Polymer nanocomposites (PNCs) are of interest for commercial applications because their wide range of properties makes them attractive materials for coatings 1,2 , membranes 3,4 , and actuators 5 . Typically, PNCs contain inorganic nanofiller dispersed in a polymeric matrix. PNCs have been of interest in academia, national laboratories and industrial laboratories [6][7][8] because of their superior performance as compared to unfilled polymers. For instance, by adding nanoparticles into a polymer matrix, PNCs with ultrahigh strength and toughness can be designed as protective coatings 9,10 . In part, the properties of the PNC depend on processing conditions which determine nanoparticle dispersion and material properties, such as nanoparticle loading, nanoparticle type and matrix polymer properties. In most systems, the thermodynamics of mixing is unfavorable and nanoparticles aggregate, particularly at high loadings. Even for the rare cases where the nanoparticle and polymer have a favorable thermodynamics of mixing, slow nanoparticle diffusion due to the high viscosity matrix can lead to kinetically trapped aggregates of nanoparticles. This arrested state is even more prevalent when producing PNCs with high loadings. For example, below 0.05 vol%, nanoplates uniformly sequester in one domain of a lamellar block copolymer (BCP), whereas at higher loadings nanoplates aggregate and frustrate BCP ordering 11,12 . In summary, PNCs with a high loading of nanoparticles (e.g., near percolation) are typically difficult to prepare while maintaining control over PNC morphology.
In our previous studies 13,14 , we circumvented the difficulties of nanofiller-limited loading and inhomogeneous dispersion by infiltrating polymer into the pores of a prefabricated bicontinuous nanoporous gold (NPG). This polymer-infiltrated NPG (PING) nanocomposite exhibits inorganic loadings of ~50 vol%. PING preparation utilizes a capillary force to drive molten polymer into the NPG with pore diameters from 15 to 75 nm 15 , and similar strategies have been used in previous work to infiltrate densely packed nanoparticles [16][17][18][19][20][21][22][23][24] and anodized aluminum oxide (AAO) pores [25][26][27][28] . Starting with a polymer film on top of the NPG, the bilayer is heated above the polymer glass transition temperature (𝑇 𝑔 ). Subsequently, capillarity drives the polymer melt through the porous network spanning the NPG thickness, resulting in a PNC that retains the original NPG structure. Capillary rise infiltration (CaRI) has been used to prepare PNCs using scaffolds of densely packed nanoparticles [16][17][18][19][20][21][22][23][24] and anodized aluminum oxide (AAO) pores [25][26][27][28] . Through capillary-driven infiltration, high nanofiller loading was achieved.
Confinement can perturb polymer characteristics and properties compared to bulk behavior 13,14,25,27,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] . The conformations of polymer chains are distorted when confined to pores with a size comparable to the polymer, and this distortion, in turn, influences polymer dynamics. Previous work has shown that polymers can exhibit a higher 𝑇 𝑔 in confined geometries 13,19,24,48,49 , depending on the nature of the interactions of the polymer with the confining surfaces. As confinement increases, the polymer segmental relaxation dynamics slow down, and 𝑇 𝑔 increases 50 . For example, Maguire et al. (2021) found that the 𝑇 𝑔 of PS increased by 6℃ when confined in NPG with a pore size (𝑅 𝑝 ) greater than the radius of gyration (𝑅 𝑔 ) 13 . In a complementary study, for PS highly confined in packed nanoparticles (𝑅 𝑔 < 𝑅 𝑝 ), the 𝑇 𝑔 increased by 57℃ compared to the bulk 49 . Despite this increase in 𝑇 𝑔 for completely filled nanocomposites, polymer infiltration into confined or semi-confined pores shows enhanced kinetics 14,16,19,24,51,52 . For entangled PS infiltrating NPG under moderate confinement, the effective viscosity decreased by over an order of magnitude relative to the bulk viscosity, and this difference increased as 𝑀 𝑤 increased 14 . For entangled PS infiltration in highly confined SiO2 packing, the effective viscosity also decreased 16 . However, for unentangled PS and P2VP infiltrating into SiO2, a significant slowdown is observed 19 . The seemingly conflicting effect of confinement on polymer infiltration kinetics has remained largely unresolved.
In this study, we investigate the effect of polymer / wall interactions on the kinetics of polymer infiltration into NPG structures. In our preceding study 14 , polystyrene (PS), which weakly interacts with the NPG, exhibited a reduced effective viscosity relative to the bulk and a weaker viscosity dependence on 𝑀 𝑤 over the range 424k to 1133k Da. To better understand the underlying mechanism, molecular dynamics (MD) simulations were used to show that the weak 𝑀 𝑤 dependence and the enhanced kinetics were attributed to a reduction in the chain entanglement density and a reduction in the polymer-wall adsorption fraction as 𝑀 𝑤 increases 14 .
Some prior studies indicated that interfacial energy did not affect chain-scale polymer dynamics 19,53,54 . For instance, Hor et al. (2018) investigated the infiltration of unentangled P2VP and PS for confinement parameter 𝛤 >1, where 𝛤 = 𝑅 𝑔 /𝑅 𝑝 , and found that the normalized viscosities were impacted in the same way for stronger polymer-wall interaction system (P2VP) as well as the weaker polymer-wall interaction system (PS) 19 . However, other studies suggest that stronger interfacial interactions decrease polymer kinetics. As a comparison, Maguire et al. (2021) found that infiltration time of entangled P2VP in NPG was an order of magnitude longer than that of PS under the same conditions 13 . In summary, prior studies are inconclusive about the effect of the polymer-wall interactions on infiltration kinetics.
The present study focuses on the kinetics of infiltrating poly(2-vinylpyridine) (P2VP) into nanoporous scaffolds with 𝑅 𝑝 of 34 nm. For 𝑀 𝑤 from 51k to 940k, infiltration conditions are "moderate" with 𝛤 ranging from 0.18 to 0.78. For comparison, 𝛤 > 1 would correspond to stronger confinement of chains. A key finding is that infiltration time scales as 𝜏 80% ∝ 𝑀 𝑤 1.43 , which is much weaker than the prediction based on the bulk behavior, 𝜏 ∝ 𝑀 𝑤 3.4 . For 𝑀 𝑤 < 180,000 Da., the effective viscosities are greater than the bulk values, whereas for 𝑀 𝑤 > 180,000
Da., the effective viscosities are lower than the bulk values. This transition occurs when the 𝑀 𝑤 is approximately 5x above the bulk critical 𝑀 𝑤 and is consistent with confinement reducing chain entanglements. The similarity of the molecular weight dependence of infiltration time for P2VP and PS is attributed to a strongly bound layer in the P2VP case. To investigate the effect of polymer-wall affinity, coarse-grained MD simulations were performed for systems with varying polymer-wall interactions. MD simulations support experimental results and show that polymers with a strong attraction for the wall results in slower infiltration. MD simulations show that infiltration time scales as 𝜏 ~ 𝑀 𝑤 1.4 in good agreement with experiments. This study allows us to better understand the effect of polymer-wall adsorption on infiltration into nanoporous channels, and to prepare nanocomposites at high filler loadings that are difficult to achieve by blending polymers and discrete particles.
Samples. The poly(2-vinylpyridine) (P2VP) and polystyrene (PS) samples with different molecular weights were purchased and used as received. Important molecular characteristics and length scales are described in Table 1. , where the Kuhn monomer molar mass is 720 Da 55 . P2VP and PS solutions are prepared using 2.4 wt.% of polymer in methanol and toluene, respectively. After stirring overnight, solutions are spin coated onto silicon wafers (1 cm x 1 cm) at 4000 rpm for 1 minute. After that, the polymer films are annealed at 60°C in the Mettler heating stage (Mettler FP-82) under argon flow for 10 minutes to ensure evaporation of the solvent. The polymer thicknesses range from 100-300 nm as measured by reflectometer (Filmetrics F3UV).
The 𝑇 𝑔 ′𝑠 for bulk PS and P2VP are nearly identical when measured at the same cooling rate, 𝑇 𝑔 = 100 ℃ 56,57 . The 𝑇 𝑔 of PS-168k and P2VP-153k films on silicon substrates were measured using in-situ SE. To ensure equilibrium, the polymer films were first heated to 150 ℃, held at 150 ℃ for 5 min., and then cooled down at a rate of 10 ℃/min. Analysis of the SE output to determine 𝑇 𝑔 is described in SI information (Fig. S2). The PS-168k film (90 nm) has a 𝑇 𝑔 = 97 ± 2 ℃, whereas the P2VP-153k film (130 nm) has a 𝑇 𝑔 = 98 ± 2 ℃.
Nanoporous Gold (NPG) Fabrication. NPG is crucial and is used as the scaffold for measuring polymer infiltration kinetics during the PING formation. NPG are prepared using a gold alloy anodic corrosion method 58 . A Au-Ag (12 karat) foil with Au35Ag65 at %, is purchased and used as received. 15.8 M Nitric Acid is used to selectively etch Ag from the 12 karat composite. As the Au-Ag foil is immersed in nitric acid, HNO3 first dissolves the less noble Ag atoms at the interface, leaving behind the Au rich layer. Subsequently, the Au atoms nucleate and grow Au-rich islands, which in turn exposes the underlying layer containing Ag. The Au islands eventually form a bicontinuous structure. The fabrication and structural characterization of the NPG has been previously studied [13][14][15]59,60 . Due to the high mobility of the gold atoms, the NPG scaffolds are annealed at 175°C for 3 h prior to forming a bilayer with the polymer. This preannealing step prevents structural changes in the NPG during polymer infiltration at 140°C 13,14 .
Bilayer Formation. This NPG scaffold is then deposited on a P2VP film using a float lifting method. To form the NPG/P2VP bilayer, the pre-annealed NPG (1cm x 1cm) is floated onto a DI-H2O surface. The suspended NPG is then lifted from underneath by a silicon wafer previously coated with a thin P2VP film. The bilayer is then dried on a hot plate at 60°C until water evaporates from the sample surface.
In-Situ Ellipsometry. Spectroscopic ellipsometry (SE) (J.A. Woollam, Alpha SE) is used to determine the infiltration extent of polymers in the NPG. The wavelength range is 380-900nm.
A Linkam THMSEL350V heating stage with a vacuum chamber is used to heat the bilayer. The accuracy of the heating stage is 0.1°C with respect to the set temperature. The heating rate is 30°C/min. The samples are heated to 70°C and held at this temperature for 5 minutes to ensure system equilibrium before ramping to 140°C. Subsequently, the temperature is heated at a rate of 30°C/min and then held at 140°C to study infiltration. Because the P2VP and PS both have 𝑇 𝑔 around 100°C, temperatures higher than 100°C will induce polymer infiltration into NPG.
Because the heating stage takes ca. 1.3 min to ramp from 100°C to 140°C, the infiltration time includes this initial transient contribution. During infiltration, the temperature is held at 140°C.
The Effective Medium Approximation (EMA) Model with two material components is used to model the change in optical constants within the NPG composite as polymer fills the pores and approaches the top surface. The detailed SE modeling has been described in our previous publications 13,14 . In addition to this two layer model (Au/P2VP filled Au), we have incorporated a bound layer into the P2VP filled Au and compared results at infiltration extent of 60%. At the same level of fitting quality, the refractive indexes used in both fits differed by only 0.00009.
This result supports the use of the simpler model used here and elsewhere 13,14 . The infiltration extent (IE) is given by, 𝐼𝐸 = (𝑛 𝑡 -𝑛 𝑖 ) (𝑛 𝑓 -𝑛 𝑖 ) . The initial refractive index, 𝑛 𝑖 , is calculated by averaging the refraction index values during the first six min (i.e., prior to the P2VP infiltration). The final refractive index (after complete infiltration), 𝑛 𝑓 , is calculated by averaging the refraction index during the last two minutes when infiltration is complete. Small Angle X-Ray Scattering (SAXS). Dual Source and Environmental X-Ray Scattering (DEXS, Xenocs Xeuss 2.0) at the University of Pennsylvania is used for measuring the NPG ligament to ligament distance. Six tubes with sample to detector distance of 6390 mm results in a q0 range of 0.003-0.09 Å -1 . Cu Kα, with a wavelength of 1.54 Å, is used as the light source. NPG samples are peeled off from the substrate using Kapton tape. The scattering data is collected for 20 mins for each sample. The collected spectra are then azimuthally integrated for analysis. A control scattering experiment from pure Kapton tape is also performed for 20 mins to eliminate contributions from the tape to the scattering curve. Water Contact Angle Goniometry. Static Water Contact Angles are used to measure the surface energy of the P2VP:NPG composite. Uniform DI-H2O droplets were deposited onto the sample surface using a Gilmont Micrometer Dispenser. The system is illuminated using a Stocker Yale Imagelite Lite Mite -Model 20. Pictures of the water droplets were captured using a Sony CCD N50 Video Camera Module with a Navitar Zoom 7000 close-focusing macro video lens mounted on an optical table . The captured pictures are analyzed using Image J, plugin "LB-ADSA," which uses the Young-Laplace equation to fit the shape of the water droplet for the exact contact angle.
probe the surface morphology of the NPG/composite. The images collected are 2 x 2 µm 2 .
Tapping mode AFM tips, Tap300Al, have a tip height of 17 μm and radius of 10 nm. The AFM images are analyzed using Gwyddion software. An LJ potential also controls interactions between monomers and simulated "gold" surface particles, with a separate potential strength, 𝜖gold. For weak polymer-gold interactions, 𝜖gold = 1.0 kbT, the same strength as nonbonded monomer interactions, which is meant to qualitatively capture PS-gold interactions. In the attractive polymer-gold interaction simulations, 𝜖gold = 5.0 kbT to capture the physics of strong adsorption 64 , meant to mimic P2VP-gold interactions. At our simulation temperature of 𝑇 = 1.2, the strong interaction with 𝜖 𝑔𝑜𝑙𝑑 = 5 is comparable to the energy of a hydrogen bond, so our range of interactions cover the approximate relevant range.
The pore radii of as-prepared and annealed, 175℃ for 3 h, nanoporous gold (NPG) were determined by small angle x-ray scattering (SAXS). For bicontinuous structures, the ligament to ligament distance (d-spacing) is given by 59,67
. Figure 1 shows that the SAXS intensity from the as-prepared and annealed NPG exhibits distinct scattering peaks with the peak for the annealed sample shifted to lower q. In both cases the intensity scales as q -4 at high q. The as-prepared NPG exhibits an average d-spacing of 62 nm, whereas the d-spacing increases to 136 nm for the annealed NPG. Using a porosity of ~ 50% measured previously 13,14 , the radius of pore (𝑅 𝑝 ) can be determined from the d spacing using 𝑅 𝑝 = 𝑑 4 . Thus, the as prepared NPG has a radius of 𝑅 𝑝,𝑎𝑠 𝑝𝑟𝑒𝑝𝑎𝑟𝑒𝑑 = 15.5 𝑛𝑚, whereas the value for the annealed NPG is 𝑅 𝑝,𝑎𝑛𝑛𝑒𝑎𝑙𝑒𝑑 = 34 𝑛𝑚. For the annealed NPG, a shoulder exists at q = 0.025 Å -1 , corresponding to a 𝑅 𝑝 = 7.7 𝑛𝑚. The shoulder may reflect the scattering from smaller NPG pores or Au nanoparticles resulting from incomplete ligament formation. In our prior work 13 , we demonstrated that annealing of the NPG at 175℃ for 3 h prevents the NPG structure from coarsening during infiltration at 150℃ at times up to 3 h. In the present study, only the annealed NPG will be utilized to study infiltration of P2VP. In the remainder of the paper, "NPG" will refer to the annealed NPG. At high q, the intensity scales as q -4 . The NPG thickness is 120 nm.
To complement SAXS, SEM images of the annealed NPG scaffolds were taken at different magnifications from increasingly smaller areas. Figure 2 shows the morphologies with scale bars of 5 μm, 2 μm and 500 nm (left to right). The SEM images show that the NPG ligaments are relatively uniformly distributed across the sample with few defects at higher magnifications. The uniform morphology ensures similar infiltration at different locations across the film. Previous SEM studies 14 of the cross-section of the NPG shows that the nanoporous are randomly ordered across the film. From this top view, the Au ligaments appear interconnected and form a bicontinuous structure of gold ligaments and open pores. From a line scan analysis, the 𝑅 𝑝 from the SEM images is 31 ± 7 nm, in statistical agreement with the SAXS results. In summary, SAXS and SEM characterization of the ca. 120 nm thick NPG are consistent with a bicontinuous structure exhibiting pores of 34 nm.
In this work, the effective viscosities as compared to the bulk, as well as the effect of polymer-wall interactions on polymer infiltration are studied by selecting a polymer, P2VP, that is attractive towards the Au surface of the scaffold. Several factors influence polymer infiltration into pores including polymer radius of gyration, polymer viscosity and polymer affinity with the wall. Polymer infiltration inside porous media is often described by the Lucas-Washburn Equation (LWE) 68,69 ,
In Eq. 1, ℎ(𝑡) is the height infiltrated by the fluid (polymer), t is the infiltration time, 𝑅 𝑝 is the radius of the pore, ϒ is the surface tension of the liquid, 𝜃 𝑒 is the equilibrium contact angle, and 𝜂 𝑜 is the bulk viscosity. Originally, the LWE was derived for a Newtonian simple fluid, treated as a continuum medium, infiltrating a cylinder. According to Eq. 1, 𝑡 ~ ℎ 2 , implying that if the medium is a Newtonian fluid, ℎ 2 should be linearly related to the t of infiltration. In our previous study 14 , we demonstrated that the infiltration height of polystyrene (PS) into a NPG scaffold scales as 𝑡 0.5 during the early time of infiltration in agreement with Eq. 1.
Using in-situ spectroscopic ellipsometry (SE), Figure 3a shows the infiltration height of P2VP-940k and P2VP-85k plotted as a function of 𝑡 0.5 at 140℃. For ease of comparison with MD results, the same data was also plotted as ℎ 2 vs. t in the SI (Fig. S1). However, Figure 3a better distinguishes the difference between the P2VP-940k and P2VP-85k results when plotted as ℎ vs. 𝑡 0.5 . The maximum height corresponds to the thickness of the NPG, 120 nm 14 . From Figure 3a, the P2VP-940k infiltration height deviates from linearly, even at early times, and the slope decreases with increasing time in contrast to the infiltration of PS. This slowing down may be attributed to the affinity of the P2VP for the Au surface and the weak interaction of PS with Au 14 . As described later, MD simulations of the infiltration height capture this slowing down.
Figure 3a also shows that infiltration slows as the Mw of P2VP increases from 85k to 940k. We use 𝛕80% to quantify the infiltration time for P2VP to reach a height of 96 nm in the NPG. As shown in Figure 3a, 𝛕80% increases from 5 min. to 106 min. as Mw increases from 85k to 940k, respectively. The infiltration kinetics for P2VP was measured for seven values of Mw ranging from 51k to 950k, corresponding to confinement ratios from 0.18 to 0.78. For P2VP:NPG bilayers annealed at 140°C, Figure 3b shows that infiltration time increases as Mw increases. If bulk viscosity determines the scaling of the molecular weight dependence, then 𝜏 80% ∝ 𝑀 𝑤 3.4 .
However, as shown in Fig. 3b, 𝜏 80% ∝ 𝑀 𝑤 1.43 ±0.03 , implying that the molecular weight dependence of P2VP infiltration is weaker than expected from bulk behavior. Interestingly, the scaling of the infiltration time for P2VP is similar to that of PS 14 (slope = 1.30 ± 0.20), even though P2VP and PS have different affinities for the Au surface. This observation will be discussed later. In summary, P2VP infiltration height exhibits a nonlinear ℎ vs. 𝑡 0.5 relationship, infiltration time scales as and scales as 𝑀 𝑤 1.43 , and the scaling of infiltration times with Mw for P2VP and PS are similar. The effective viscosity determined from infiltration studies can be compared to the bulk viscosity. The effective viscosity (𝜂 𝑒𝑓𝑓 ) of P2VP can be calculated using a modified Lucas-Washburn Equation 70,
where the bulk fluid viscosity is replaced by the effective viscosity, 𝜂 𝑒𝑓𝑓 Because the pores are non-linear, the slowing down due to the longer path length is represented by the pore tortuosity, 𝜎. As a reference, 𝜎 = 1 for a straight pore. For the P2VP:NPG system, the ϒ of P2VP is 37.9 mN/m 19 at 140°C, the average 𝑅 𝑝𝑜𝑟𝑒 is 34 nm, 𝜎 is 1.5 71 , and θ between P2VP and gold 72 is 9°.
Using these values, experimental data (e.g., Fig. 3) and Eq. 2, 𝜂 𝑒𝑓𝑓 of P2VP can be determined.
As shown in Figure 4a, the effective viscosity increases from 1.03 * 10 6 to 6.14 * 10 7 𝑃𝑎 * 𝑠 as Mw increases from 51k to 940k, respectively. The bulk viscosities were taken from the literature 57 and scale as 𝜂 𝑏𝑢𝑙𝑘 ~ 𝑀 𝑤 3.4 . Figure 4a shows that the effective viscosity is lower than the bulk viscosity at low Mw and greater at high Mw. This trend is reiterated by plotting the ratio (
) as
shown in Figure 4b. As Mw increases,
is greater than 1, approaches 1 near 180k Da (𝛤 = 0.34), and then decreases below 1. In our previous study of PS infiltration 14 , the 𝜂 𝑒𝑓𝑓 was lower than the bulk for Mw values from 424k (𝛤 = 0.47) to 1133k Da (𝛤 = 0.77). For PS under confinement, we attributed this reduced 𝜂 𝑒𝑓𝑓 to a decrease in entanglements and a relative reduction in the fraction of highly adsorbed chains as 𝑀 𝑤 increases. Both contributions also explain the reduction in 𝜂 𝑒𝑓𝑓 for P2VP-302k (𝛤 = 0.44) and above, as detailed in the MD studies. However, for the range P2VP-51k to P2VP-153k, 𝜂 𝑒𝑓𝑓 < 𝜂 𝑏𝑢𝑙𝑘 with the viscosity difference, 𝜂 𝑒𝑓𝑓 -𝜂 𝑏𝑢𝑙𝑘 , decreasing as 𝑀 𝑤 increases. For unentangled P2VP (8k, 𝛤 = 0.70 and 22k Da., 𝛤 = 1.13) infiltrating into a dense SiO2 structure, the effective viscosities increased by nearly 100x and 30x, respectively 19 . Although these studies are for unentangled chains and ours are above the bulk Mc (Figure 4), the results are consistent with each other. In summary, the effective viscosities are greater than the bulk values below 180k (𝛤 = 0.34) and less than the bulk values above this molecular weight.
The effective viscosity of polymer inside a channel can be divided into three regimes 23 .
For low confinement, 𝛤 = 𝑅 𝑔 𝑅 𝑝 << 1, 𝜂 𝑒𝑓𝑓 increases due to the narrowing of the channel due to adsorbed polymer, also called the dead zone 73 . In the intermediate range, 0.1 < 𝛤 ≤ 1, the friction with the wall. However, for high confinement, 𝛤 > 1, 𝜂 𝑒𝑓𝑓 increases again because chains are strongly confined, resulting in an enhanced entropic barrier to infiltrate 23 . These three regimes agree with experiments 23,73 . As shown in Table 1, the confinement ratio in this study ranges from 0.18 and 0.78, corresponding to the second regime where 𝜂 𝑒𝑓𝑓 is expected to be less than the bulk value 23 according to Ren et al. (2024). However, for 𝛤 = 0.18, 0.23 and 0.31, 𝜂 𝑒𝑓𝑓 for P2VP is greater than the bulk values; whereas for 𝛤 = 0.44, 0.52, 0.65 and 0.78, the effective viscosities are less than the bulk values. Based on the regimes defined above, for the P2VP:NPG system we expect 𝜂 𝑒𝑓𝑓 < 𝜂 𝑏𝑢𝑙𝑘 , however this is only observed for 𝛤 = 0.44 and above. plotted as a function of 𝑀 𝑤 . The ratio of 𝜂 𝑒𝑓𝑓 𝜂 𝑏𝑢𝑙𝑘 =1 near 𝑀 𝑤 = 180k Da.
As shown in Figure 4, the effective viscosities of P2VP can be divided into regions I (orange) and II (blue) with a crossover near 180k Da (𝛤 = 0.34). The transition suggests that ca.
180k Da represents an effective critical molecular weight (𝑀 𝑐 ) under confinement. For PEO infiltrating into cylindrical pores with 𝑅 𝑝 = 35 nm, a similar transition was observed between 100k (𝛤 = 0.35) and 280k Da (𝛤 = 0.58) 29,73 . For bulk melts, 𝑀 𝑐 separates Rouse from reptation dynamics 74 where 𝜂 ~ 𝑀 𝑤 , and 𝜂 ~ 𝑀 𝑤 3.4 , respectively. For both PS and P2VP, 𝑀 𝑐 is 31,000
Da 74 . The finding that 𝑀 𝑐,𝑐𝑜𝑛𝑓𝑖𝑛𝑒𝑑 > 𝑀 𝑐 is consistent with a reduction of entanglements for weak polymer/wall attraction 14 . For stronger polymer-wall attraction (ɛ = 5.0), MD simulations described later indicate that confinement reduces polymer entanglement. Thus, in region 1, the higher effective viscosity is attributed to the formation of a physisorbed layer resulting in an effective pore size 𝑅 𝑝 -𝛥𝑅, where 𝛥𝑅 is the physisorbed layer thickness 73 . Results found in Region II (𝜂 𝑒𝑓𝑓 < 𝜂 𝑏𝑢𝑙𝑘 ) are consistent with our previous studies of PS infiltration across a similar range of 𝛤 14 . Because 𝛤 is between 0.18 and 0.78, our experiments would fall into the intermediate regime described above 23 . Our results suggest that the 𝛤 denoting the transition between the low and intermediate confinement regimes may be greater than expected.
Here we focus on how the polymer melt/Au interface impacts infiltration kinetics, noting that P2VP has a stronger attraction for Au than PS. The different interfacial properties of polar P2VP and hydrophobic PS are reflected in their water contact angle (WCA) values 14 of 60.0° (Fig. S5) and 89.9°, as well as equilibrium melt contact angle 14,72 of 9° and 20° respectively.
For comparison the WCA of gold is 64.4° 14 . Figure 5 compares the infiltration extent in NPG for PS-168k (𝑅 𝑔 = 11.2 𝑛𝑚, 𝛤 = 0.33) and P2VP-153k (𝑅 𝑔 = 10.7 𝑛𝑚, 𝛤 = 0.31 ) at 140℃.
Whereas PS-168k reaches 𝜏 80% in 3.1 min, P2VP-153k is slower with 𝜏 80% = 5.8 min., nearly twice as long as PS. Similarly, PS-168k reaches 99% infiltration extent, 𝜏 99% , after 7.9 min, whereas for P2VP-153k, 𝜏 99% =17.9 min. The 𝜏 80% and 𝜏 99% values are both longer for P2VP as compared to PS at similar 𝛤. The effective viscosity of P2VP-153k is given in Figure 4, whereas the value for PS-168k is calculated from Eq. 2 using ϒ = 29.60 mN/m and θ = 20° 14 . Whereas 𝜂 𝑒𝑓𝑓 for PS-168k is 1.3 * 10 6 Pa*s, the value for P2VP-153k is 3.4 * 10 6 Pa*s, which is 2.6x greater than PS. Because the 𝑇 𝑔 for these polymers are similar 56,57 as noted in the methods section, the slower infiltration of P2VP should be attributed to other factor(s) such as the affinity of P2VP for the Au surface of the scaffold.
After the NPG scaffold is completely infiltrated by PS-168k or P2VP-153k, the surface topography was characterized. Figures 6a-c show AFM phase images of pristine NPG, P2VP-153k infiltrated NPG and PS-168k infiltrated NPG, whereas Figures 6d-f represent drawings of the cross-sections corresponding to the images in the top row. The corresponding height images are given in the SI (Fig. S4). Figure 6a shows that the surface of the pristine NPG exhibits interconnected ligaments (bright) and unfilled pores (dark). The 𝑅 𝑝 is 30.7 ± 7.3 nm, which agrees with SEM and SAXS measurements. Compared to the pristine NPG, the P2VP-153k:NPG displays a more uniform morphology suggesting a surface covered by polymer. From height images (Figure S3), the roughness for pristine NPG and P2VP:NPG are 15.5 nm and 5.8 nm, respectively. Furthermore, hemispherical bumps due to the P2VP appear at the surface that are ca. 15 nm high by 80 nm wide. This observation suggests that molten P2VP spreads on the Au ligaments, as sketched in Figure 6e. However, the molten hydrophobic PS doesn't spread, leaving the top-most NPG ligaments exposed as sketched in Figure 6f. The roughness of PS:NPG is 4.7 nm, 3x lower than the pristine NPG and slightly less than P2VP:NPG surface.
After PS completely fills the NPG (phase image in Fig. 6c), the NPG ligaments remain visible, thus supporting the claim that PS does not form a wetting layer over the Au ligaments. To qualitatively demonstrate that P2VP forms a bound layer, the P2VP filled NPG (e.g., Figure 6b) was rinsed in a good solvent to remove unbound P2VP. AFM images (Figure S6) shows that residual P2VP remains on the ligaments near the surface. Maguire et al. (2021) found P2VP inside the NPG exhibits a higher Tg than the bulk P2VP 13 . In summary, the attraction of P2VP
for Au produces surface features that cover the entire surface, whereas the weaker interaction between PS and Au results in a surface exhibiting a mixture of Au ligaments and PS. The main experimental results for P2VP infiltration into NPG are as follows. The infiltration time of entangled P2VP scales as 𝑀 𝑤 1.43 ±0.03 , similar to that of entangled PS 𝑀 𝑤 1.30 ±0.20 . Additionally, the effective viscosities of P2VP are greater than the bulk values for 𝑀 𝑤 < 180,000 𝑔/𝑚𝑜𝑙, but lower than the bulk values above this 𝑀 𝑤 . We attribute a crossover above the bulk Mc to polymer disentanglement under confinement as described in the next. P2VP
infiltration into NPG is found to be slower than PS because of its stronger affinity for the Au surface of the pore. After complete infiltration, the surface of the NPG becomes covered by P2VP, whereas a heterogeneous surface with exposed Au ligaments is observed for PS infiltration. In the next section, MD simulations are compared with experimental results and provide insight into how molecular properties are perturbed for weak and stronger attraction between polymer-wall conditions.
To provide insight into experimental results, we performed MD simulations of infiltrating entangled polymers into nanoporous gold. Figure 7 shows simulation images and density profiles of polymer infiltration into the gold scaffold for weak and strong polymer/gold interaction strengths, ɛ = 1.0 and 5.0 kbT, respectively. The local density of the polymer in the z direction, ρ(z), is used to calculate the height of the polymer infiltration front. To track infiltration, two thresholds are utilized: z′99 and z′85, where ∫ z′99 ρ(z)dz = 0.99ρtotal and ∫ z′85 ρ(z)dz = 0.85ρtotal, indicating where 99% or 85% of the total polymer density is contained, respectively.
These thresholds, represented by red dashed lines in the density plots of Figure 7, denote the infiltration front (z′99) and the infiltration height of the bulk of the polymer (z′85). Additionally, the dashed gold lines plots indicate the z position of the bottom of the nanoporous gold, zgold. The polymer height, h99 or h85, is defined as z′ -zgold and serves as our primary measure of infiltration. This figure will be further discussed when comparing simulations with experiments. Simulations are presented for weak and strong attractive interactions between the polymer and scaffold wall. Figures 8a and 8b show how the squared infiltration heights, h 2 99 and h 2 85, respectively, increase with simulation time for N = 25, 50, and 100 and polymer-gold interaction strengths 𝜖 = 1.0 (open symbols) and 𝜖 = 5.0 (solid symbols). For this range of N, N/Ne increases from 1.5 to 6.0; correspondingly, the confinement ratio, Γ, ranges from 0.46 to 0.95. For comparison, Γ for P2VP experiments are from 0.18 to 0.78 (Table 1). Figures 8a and 8b show that both h 2 99 and h 2 85, respectively, increase more slowly as N increases from 25 to 100. At early infiltration times for N = 25 and 50, infiltration is faster for 𝜖 = 5.0 compared to 𝜖 = 1.0. However, at later times, the polymer with weaker interactions (open symbols) infiltrates more quickly than the stronger interaction case; this is observed for both h 2 99 (Figure 8a) and h 2 85 (Figure 8b). We do not observe the crossover for N = 100, which we speculate is due to the limited simulation time. For the weaker interaction case, a relatively linear relationship with time is observed for both h 2 99 and h 2 85. However, for stronger attractive interaction, the h 2 85 values increase linearity at early times whereas h 2 99 is nonlinear for N = 25, 50 and 100. Due to this loss of linearity, the slope of the h 2 85 plot is used to calculate the infiltration time shown in Figure 8c.
For strong polymer attraction for the wall (𝜖 = 5.0), the infiltration time scales as N 1.4 in good agreement with the experimental results for P2VP:NPG (Fig. 3b), where 𝜏 80% ∝ 𝑀 𝑤 1.43 ±0.03 .
Previous MD studies 14 for 𝜖 = 1.0 also shows that infiltration time scales as N 1.4 . The similar scaling for the weaker and stronger attractive interactions between polymer and wall will be discussed later in the context of physisorption changing the interface for the latter case. as a function of simulation time. (c) Inverse infiltration rate, 1/ 𝑑ℎ 85 2 𝑑𝑡 , as a function of degree of polymerization for 𝜖 = 5.0. The linear region of the plots in Figure 8b are used to calculate the infiltration rate, 𝑑ℎ 85 2 𝑑𝑡 . Taking the inverse of the infiltration rate allows the data to be interpreted as an infiltration time for more direct comparison with experimental results. A log-log plot is shown to determine scaling with polymer length. The infiltration time scales with N as τ infiltration ∝ N 1.4 . h 2 85 was used rather than h 2 99 due to the lack of linear scaling for the latter. The presence of strong attractive polymer-surface interactions (𝜖 = 5.0) may lead to the formation of a strongly adsorbed polymer layer on the gold surface that perturbs infiltration. To 0.5. Overall, this analysis shows that the velocity of chains near the surface is strongly reduced by attractive interactions.
To further discern the adsorption behavior as a function of N and polymer-gold interaction strength, the fraction of total chains at each value of 𝑓 𝑎𝑑𝑠𝑜𝑟𝑏𝑒𝑑 is determined. This fraction is calculated using all time points throughout infiltration. The results for 𝜖 = 1.0 was presented in our previous work 14 . Briefly, the largest fractions of weakly interacting chains have a low fraction of adsorbed monomers 𝑓 𝑎𝑑𝑠𝑜𝑟𝑏𝑒𝑑 , and 𝑓 𝑐ℎ𝑎𝑖𝑛 decreases mostly monotonically as 𝑓 𝑎𝑑𝑠𝑜𝑟𝑏𝑒𝑑 increases (open circles). In simulations with stronger polymer-gold interactions (𝜖 = 5.0), the behavior is quite different, and the largest populations of chains are either weakly adsorbed with 𝑓 𝑎𝑑𝑠𝑜𝑟𝑏𝑒𝑑 < 0.1 or strongly adsorbed, 𝑓 𝑎𝑑𝑠𝑜𝑟𝑏𝑒𝑑 > 0.9. This data supports the physisorption of attractive chains on the pore surface that form a bound layer, while a subset of free chains infiltrate the narrowed pore. 100. A monomer is adsorbed if the chain bead is within 1.5𝜎 of any gold surface bead. The adsorbed fraction is defined as 𝑓 𝑎𝑑𝑠𝑜𝑟𝑏𝑒𝑑 = ( # 𝑜𝑓 𝑎𝑑𝑠𝑜𝑟𝑏𝑒𝑑 𝑏𝑒𝑎𝑑𝑠 𝑁 ). For each N, open circles and closed squares represent polymer-gold interactions with 𝜖 = 1.0 and 𝜖 = 5.0, 𝑟𝑒𝑠𝑝𝑒𝑐𝑡𝑖𝑣𝑒𝑙𝑦. (b) The fraction of total chains (𝑓 𝑐ℎ𝑎𝑖𝑛𝑠 ) at each adsorbed fraction for each N. (c) Normalized radius of gyration versus adsorbed fraction (𝑓 𝑎𝑑𝑠𝑜𝑟𝑏𝑒𝑑 ). A value of 1.0 for 𝑅 𝑔 /𝑅 𝑏𝑢𝑙𝑘 represents a polymer size in the pore equal to the radius of gyration in the bulk.
Previous work exploring the conformations of polymers during capillary infiltration has demonstrated a variety of effects, finding both unperturbed dimensions 25 and chain extension in the direction of flow 75 . To understand the interplay between chain stretching and adsorption, we examine the impact of adsorbed fraction on the polymer chain radius of gyration. Figure 9c shows the normalized radius of gyration 𝑅 𝑔 /𝑅 𝑏𝑢𝑙𝑘 for the polymer chains versus the adsorbed fraction 𝑓 𝑎𝑑𝑠𝑜𝑟𝑏𝑒𝑑 . Values are normalized to the bulk polymer 𝑅 𝑔 in each direction such that a value of 1 represents a chain that has retained bulk dimensions in that respective direction. ⟩ -⟨𝑍 〉 𝑏𝑢𝑙𝑘 . For N =100, chains have only partially penetrated the porous structure as shown in Figure 7. For each chain length, open circles and closed squares represent simulations using 𝜖 = 1.0 and 𝜖 = 5.0, respectively.
Experiments and simulations are consistent with the formation of a physisorbed bound layer followed by infiltration of P2VP into narrowed pores in a nanoporous scaffold. In experiments, the physisorbed layer is driven by the affinity of P2VP to wet the gold surface. In simulations, for N = 50, Figure 7 shows the infiltration of polymer with weaker, 𝜖 = 1.0 (top), and stronger, 𝜖 = 5.0 (bottom), attractive interactions for the gold surface. Comparing the polymer infiltration front (red) for 𝜖 = 1.0 and 𝜖 = 5.0, the former shows mainly filled pores whereas the latter shows a polymer wetting layer on the pore surface at the growth front. This qualitative observation is supported by the broader front edge of the polymer density profile in Figure 7 for 𝜖 = 5.0 (bottom right). Further analysis is needed at various infiltration times to examine this precursor layer at the growth front. For 𝜖 = 5.0, the formation of a physisorbed layer is supported by the near zero velocities for highly adsorbed chains shown in Figure 9a, as well as the increase in the fraction of highly observed chains shown in Figure 9b. As noted later, the formation of this physisorbed layer is similar to the dead zone 73 proposed by Yao et al.
(2018).
For PS and P2VP, the similar scaling of infiltration time with molecular weight, 𝑀 𝑤 1.4 , can be attributed to the formation of a physorbed P2VP covering the Au surface. Namely, the backfilling P2VP interacts with pore having the composition of P2VP (rather than Au). We attribute the similar molecular weight dependence of P2VP and PS infiltration to the weak interactions that both polymers have with the confining walls, P2VP and Au, respectively. For weak interactions (𝜖 = 1.0), MD simulations yield 𝜏 ~ 𝑀 𝑤 1.4 14 . Similarly, for stronger attractive interactions (𝜖 = 5.0), Figure 8c shows that 𝜏 ~ 𝑀 𝑤 1.4 . This agreement in scaling behavior for experiments and simulations is consistent with the formation of a physisorbed P2VP layer followed by backfilling of P2VP through the coated pore.
Lastly, P2VP is found to infiltrate more slowly than PS when compared at similar confinement ratios. Simulations in this study provide insights into three factors that influence kinetics of infiltration. First, the larger reduction in entanglement density for 𝜖 = 5.0 (Fig. 10)
suggests that stronger adsorption increases infiltration kinetics. Second, the chain velocity along the pores is greatly reduced for 𝜖 = 5.0 (Fig. 9a). Third, for 𝜖 = 5.0, a physisorbed layer first forms and then polymer infiltrates through this narrowed pore. The effective radius (𝑅 𝑒𝑓𝑓 ) of the pore is now 𝑅 𝑒𝑓𝑓 = 𝑅 𝑝 -𝛥𝑅. Previous studies 23,73 have qualitatively shown that a bound layer will increase the effective viscosity. Previous simulations 18,80 of solvent-driven polymer infiltration identifies dissolution-dominated and adhesion-dominated modes, which depend on the interaction strength between each component. The adhesion-dominated mode results in a slower kinetics when the interaction is strong. Our experimental and simulation studies imply that the P2VP:NPG system belongs to the adhesion-dominated mode, consistent with slower kinetics. In summary, the slower infiltration of P2VP compared to PS has its origin in the formation of the physorbed layer on the Au pore surface, which could provide entanglements while narrowing the pore size.
In this work, experiments and simulations are used to investigate the infiltration of moderately confined polymers into nanoporous scaffolds. Experimentally, poly(2-vinylpyridine) (P2VP) with molecular weights from 51k to 940k are infiltrated nanoporous gold (NPG)
scaffolds to form polymer infiltrated nanoporous gold (PING) composites at 140℃. For a pore diameter of 34 nm, the confinement ratios vary from 0.18 to 0.78. In-situ spectroscopic ellipsometry is used to determine when 80% of the NPG (𝜏 80% ) has been filled with P2VP. This infiltration time scales as 𝑀 𝑤 1.4 which is similar to PS infiltration across similar confinement ratios. Both the PS and P2VP infiltration times have a much weaker 𝑀 𝑤 dependence than expected from bulk viscosity where 𝜏 𝑏𝑢𝑙𝑘 ~ 𝑀 𝑤 3.4 . The infiltration time for simulations with strong attractions between polymer and pore walls agree with experimental scaling results. At similar conditions, P2VP infiltration is slower than PS in the same scaffold. Simulations show that polymer with a stronger attraction to the scaffold (𝜀 = 5; 𝑃2𝑉𝑃) infiltrates more slowly than polymer with a weaker interaction (𝜀 = 1; 𝑃𝑆). For P2VP, the effective viscosity crosses over from greater than to less than the bulk viscosity near 180 kDa. This transition is attributed to the narrowing of the pore walls and a reduction in entanglements, respectively.
Simulations of the infiltration process of polymers with strong and weak attraction for the pore wall provide important macro and molecular insights. First, the dynamics of infiltration exhibited a scaling with chain length that was consistent with experimental results. Furthermore, for chains that strongly wet the pore surface, the structure of the infiltrating polymer chains was altered compared to polymers with weaker interactions. Simulations revealed a growth in the population of chains that have a larger fraction of their monomers adsorbed to the pore wall for the strong attraction case compared to the weaker case. This observation is consistent with the formation of a physisorbed layer on the wall. This strong attraction of polymer for the pore wall led to significant changes in the polymer conformations, disentanglement of the polymers that had infiltrated the pores, and the emergence of a population of chains with drastically reduced infiltration rate. Presumably, the disentanglement plays a key role in the change of the scaling of
𝜂 𝑒𝑓𝑓 with 𝑀 𝑤 , though the precise origin of the observed scaling with 𝜂 𝑒𝑓𝑓 ∝ 𝑀 𝑤 1.4 remains unknown. supported by National Science Foundation grants #2138259, #2138286, #2138307, #2137603, and #2138296.