where C is the concentration (or density), D is the diffusion constant, and z is the interfacial coordinate. The derivative dC is

Figure 5. Estimate of the flux, J, from the MD simulations (see text for details).

chloroform acetone acetonitrile hexane 1-propanol

dC dz

experimental

1.7 × 10−7 ± 1.8 × 10−8 3.7 × 10−7 ± 9.8 × 10−8 6.2 × 10−7 ± 8.9 × 10−8

a

See text for details. Specifically for acetonitrile, the experimental diffusion coefficient was determined for the first 500 s.

dz

The number of solvent molecules crossing the PS−solvent interface and their corresponding linear fits, used to estimate J, are shown in Figure 5. Estimates of the diffusion coefficients are listed in Table 2. Even these rough estimates of the diffusion 10585

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ACKNOWLEDGMENTS S.S.X. was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences. Pacific Northwest National Laboratory (PNNL) is a multiprogram national laboratory operated for DOE by Battelle. This research also used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DEAC02-05CH11231. A.E.V. acknowledges funding from the INBRE program (Project ID: P20 GM103408), the National Institutes of Health (NIH), and the Pacific Northwest National Laboratory (Linus Pauling Fellowship − PN12005/2406). Part of the research was performed at EMSL, a national user facility sponsored by the Department of Energy’s Office of Biological and Environmental Research located at Pacific Northwest National Laboratory.

constants, limited by the poor statistics, were found to qualitatively capture the trend in the relative diffusion coefficients between the solvents, seen experimentally for hexane and 1-propanol. The simulation results suggest a larger diffusion of both chloroform and acetone into the PS matrix (solvents having similar δ’s to those of PS), a result that is consistent with the finding that it cannot be captured experimentally by following the temporal Raman profiles. The next larger diffusion coefficient is for acetonitrile, with that for hexane and 1-propanol being smaller. Experimentally, the diffusion coefficient of acetonitrile during the first 500 s is consistent with the experimental observations shown in Figure 1, which is approximately 1.7 × 10−7 ± 1.8 × 10−8 cm2/s. As previously mentioned, this is largely due to the limited sorption kinetics at the solvent−polymer interface, which is not currently captured by the simulation results. The experimental diffusion constants for the binary PS− solvent system were estimated from Fick’s second law, which was used to model a macroscopic process that entails several steps. The first step in this process is always slow, and perhaps, this is the one actually probed from the (short) 100 ns MD simulations, a fact that explains why the theoretically estimated diffusion constants are much smaller (by approximately 1 order of magnitude for acetonitrile and hexane and 2 orders of magnitude for 1-propanol) than the experimental ones. In addition to the poor statistics mentioned earlier, the theoretically estimated diffusion constants were also obtained via eq 3 by assuming a steady state, which is likely to be a gross approximation for the early slow step of the diffusion process. Additionally, the discrepancy between the experimental and computational results with regard to the non-Fickian process of acetonitrile further supports the need to incorporate additional interfacial mass transfer coefficients into the models used to study these processes. In conclusion, Hildebrand parameter δ was identified as a useful descriptor of the solvent−polymer dissolution process. In particular, binary systems with similar values of δ were found to exhibit fast diffusion into each other. The diffusion process slows down significantly when the binary system is comprised of components with different values of δ. For the cases of binary systems exhibiting non-Fickian diffusion, more advanced models need to be used to capture the underlying molecularlevel interactions and mesoscale responses.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b05565. Additional information regarding the experimental (Raman spectra and their integration ranges) and computational (density profiles at various simulation times) results (PDF)

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Article

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (S.S.X.). *E-mail: [email protected] (A.E.V.). Notes

The authors declare no competing financial interest. 10586

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