Central to the advancement of many technologies is the miniaturization of functional devices to the nanometer length scale. As polymers continue to play a prominent role in material solutions in meeting the challenges of reducing size, they are undoubtedly being utilized at length scales that are approaching the dimensions of the unperturbed macromolecule. Furthermore, with decreasing the confining dimension to the nanoscale an increasingly larger fraction of molecules are in direct contact with interfaces. Often, the average properties or the distribution in properties away from the interfaces of a confined polymer can be strongly perturbed from the bulk. It is the deviation in properties of confined polymers relative to the bulk that is commonly referred to as the confinement effect, and in the special case when the property of interest is the glass transition temperature (Tg), the Tg-confinement effect.
The study of the Tg-confinement effect for polymers has been predominately investigated for thin films, that is, the case of one-dimensional confinement. In 1994, Keddie et al.1, 2 published the first systematic study on the Tg of polymer films supported on solid substrates as a function of thickness. In their investigations, in which ellipsometry was used to detect the Tg, polystyrene (PS)1 and poly(methyl methylacrylate) (PMMA)2 films supported on silicon exhibited a reduction and enhancement in Tg, respectively with confinement. Conversely, when supported on a gold substrate, the Tg of PMMA films decreased with confinement.2 Later, Dutcher and coworkers,3–8 reported that in the absence of a solid interface, PS3–6 and PMMA7, 8 films exhibited a reduction in Tg with confinement. These results suggested that the change in Tg of nanoscopically confined polymer films was intimately related to the presence or lack of solid and free interfaces, or in other words, interfacial effects.
In the case of supported films, interfacial effects occur from the free surface or polymer–substrate interface, with the conventional view being that free surfaces act to locally enhance segmental dynamics leading to a Tg decrease while attractive interactions between the polymer and substrate act to locally reduce segmental dynamics leading to a Tg increase.9–18 Based on this viewpoint, the direction and magnitude of a change in Tg with confinement for supported films is dictated by competitive interfacial effects. For freely standing films, only free surface effects would be present. In agreement with the above mentioned studies, the importance of interfaces in modifying the Tg of polymer films has been highlighted by the ability to suppress the Tg-confinement effect of supported PS films by capping the free surface9, 10 and the finding that doubly silica-supported PMMA films exhibited a greater Tg increase with confinement than singly supported films.15 Furthermore, Torkelson and coworkers11, 16 using a novel fluorescence/multilayer approach that allowed for spatially resolved measurements of the local near free surface Tg of PS and PMMA and near substrate Tg of PMMA reported lower and higher interfacial Tgs, respectively, a trend in agreement with the size dependence of Tg for the corresponding supported or freestanding polymer films. Numerous studies have observed systematic changes in Tg of thin polymer films via modification of the nature of the substrate/polymer interface or significant reductions in the Tg of freely standing films using fluorescence spectroscopy,11, 16, 19, 20 dielectric relaxation spectroscopy,14, 21–23 differential scanning calorimetry,23, 24 and mechanical measurements.25, 26 Key factors that are known to influence the deviation in Tg with confinement include geometry,3, 15, 27, 28 sample preparation and measurement environment,29 annealing conditions,30 and chemical structure.7, 11 We refer the reader to Refs.31 and32 for comprehensive reviews on the Tg-confinement effect for thin films, Refs.33 and34 for articles highlighting the challenges associated with understanding the behavior of thin films, Refs.35–37 for theoretical contributions to the field, and Refs.38–41 for studies that challenge the premise of the Tg-confinement effect for thin films.
Although thin films are an attractive model system to investigate the impact of confinement on Tg, due to the ease of processing, extending Tg-confinement effect studies beyond thin films to other geometries is vital from both technological and scientific viewpoints. Polymer nanoparticles represent an alternative model system to explore size effects on Tg and related glassy dynamics. From an applications perspective, polymer nanoparticles can act as vehicles in controlled drug delivery,42 components in fluorescent imaging,43 performance reinforcing additives,44 and components in photonic structures.45 In these applications, it is the physical properties (e.g., the glass transition temperature) of the nanoparticle core that are of paramount importance. If the properties of nanoparticles change due to confinement (i.e., reduction in diameter), our understanding of such effects will be essential in assessing their potential use in applications.
Scientifically, exploring the generality of the Tg-confinement effect and related glassy dynamics beyond thin films could help usher in a more complete understanding of confined polymer properties. As recently highlighted by Reiter and Napolitano,46 thin films are inherently meta-stable with respect to polymer chain confirmations. That is, the typical process of creating thin films (i.e., spin coating) results in polymer chain conformations that are different from the equilibrium melt. Although interfaces are known to impact the properties of thin polymer films, how non-equilibrium chain conformations influence the properties of thin films is a central unresolved issue. In addition, questions remain as to whether thin films prepared by spin coating may be equilibrated and residual stresses relaxed by thermal annealing or if other approaches to producing thin films with controlled polymer chain conformations may be developed. One advantage for studying confined polymer properties using nanoparticles, in addition to thin films, is that the former is processed in a very different manner. Hence, the polymer chain conformations within nanoparticles may be different from that of thin films. Nanoparticles suspended in solution may be annealed above Tg for prolonged periods of time for equilibration. We speculate that polymer nanoparticles could represent a stress-free state of confinement. A second advantage for studying polymer nanoparticles is that the surface area to volume ratio is much greater for nanoparticles than for thin films. Hence, the influence of interfaces on the properties of nanoparticles may be probed under conditions in which the extent of confinement is not extreme.
This feature article highlights the impact of nanoscale confinement on the glassy properties of polymer nanoparticles. The article aims to showcase what we have learned about the properties of confined polymer via investigations on nanoparticles. We first discuss both synthetic and physical approaches to form polymer nanoparticles. Next, we review prior studies that have pursued an understanding of the glassy properties of polymer nanoparticles. We then highlight our recent contributions to field. Finally, we conclude with challenges and future work.
Beyond their technical importance, one possible reason for the abundance of confinement studies on polymer thin films is that processing of the films is straightforward and easy through spin coating. Both film thickness and polymer molecular weight can be tuned independently. Conversely, polymer nanoparticles generally need to be synthesized via polymerization techniques. For example, in a typical emulsion polymerization route, controlling both the nanoparticle size and the polymer molecular weight is difficult since particle diameter and molecular weight increase concurrently with increasing extent of polymerization.47 However, recent work on polymer nanoparticles generated from nanoprecipitation techniques has shed light on facile independent control of nanoparticle size and polymer molecular weight.48–52
A common technique to generate polymer nanoparticles is via the synthesis of polymer chains from their monomer building blocks, e.g., emulsion and dispersion polymerizations.53–58 In the case where the end goal is to examine confinement effects in nanoparticles, emulsion polymerization is the most relevant synthetic protocol since it is capable of generating particles with diameters ranging from ∼50 to 600 nm,53–55 whereas dispersion polymerization is typically used to generate particles with diameters >600 nm.56–58 In conventional emulsion polymerization, monomers are combined with an initiator (e.g., peroxides or persulfates) and surfactants (e.g., sodium dodecyl sulfate) in an aqueous medium. The mixture is then allowed to react for several hours to create small emulsions of the polymerizing system. The resulting polymer nanoparticles are typically monodisperse. Sizes of synthesized nanoparticles are controlled by the initial concentrations of monomer and/or initiator; for example, increasing monomer concentration increases size.53–55 To generate nanoparticles with diameters <50 nm, a modified version of emulsion polymerization may be used, that is, mini-emulsion polymerization.59–61 Here, the use of a much greater emulsifier content allows for the generation of nano-sized polymer particles with narrow size-distributions and high stability.62
The presence of surfactant molecules on the surface of polymer nanoparticles as a stabilizing agent in emulsion polymerization may significantly modify the observed confinement effects and needs to be removed prior to measurements, which could prove to be a difficult task. An alternative method to generate “clean” surfaces is via surfactant-free emulsion polymerization.47, 63, 64 Here, the main difference is that surfactants are not introduced into the system during the reaction; rather, the nanoparticles generated are stabilized by the intrinsic charge on the initiator. Additionally, the introduction of an ionic co-monomer may be added to the polymer chain, for example, acrylic acid, which greatly aids in the stabilization of the synthesized nanoparticles.54, 65 In the case of using acrylic acid in the synthesis of PS nanoparticles as a stabilizer, 0.5–5 wt % with respect to the monomer is typically added to the reaction.
The main disadvantage of polymerization techniques is that it is difficult to independently control both nanoparticle size and the polymer-chain molecular weight. Since both the diameter and the molecular weight tend to increase with increasing extent of polymerization, it is extremely challenging to generate, for example, a sample set of 100 nm diameter nanoparticles with weight-average molecular weight (Mw) ranging from 50 to 1000 kg/mol. Thus, in order to study any molecular weight effects on the Tg-confinement effect in polymer nanoparticles, emulsion polymerization may not be a suitable sample preparation method. Moreover, residual components, such as monomers, oligomers, and initiators, can be difficult to remove from these polymerized nanoparticles and may modify the physical properties of the polymer core, thus frustrating measurements of the effect of confinement on polymer nanoparticle properties.
A physical method to generate monodisperse polymer nanoparticles is via nanoprecipitation. Here, rather than generating polymer nanoparticles from its constituent monomers, polymer chains dissolved in a solvent are mixed with a non-solvent (typically water), to precipitate out nanoparticles.66, 67 In the past, nanoprecipitation has been primarily used to form biodegradable polymer nanoparticles as vehicles for drug delivery, including poly(lactic acid),68, 69 poly(lactic-co-glycolic acid),70, 71 poly(ε-caprolactone),72 and several amphiphilic block copolymers.73–75 The fact that nanoprecipitation has been applied almost exclusively for the formation of these biodegradable polymers is surprising since the original patent on nanoprecipitation described the process as a method to generate nanoparticles from a wide-range of polymers.66
The main advantage of nanoprecipitation over traditional polymerization techniques is that since bulk polymer of a known molecular weight is used as a precursor, size and molecular weight can be independently controlled. Furthermore, nanoprecipitation is a three-component process, that is, the bulk polymer, the solvent, and the non-solvent, thus the cores of the generated nanoparticles are pure and should contain minimal residual contaminants. Additional advantages include fast processing time, low energy consumption, and high reproducibility.48, 52 Disadvantages of nanoprecipitation may include low mass fraction of nanoparticles in the prepared samples and a broad size distribution for samples with large diameters, that is, monodisperse nanoparticles with diameters >200 nm are difficult to generate using nanoprecipitation.52
Recent developments have shown that nanoprecipitation can be successfully applied to generate traditional non-biodegradable polymers, such as PS48, 50, 51, 76 and PMMA.48, 52, 77 For example, using a pouring technique which adds water rapidly to a PMMA solution, Aubry et al.52 successfully generated PMMA nanoparticles. In addition, we have generated monodisperse PS nanoparticles from rapid solvent displacement by means of a novel high intensity mixing geometry, termed Flash NanoPrecipitation (FNP), as shown schematically in Figure 1(a).50 Here, the solvent stream containing PS dissolved in tetrahydrofuran (THF) is rapidly mixed with an incoming water stream, which causes collapse of the hydrophobic polymer chain in the aqueous solvent and subsequent aggregation. The mixed exit stream is then diluted into a 27 mL water reservoir, which acts to quench the precipitated nanoparticles. Utilizing FNP, we have successfully generated monodisperse PS nanoparticles up to ∼150 nm in diameter with molecular weights ranging from ∼100 to 800 kg/mol. Figure 1(b) shows a representative scanning electron microscopy (SEM) image of ∼100 nm diameter PS nanoparticles generated from FNP. By altering the concentration of PS in the solvent stream, nanoparticle size can be varied, as shown in Figure 1(c) for three different polymer molecular weights: 92 kg/mol (circles), 376 kg/mol (squares), and 770 kg/mol (triangles). Here, the intersections between solid lines and the dashed line demonstrate PS concentrations to use for each molecular weight in order to generate 90 nm diameter nanoparticles with three distinct polymer molecular weights. Thus, it is apparent that the FNP process can be used to control nanoparticle diameter and polymer molecular weight independently. More recently, we have applied a dialysis nanoprecipitation technique, that is, dialyzing a PS solution against an aqueous environment, to successfully generate larger-sized PS nanoparticles.51
An alternative technique to generate nanoparticles is emulsification and solvent stripping.78–80 Similar to the nanoprecipitation technique, bulk polymer chains are used in this physical process, which may allow for the study of molecular weight effects on glassy properties of polymer nanoparticles. In the emulsion stripping process, a polymer solution is emulsified and then the volatile solvent for the polymer is removed to condense and solidify the particles. These techniques, often called “pseudo-latex” formation processes, enable the formation of submicron nanoparticles from polymers that cannot be polymerized by normal free-radical polymerization techniques.78–80 However, they suffer from the polydispersity that inherently arises from the size distribution of the parent emulsion drops. Other techniques to generate the nanoparticle morphology include spray-drying and freeze-drying.28, 81 In the spray-drying process, rapid evaporation of dilute polymer solutions is invoked, while in freeze-drying, dilute polymer solutions are quenched rapidly in liquid nitrogen, then sublimed under high vacuum, to generate polymer nanoparticles.28, 81
POLYMER NANOPARTICLES: PRIOR INVESTIGATIONS
Although the preferred geometry for exploring the effects of nanoscale confinement on glass transition dynamics has traditionally been polymer thin films, there have been (albeit only a handful) previous contributions to the confinement-field in which the polymer nanoparticle geometry has been utilized. Here, we highlight the main experimental observations from these previous studies. The general consensus among the studies is that glass transition dynamics, whether the Tg itself or the breadth of the glass transition are perturbed in polymer nanoparticles with increasing confinement.27, 81–83 However, it is important to note that these investigations utilized various nanoparticle preparation methods (e.g., emulsion polymerization vs. freeze-drying vs. spray-drying, and so forth) and various measurement environments (e.g., dried nanoparticles vs. nanoparticles suspended in an aqueous solution vs. nanoparticles embedded in a soft matrix). The ability to prepare nanoparticles via numerous methods and perform measurements under different environmental conditions is a valuable benefit, as it will allow us to systematically study how processing and environment influence the properties of confined polymers. For example, an ability to generate polymer nanoparticles of constant diameter but different density may enable investigations related to the impact of sample density and interfacial free volume on the effect of confinement on the glass transition, which have been suggested to be of importance.84, 85
One of the earliest investigations on the glass transition of polymer nanoparticles was conducted by Gaur and Wunderlich,82 who used differential scanning calorimetry (DSC) to examine the thermal properties of dried PS nanoparticles prepared by emulsion polymerization. They observed that as the PS nanoparticle diameter was reduced from 860 nm to 85 nm, a decrease in the onset Tg was observed, although the Tg taken from enthalpy extrapolations was unperturbed from the bulk. Furthermore, it was observed that a reduction in onset Tg was accompanied by a decrease in the heat capacity (ΔCp) at Tg. Gaur and Wunderlich attributed both the reduction in onset Tg and ΔCp to an increase in the surface area per mass of nanoparticles (therefore producing a larger effect of the polymer-air interface) with reduced diameter.
Later, Ding et al.81 observed a significant decrease (∼40 K) in the Tg (as compared to the bulk) on the first DSC heating for both freeze-dried (20–60 nm in diameter) and spray-dried (60–200 nm in diameter) PS nanoparticles. More recently, Rharbi83 examined the Tg of PS nanoparticles blended into a soft cross-linked polybutylmethacrylate (PBMA) matrix and observed a moderate Tg reduction with decreasing nanoparticle size. In that work, PS nanoparticles ranging from 27 to 130 nm were synthesized from emulsion polymerization and subsequently mixed with a PBMA nanoparticle dispersion. Solid films were obtained after allowing the nanoblend to dry. Using small angle neutron scattering, Rharbi showed that as the PS nanoparticle diameter was reduced from 130 to 27 nm, the Tg decreased by ∼16 K.
Not all previous investigations on the Tg-confinement effect in polymer nanoparticles have shown a clear reduction in Tg with size. In particular, Sasaki et al.,27 via DSC measurements, did not observe a size dependent Tg for PS nanoparticles suspended in an aqueous solution with diameters ranging from 42 to 548 nm. It is worth noting that the samples used in that study contained residual surfactant molecules (from emulsion polymerization) on the nanoparticle surface and also exhibited a large molecular weight polydispersity index (i.e., PDI ∼10 for smallest diameters). Although a Tg-confinement effect was not observed for PS nanoparticles in water, Sasaki et al. did observe that the glass transition occurred over a wider temperature range with confinement, in qualitative agreement with a reduced onset Tg observed by Gaur and Wunderlich82 for small nanoparticles. Furthermore, a decrease in the ΔCp across the glass transition was observed with reduced nanoparticle diameter, which was attributed to the presence of a shell layer with enhanced dynamics surrounding the core with bulk dynamics. The concept of an enhanced mobile layer at the polymer free surface is consistent with viewpoints from the thin film geometry4, 12, 14 and supported by direct experimental evidence of a well-defined molten layer at the surface of PS emulsions, as measured from nuclear magnetic resonance.86 In line with the observations of Sasaki et al., Ming et al.87 did not observe a clear Tg deviation for PS nanoparticles ranging from ∼20 to 50 nm in diameter prepared from emulsion polymerization and measured in the dried state using DSC. Finally, it is important to note, that despite the ongoing debate of whether the Tg decreases or is just broadened with confinement for polymer nanoparticles, no studies have reported a Tg increase with confinement.
POLYMER NANOPARTICLES: OUR RECENT CONTRIBUTIONS
One reason we have chosen to investigate the glassy properties of confined polymers via nanoparticles is to gain fundamental insight into how geometry influences their properties. By comparing our work on nanoparticles with the thin film literature, we seek to discover commonalities or differences in the deviations of material properties from the bulk with nanoscale confinement, despite differences in the confining geometry. Furthermore, nanoparticles, as we illustrate below, offer the possibility for unique measurements at the nanoscale that would be difficult to achieve with thin films.
Glass Transition Temperature
Notwithstanding processing issues, it is now accepted that the presence of free and solid interfaces is highly important in dictating the average properties of thin polymer films. The significance of interfaces (and the effects they cause) was first evident in the comparison of the Tg-confinement effect for PS films supported on a silicon substrate and in the freestanding geometry, as discussed in the Introduction. In our quest to find commonalities in size-effects on material properties, we have recently investigated the Tg of PS nanoparticles exposed to different interfacial conditions via calorimetry.88 The Tg of PS nanoparticles was measured under two conditions: particles suspended in an aqueous environment (the case of soft confinement) and particles capped via a rigid silica shell (the case of hard confinement).
Figure 2 provides representative SEM images of bare PS nanoparticles and transmission electron microscopy (TEM) images of silica-capped PS nanoparticles before and after the measurement of Tg. PS nanoparticles were prepared by surfactant free emulsion polymerization and capped with a silica shell via a modified Stöber method. The silica shell thickness was approximately 30 nm. As illustrated, smooth and fairly monodisperse nanoparticles could be prepared. More importantly, Figure 2 shows that the thermal protocol employed to measure Tg of the aqueous-suspended and silica-capped nanoparticles did not result in coalescence or damage to the morphology.
Figure 3(a) shows representative DSC thermograms of aqueous-suspended PS nanoparticles (solid lines) and the corresponding bulk PS (dashed lines), as measured from specimens of coalesced nanoparticles, while Figure 3(b) shows representative DSC thermograms of silica-capped PS nanoparticles. We note here that the Mw of the synthesized polymer nanoparticles range from ∼100–400 kg/mol. As shown in Figure 3, the Tg of silica-capped PS nanoparticle and bulk PS, are within error, the same value. However, it is clear that the Tg-value of the aqueous-suspended nanoparticles decreases with decreasing nanoparticle diameter. Figure 4(a) plots the diameter dependence of Tg – Tg,bulk for aqueous-suspended and silica-capped PS nanoparticles. Also, plotted are Tg – Tg,bulk values for dried bare PS nanoparticles exposed to a nitrogen environment obtained by capacitive dilatometry.89 Clearly, with decreasing diameter for the aqueous-suspended and dried bare PS nanoparticles, there is a systematic decrease in Tg. Furthermore, the suppression in Tg with nanoscale confinement is nearly identical for both the aqueous-suspended and dried PS nanoparticles. This result suggests that the water-polymer interface effectively acts as a free surface, i.e., an air-polymer interface, with respect to modifying Tg with confinement. Qualitatively, these results are in agreement with reports on freestanding PS thin films.3, 5 That is, the presence of free interfaces generally results in a suppression of Tg.
We explored the importance of the free interface as the cause of the Tg reduction of PS nanoparticles by removing it. Bare PS nanoparticles were coated with a thin silica shell via a modified Stöber method, that is, the silica-capped PS nanoparticles. As illustrated in Figure 4(a), we observed no systematic change in the Tg of the silica-capped PS nanoparticles. This effect can be partially understood if the free surface is considered a requirement of the size dependence of Tg for PS nanoparticles. Then it follows that by eliminating the free surface, the Tg-confinement effect, which we argue is a consequence of surface effects, is diminished. We note that the key observation from Figure 4(a), that is, the elimination of the size-dependent Tg for PS nanoparticles with the removal of the water-polymer/air-polymer interfaces, is in qualitative agreement with an earlier report on PS thin films.10 In that study, the thickness dependence of Tg for PS films supported on a silicon substrate was eliminated by removing the air-polymer interface with an evaporative layer of Au. These results are reprinted in Figure 4(b) for comparison. Combined, our work on bare and capped PS nanoparticles and many studies from the PS thin film literature hint at a common origin of the size-dependent Tg irrespective of sample geometry, that is, the free surface. However, we note that for a direct quantitative comparison between polymer samples confined to different geometries, it will be important to understand how the processing method and molecular chain conformations are related at the nanoscale.
Regardless of whether Tg is modified with confinement, confined glasses undergo structural relaxation (that is, physical aging). Structural relaxation is the spontaneous relaxation process toward equilibrium, which results in time-dependent properties of glassy materials. In recent years, the influence of confinement on structural relaxation of thin films has received growing attention. Except for studies on polymeric films for gas separation,90, 91 there exist few studies that have characterized the physical aging of polymer glasses confined to the nanoscale.92–101 Reductions in physical aging rate were reported for some supported polymer films such as PMMA93 and poly (2-vinyl pyridine),97 and polymer-silica nanocomposites of PMMA and P2VP95, 97, 102 compared to the corresponding bulk polymer. The observed suppression in physical aging under confinement has been attributed to interfacial effects which perturb glassy dynamics.93, 95, 97 This mechanism has been supported by both experiments and simulations. Local aging measurements of supported PMMA films showed a nearly complete suppression of aging within the first 25 nm of the interface,94 while simulations revealed that impeded glassy-state dynamics at the polymer-substrate interface can lead to a reduction of aging in confined polymers.103, 104 In the absence of strong polymer-substrate interactions, the physical aging rate of PS thin films has been reported to be comparable to or enhanced relative to that of the bulk.93, 96, 100, 101 Another element tuning aging rates of thin polymer films is the molecular architecture. The aging rate of star-shaped PS thin films on silicon oxide is reduced compared with its linear counterpart, and physical aging is also suppressed with reducing the degree of polymerization per arm in thin films of star-shaped PS.105
Notwithstanding a few studies that have probed structural relaxation of single-chain polymer nanoglobules,106–108 we have recently reported the first systematic investigation of structural relaxation of polymer nanoparticles.109 It is well known that the properties of glasses depend on the conditions of glass formation.110 Different environmental conditions and thermal histories during vitrification lead to glasses with different properties. Utilizing aqueous-suspended and silica-capped PS nanoparticles as model systems, we have been able to investigate the structural relaxation of confined glass formed under isobaric (constant pressure) and isochoric (constant volume) conditions.109
In that work, polymer nanoparticles were first annealed at temperature Tg + 20 K for 20 min to erase residual stresses in prior thermal history. Subsequently, samples were quenched to the desired aging temperature at a cooling rate of 40 K/min. Structural relaxation at various aging times (i.e., taging) was measured by DSC. Figure 5 illustrates heat capacity curves which show thermal peaks related to enthalpy recovery at Tg – Ta = 8 K for different aging times for bulk PS and 200 nm diameter aqueous-suspended and silica-capped PS nanoparticles, where Ta is the aging temperature. The enthalpy peaks represents the recovery of energy relaxed during physical aging. Larger enthalpy peaks signify greater structural relaxation. In comparison to bulk PS, both PS nanoparticles samples exhibited aging for much greater times.
Figure 6 depicts structural relaxation curves (aging isotherms) for bulk PS and 200 nm diameter PS nanoparticle systems at different temperatures. The quantity Tf – Ta is a measure of the departure from equilibrium and by definition equals zero at equilibrium, where Tf, the fictive temperature, is a measure of the glass structure. For all systems, structural relaxation curves asymptotically approached Tf – Ta = 0, which indicate the attainment (or approach) to equilibrium. In addition, increasing quench depth resulted in longer equilibration times. However, for the same value of Tg – Ta, time required for the attainment of equilibrium was longest for the aqueous-suspended nanoparticles while shortest for bulk PS. We observed that the time required to age into equilibrium did not strongly depend on the extent of confinement.
From data presented in Figure 6, it is possible to extract a rate of structural relaxation from the linear portion of the aging isotherms given as R = d(Tf − Ta)/d log taging. In comparison to bulk, the aging rate increased with confinement for aqueous-suspended nanoparticles. All things being equal, silica-capped PS nanoparticles aged at reduced rates compared to the analogous aqueous-suspended bare nanoparticles. This result indicated that the path to the glassy state does have an impact on the physical aging dynamics of confined glass. We note that the solid lines in Figure 6 are fits to the experimental data using the Tool–Narayanaswamy–Moynihan (TNM) model;111 see Ref.109 for a complete discussion.
The work of Koh and Simon,101 who used DSC to measure structural relaxation of stacked freestanding PS thin films, provides the best comparison to the observations for aqueous-suspended PS nanoparticles, the case of isobaric aging. They found that with decreasing film thickness the time required to reach equilibrium increased and the physical aging rate showed no systematic deviation from bulk. We contend that the two studies are in reasonable agreement. As discussed above, longer aging times were required to reach equilibrium for aqueous-suspended PS nanoparticles, a result in qualitative agreement with stacked PS thin films. Figure 7 illustrates the time required for the attainment of equilibrium for PS nanoparticles and stacked PS thin films. We have discussed that the apparent discrepancy of confinement effects on aging rates between nanoparticles and thin films may be resolved when the comparison is made via a characteristic length, that is, the surface area to volume ratio; see Ref.88 for more discussion. Similar to the Tg-confinement effect, the consistency in size-dependent aging rates of nanoparticles and thin films suggest a common origin of the aging-confinement effect irrespective of the confining geometry, i.e., interfacial effects.
A recent study by Roth and coworkers has investigated the influence of quenching condition (freestanding geometry vs. substrate-supported geometry) on glassy-state structural relaxation.112 They observed that thin (in micrometer scale) films quenched in the freestanding geometry exhibited a stronger aging-confinement effect. These differences were explained by thickness-dependent stresses introduced into the freestanding film during vitrification, which trapped the glass into different thermodynamic states. We suggest that silica-capped PS nanoparticles will allow for novel studies to systematically explore the influence of different stress levels on the physical aging response of confined polymer to test the above assertion. The reaction temperature under which the silica shell is grown atop the nanoparticle sets the stress-free temperature of the confined polymer. Because of the isochoric confinement condition of polymer nanoparticles encompassed in a rigid inorganic shell, temperature changes away from the reaction temperature will induce a significant internal pressure change. Furthermore, the stress imposed on the confined polymer may be tuned to be positive or negative depending on the relative values of the reaction and aging temperatures.
Beyond exploiting polymer nanoparticles to explore the influence of geometry on confined polymer properties, nanoparticles also allow for unique measurements that would be difficult to achieve via thin film studies. Understanding the impact of confinement on Tg is useful, but it alone fails to provide information about the temperature dependence of cooperative segmental dynamics, a phenomenon described by the dynamic fragility index. The dynamic fragility index (m) describes how fast dynamics change for glass-forming liquids as Tg is approached.113, 114 Mathematically, m is defined as:
where τ is the relaxation time and T is temperature. The fragility is normally measured under isobaric conditions; hence, m may be expressed as mp, the isobaric fragility. Several studies have examined mp of confined polymer.101, 115–119 For PS thin films supported on an Al substrate, mp has been observed to decrease as a function of decreasing film thickness when h < 50 nm.115 In the absence of strong polymer-substrate or polymer-inorganic nanofiller interactions, recent experiments101, 116 and simulations117–119 also suggest that mp decreases with increasing the extent of confinement.
When temperature is reduced toward Tg at constant pressure, there is a simultaneous reduction in thermal energy and specific volume of the polymer. Hence, it is possible to define mp in terms of an isochoric fragility, mv, via the following relationship:
when both are evaluated at the same thermodynamic point.120 The isochoric fragility describes the intrinsic effect of temperature on structural relaxation, as volume (V) is held constant. With respect to confined polymer, no experimental measurements exist of the isochoric fragility.
We have recently illustrated that silica-capped nanoparticles provides a facile means to assess the isochoric fragility of confined polymer. As we discussed above, capping polymer nanoparticles with a silica shell results in the polymer being confined under isochoric conditions. Using variable cooling rate DSC it is possible to determine fragility from the following equation:121, 122
which relates m to the cooling rate, Q, and Tf. In the above expression Tf,std is the standard fictive temperature determined via a standard cooling rate, Qstd. Here, m represents mv, as the polymer is isochorically confined. Figure 8 plots log (Q/Qstd) vs. (Tf,std/Tf) for bulk PS and a silica-capped PS nanoparticle sample with diameter of 460 nm, which we suggest represents the bulk isochoric condition. As noted from eq 3, both the slope and intercept is a measure of fragility. Here, as PS is confined isochorically, it is apparent that the slope of the linear fit of log (Q/Qstd) versus (Tf,std/Tf) is decreased slightly in magnitude, which indicates a decrease in the fragility. For bulk PS measured under isobaric conditions, mp = 150, while for silica-capped 460 nm diameter PS nanoparticles, mv was determined to be 140. For bulk polymer, the following empirical relationship has been established between mp and mv:123
Applying the experimentally determined mp and mv values to Eq. 4 shows good agreement of the relationship, which provides evidence that PS nanoparticles capped with a silica shell are indeed under isochoric conditions and that we are able to measure the isochoric fragility. Then, it follows that the isochoric fragility of confined polymer may be simply assessed by synthesizing smaller core-shell nanoparticles and undertaking similar DSC measurements. The results of such study have recently been reported and we refer the reader to Ref.124 for more information.
CONCLUSIONS AND FUTURE WORK
Although the physics of glass formation and the glassy state at the nanoscale has been an active area of research for nearly two decades, the subject remains rich in a multitude of phenomena that are not fully understood. In this feature article, we have highlighted the contributions to the field via studies on polymer nanoparticles. In addition, when possible, comparisons were made to the analogous thin film studies. We have suggested a common origin of confinement effects of the glassy properties of confined polymers, irrespective of geometry, that is, interfacial effects.
Although the prospect for future studies is plentiful, we briefly mention a few important studies that should be undertaken. With respect to PS, the influence of surfactants on the Tg of nanoparticles should be systematically investigated. Furthermore, the Tg of PS nanoparticles dispersed in solutions other than water, for example, ionic liquids, should be studied. The influence of chemical structure as well as crosslink density on the glassy properties of polymer nanoparticles has not been explored. As we have discussed above, it is now possible to prepare polymer nanoparticles with identical diameters but vastly different polymer chain molecular weights; this should allow for new studies to probe the impact of molecular weight on the glassy properties of confined polymer nanoparticles. Finally, we suggest that with the array of processing methods available to prepare polymer nanoparticles, it may be possible to symmetrically prepare nanoparticles of constant diameter but different density, as to explore the influence of chain structure on the properties of confined polymers.
The authors acknowledge usage of the PRISM Imaging and Analysis Center, which is supported in part by the NSF MRSEC program through the Princeton Center for Complex Materials (DMR-0819860). C. Zhang acknowledges support by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG). R. D. Priestley acknowledges the donors of the American Chemical Society Petroleum Research Fund (PRF 49903-DNI10) and the 3M-nontenured faculty grant program for partial support of the work.
Chuan Zhang received a B.S. in Chemistry with highest honors and highest distinction from the University of North Carolina at Chapel Hill in 2009. Currently, Chuan is a Ph.D. student in the Chemical and Biological Engineering department at Princeton University, where his research is supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG). Chuan's research interests include polymer nanoparticle preparation and polymer dynamics under nanoscale confinement.
Yunlong Guo is an Associate Research Scholar in the Department of Chemical and Biological Engineering at Princeton University. He obtained his Ph.D. in Mechanical Engineering from the University of Louisville in 2009. His research attempts to understand nanomechanics and thermodynamics of polymeric materials under confinement and to apply these physical principles to develop functional materials in applications of nanotechnology, energy and structural engineering.
Rodney D. Priestley is an Assistant Professor in the Department of Chemical and Biological Engineering at Princeton University. He obtained his Ph.D. in Chemical Engineering from Northwestern University in 2008. He completed a NSF/Chateaubriand postdoctoral fellowship at Ecole Superieure de Physique et Chimie Industrielles de la Ville de Paris. His research interests include polymer glasses, nanoconfined polymer dynamics, polymer thin film and nanoparticle formation, MAPLE and responsive polymers. He is the recipient of the Quadrant Award, an international award given for excellence in academic achievement and scientific research in polymer science and engineering, the ACS New Investigator Grant, the 3M Non-Tenured Faculty Grant, the NSF CAREER Award, and an AFOSR YIP Award. Rodney recently received the Wentz Junior Faculty Award from the School of Engineering and Applied Science at Princeton University and was named a 2013 Diverse Emerging Scholar.