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(a) Schematic of X-ray reflectivity measurement. (b) Raw data R vs 2a. (c) Normalized reflectivity profile, Rq 4 z vs q z. (d) Zoomed in region of reflectivity highlighting the importance of critical angle.
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Dispersion of nanoparticles in polymer nanocomposite films determines the application potential of
these systems as novel materials with unique physical properties. Grafting polymers to, mostly
inorganic, nanoparticles has been suggested as an effective strategy to enhance dispersion and
hence the efficacy of materials. In this review, we discuss t...
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... X-ray reflectivity from a single surface-Fresnel's formalism X ray reflectivity from a single surface can be under- stood from Fresnel's law of reflection for x-rays. Typical x- ray reflectivity measurement geometry is shown in Fig. 2(a). In XR measurements, we are concerned only with the specular part, i.e., the incident angle a i and exit angle a f are equal, i.e., a i ¼ a f ¼ a. 34 In this case, the momentum trans- fer ~ q ¼ ~ k f À ~ k i is along the surface normal, which is chosen to be the z coordinate. For a given wavelength k, momen- tum transfer ...
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... this one could understand (refer Fig. 2(b)) a typical reflectivity curve would have three parts, viz., (a) a plateau less than q c , (b) a steep decrease after q c , (c) a power law decay / q À4 z . We have so far only considered ideally smooth surfa- ces, but any real surface will have a finite roughness, character- ized by the root mean square deviation of surface height ...
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... R Nþ1 ¼ 0 (no reflection from the substrate, i.e., from below the substrate surface). The reflected waves from different interfaces would interfere and produce fringes corresponding to the thickness of the sample and of the individual layers. These fringes called the Kiessig-fringes can be related to the thickness d of the film via 2p=Dq z (Refer Fig. 2(b)). As seen, Parratt formalism takes into account multiple scattering effects and hence this approach is named ...
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... typical XR measurement consists of shining x-rays on the sample and collecting the reflected rays in the spec- ular positions (Fig. 2(a)). The raw data (Fig. 2(b)), i.e., reflectivity (ratio of intensity of reflected beam to the in- tensity of the direct beam) vs scattering angle itself could be used to extract a lot of critical information on the sam- ple. For a homogeneous thin film on a substrate, the reflec- tivity consists simply of film thickness oscillations, ...
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... typical XR measurement consists of shining x-rays on the sample and collecting the reflected rays in the spec- ular positions (Fig. 2(a)). The raw data (Fig. 2(b)), i.e., reflectivity (ratio of intensity of reflected beam to the in- tensity of the direct beam) vs scattering angle itself could be used to extract a lot of critical information on the sam- ple. For a homogeneous thin film on a substrate, the reflec- tivity consists simply of film thickness oscillations, i.e., Kiessig fringes of ...
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... beam) vs scattering angle itself could be used to extract a lot of critical information on the sam- ple. For a homogeneous thin film on a substrate, the reflec- tivity consists simply of film thickness oscillations, i.e., Kiessig fringes of constant amplitude riding on the decay corresponding to the Fresnel reflectivity (R $ q À4 z c.a., refer Fig. 2(c)). The periodicity of these oscillations, D2a, could be used to extract the film thickness. With increasing roughness, the amplitude of oscillations decays exponentially (%exp(Àg 2 z q 2 z ), where g z is the roughness along the z-direction). This raw data could then be con- verted to wavevector scale using the conversion discussed ...
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... vs q z should be flat showing a constant or decaying amplitude oscillations associated with the thickness of the film. But for any stratification of a different density material along the thickness, an additional modulation with a different periodicity (showing the thick- ness of the stratified layer) would be superimposed on the Kiessig fringes (Fig. 2(c)). Another crucial information of a sample could be extracted from the low q z , i.e., at the critical angle. From the position of the critical angle of total external reflection, the electron density of the film, the substrate, and any possible stratified layers could be extracted as shown in Fig. 2(d). In Fig. 2(d), two dips could be ...
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... be superimposed on the Kiessig fringes (Fig. 2(c)). Another crucial information of a sample could be extracted from the low q z , i.e., at the critical angle. From the position of the critical angle of total external reflection, the electron density of the film, the substrate, and any possible stratified layers could be extracted as shown in Fig. 2(d). In Fig. 2(d), two dips could be observed before the silicon critical angle which shows the electron density of the polymer nanocomposite film (q 1 c ) and for the stratified PGNP layer (q 2 c ). From this, the fraction of nanoparticles dispersed in the film and the frac- tion segregated at the interface could be verified ...
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... on the Kiessig fringes (Fig. 2(c)). Another crucial information of a sample could be extracted from the low q z , i.e., at the critical angle. From the position of the critical angle of total external reflection, the electron density of the film, the substrate, and any possible stratified layers could be extracted as shown in Fig. 2(d). In Fig. 2(d), two dips could be observed before the silicon critical angle which shows the electron density of the polymer nanocomposite film (q 1 c ) and for the stratified PGNP layer (q 2 c ). From this, the fraction of nanoparticles dispersed in the film and the frac- tion segregated at the interface could be verified ...
Citations
... 53,54 However, achieving a complete dispersion of nanoparticles for such a large fraction of nanoparticles is proven to be difficult, especially because van der Waals interactions and other long range attractive interactions often result in macroscopic aggregation of the particles. [1][2][3][20][21][22]33,42 Furthermore, the increased viscosity and the increased elastic modulus of these systems significantly reduce the applicability of conventional blending approaches for mixing polymers and nanoparticles. 9,11,13,48,52 To this end, various experimental approaches, mostly relying on polymer grafted nanoparticles (PGNPs), like polymer infiltration (via capillary rising), in situ polymerization from nanoparticle surfaces, 4,5 and layer-by-layer assembly containing oppositely charged nanoparticles and polymers 43 were devised to enhance the dispersion of nanoparticles. ...
... As confirmed by MD simulations these results can be explained by the difference in the entropic barrier of S-50k and L-50k PGNPs with matrix chains consistent with earlier results. 3,18,42,44,49 On the other hand, in contrast to the PGNP-PS systems, the PGNPs with long graft chains (L-PtBA) took a longer time to penetrate PtBA substrates than the PGNPs with shorter grafts (S-PtBA). Kim et al., 19 using simulations, revealed that the dominance of enthalpic and entropic regimes in the dispersion of PGNPs depends sensitively on the molecular weight of the grafting polymer. ...
High density functional polymer nanocomposites (PNCs) with high degree of dispersion have recently emerged as novel materials for various thermo-mechanical, optical and electrical applications. The key challenge is to attain a high loading while maintaining reasonable dispersion to attain maximum possible benefits from the functional nanoparticle additives. Here, we report a facile method to prepare polymer grafted nanoparticle (PGNP)-based high density functional polymer nanocomposites using thermal activation of a high density PGNP monolayer to overcome entropic or enthalpic barriers to insertion of PGNPs into the underlying polymer films. We monitor the temperature-dependent kinetics of penetration of a high density PGNP layer and correlate the penetration time to the effective enthalpic/entropic barriers. The experimental results are corroborated by coarse-grained molecular dynamics simulations. Repeated application of the methodology to insert nanoparticles by appropriate control over temperature, time and graft-chain properties can lead to enhanced densities of loading in the PNC. Our method can be engineered to produce a wide range of high density polymer nanocomposite membranes for various possible applications including gas separation and water desalination.
... Grafted polymer chains are selected to either modify the chemical properties of the nanoparticles or their morphology and geometry. These modifications, for instance, can sterically stabilize a dispersion of nanoparticles and prevent their aggregation, or enable us to tailor the interaction of the nanoparticles with targeted surfaces [8][9][10][11][12]. Of particular relevance to this research area is controlling the adhesion of nanoparticles to different surfaces, which is a challenge in numerous applications [13,14]. ...
Nanometer-curved surfaces are abundant in biological systems as well as in nano-sized technologies. Properly functionalized polymer-grafted nanoparticles (PGNs) adhere to surfaces with different geometries and curvatures. This work explores some of the energetic and mechanical characteristics of the adhesion of PGNs to surfaces with positive, negative and zero curvatures using Coarse-Grained Molecular Dynamics (CGMD) simulations. Our calculated free energies of binding of the PGN to the curved and flat surfaces as a function of separation distance show that curvature of the surface critically impacts the adhesion strength. We find that the flat surface is the most adhesive, and the concave surface is the least adhesive surface. This somewhat counterintuitive finding suggests that while a bare nanoparticle is more likely to adhere to a positively curved surface than a flat surface, grafting polymer chains to the nanoparticle surface inverts this behavior. Moreover, we studied the rheological behavior of PGN upon separation from the flat and curved surfaces under external pulling force. The results presented herein can be exploited in drug delivery and self-assembly applications.
... Grafted polymer chains are selected to either modify the chemical properties of the nanoparticles on the surface or their morphology and geometry. These modifications, for instance, can sterically stabilize a dispersion of nanoparticles and prevent their aggregation, or enable us to tailor the interaction of the nanoparticles with targeted surfaces [8][9][10][11][12] . Of particular relevance to this research area is controlling the adhesion of nanoparticles to different surfaces, which is a challenge in numerous applications 13,14 . ...
Nanometer-curved surfaces are abundant in biological systems as well as in nano-sized technologies. Properly functionalized polymer-grafted nanoparticles (PGNs) adhere to surfaces with different geometries and curvatures. This work explores some of the energetic and mechanical characteristics of the adhesion of PGNs to surfaces with positive, negative and zero curvatures using Coarse-Grained Molecular Dynamics (CGMD) simulations. Our calculated free energies of binding of the PGN to the curved and flat surfaces as a function of separation distance show that curvature of the surfaces critically impacts the adhesion strength. We find that the flat surface is the most adhesive, and the concave surface is the least adhesive surface. This somewhat counterintuitive finding suggests that while a bare nanoparticle is more likely to adhere to a positively curved surface than a flat surface, grafting polymer chains to the nanoparticle surface inverts this behavior. Moreover, we studied the rheological behavior of PGN upon separation from the flat and curved surfaces under external pulling force. The results presented herein can be exploited in drug delivery and self-assembly applications.
... [1][2][3][4][5] While tuning of these properties is of outstanding interest in most applied research, fundamental studies focused on the precise interactions between polymer and particles as well as on the microstructure of the nanoparticles distributed in the polymer matrix. [6][7][8][9] To prevent nanoparticles from aggregation they are stabilised by a shell. 10 The use of carboxyl acids, such as oleic acid, as shell ligands leads to a steric stabilisation of the particles. ...
The existence of magnetic dipolar nanoparticle chains at zero field has been predicted theoretically for decades, but these structures are rarely observed experimentally. A prerequisite is a permanent magnetic moment on the particles forming the chain. Here we report on the observation of magnetic dipolar chains of spherical iron oxide nanoparticles with a diameter of \SI{12.8}{\nano\meter}. The nanoparticles are embedded in an ultrathin polymer film. Due to the high viscosity of the polymer matrix, the dominating aggregation mechanism is driven by dipolar interactions. Smaller iron oxide nanoparticles (\SI{9.4}{\nano\meter}) show no permanent magnetic moment and do not form chains but compact aggregates. Mixed monolayers of different iron oxide nanoparticles and polymer at the air-water interface are characterized by Langmuir isotherms and in-situ X-ray reflectometry (XRR). The combination of the particles with a polymer leads to a stable polymer nanocomposite film at the air-water interface. XRR experiments show that nanoparticles are immersed in a thin polymer matrix of \SI{3}{\nano\meter}. Using atomic force microscopy (AFM) on Langmuir-Blodgett films, we measure the lateral distribution of particles in the film. An analysis of single structures within transferred films results in fractal dimensions that are in excellent agreement with 2D simulations.
... To describe chains grafted at planar as well as curved surfaces, the concept of the equilibrium ("effective") brush height has been often used. [46][47][48][49] In general, the equilibrium height of a layer depends upon L and N. For spherical nanoparticles, the height, H, can be determined from the local density using the expression proposed by Wijmans and Zhulina. ...
Using molecular dynamics, we evaluate the potential of mean force for two models of hybrid nanoparticles, namely, for the models with fixed and movable chain ligands. We also investigate the structure of segments of chains around nanoparticles and its change when one nanoparticle approaches the other. In the case of an isolated particle, we also employ a density functional theory to compute the segment density profiles. Moreover, to determine the structure of segments around a core, we have employed the concept of the so-called mass dipoles.
... One strategy commonly employed to achieve NP dispersion throughout a PNC is to graft polymer chains onto the NP surfaces. 74,[106][107][108][109][110][111][112][113][114] A number of parameters contribute to the overall morphology of the PNCs: the surface chemistry of the NPs, grafted chains and polymer host chains, the degree of polymerization of grafted and host chains, the NP surface grafting densities , the thermodynamic interactions between the grafted and host chains, 115 as well as the size and shape of the nanoparticles . Intermixing between the grafted and free host chains may be controlled through changes in key physical parameters. ...
The study of dynamic relaxations in polymer chains has been one of the cornerstones of polymer physics research for over half a century. Increased understanding of polymer chain relaxations has led to the development of macromolecules for packaging, drug delivery and sensor applications. As the challenges for these applications have become more demanding, it is now necessary to tailor polymer relaxation properties in more detailed and specific ways. In this thesis, we investigated two methods for tailoring polymer chain dynamics: (1) manipulation of molecular architecture and (2) introduction of inorganic nanoparticles into a polymer host. First, we demonstrate that the translational dynamics in star-shaped polystyrene can be tailored to behave as either a linear polymer or a soft colloid through the control of the star-shaped polymer molecular parameters such as functionality and arm molecular weight. We show that this is due to entropic intermolecular interactions caused by a tunable high-density core region close to the star branch point. Second, we show that in thin polymer films, the translational dynamics of the host polymer can be tailored through the introduction of inorganic polymer chain-end grafted particles. When these particles are well-dispersed throughout the polymer host, the relaxations of the host are shown to be strongly dependent on the confinement of the nanoparticles and the suppression of nanoparticle dynamics – leading to an order of magnitude increase in viscosity. If the particles are not well-dispersed, they are shown to segregate to the film interfaces and cause a region of high viscosity at the film free surface. This work highlights influences of molecular architecture, confinement and interfacial interactions on the dynamic relaxations of polymers and illustrates how these influences can be used to tailor polymer properties.
... Abbreviations: 2D, two-dimensional; AFM, atomic force microscopy; FWHM, full width half maximum; GNS, graphene nanosheets; H 2 O, water; hBN, hexagonal boron nitride; PNCs, polymer nanocomposites; PVA, polyvinyl alcohol; PVC, polyvinyl chloride; rpm, rotation per minutes; UTS, ultimate tensile strength; XRD, X-ray diffraction Background Polymer nanocomposites (PNCs) present a unique scope for many technological applications. It is an ever growing field due to their ease of processing and range of properties achieved with the addition of various nano-fillers [1]. Among the broad range of available nano-fillers, graphene is a single layer (~0.35 nm thick) of carbon atoms arranged in a two-dimensional (2D) honeycomb crystal lattice [2]. ...
Polyvinyl alcohol (PVA)-stabilized graphene nanosheets (GNS) of lateral dimension (L) ~1 μm are obtained via liquid phase exfoliation technique to prepare its composites in the PVA matrix. These composites show low levels of reinforcements due to poor alignment of GNS within the matrix as predicted by the modified Halpin-Tsai model. Drawing these composites up to 200 % strain, a significant improvement in mechanical properties is observed. Maximum values for Young’s modulus and strength are ~×4 and ~×2 higher respectively than that of neat PVA. Moreover, the rate of increase of the modulus with GNS volume fraction is up to 700 GPa, higher than the values predicted using the Halpin-Tsai theory. However, alignment along with strain-induced de-aggregation of GNS within composites accounts well for the obtained results as confirmed by X-ray diffraction (XRD) characterization.
... Thanks to the intense efforts of various researchers [25e32], a considerable understanding of the structure of PGNP-polymer mixtures have been achieved in the melt state. The phase behavior of PGNP-polymer mixtures (with identical chemical structures) can be understood through the parameter x, which is defined as the ratio of the molecular weights of grafting and matrix polymer i.e., x¼M g /M m , where M g and M m are the grafting and matrix molecular weights, respectively [26,28]. For mixtures with x>1, stretching energy of grafting polymers are lower than the gain in the entropic contribution due to the interpenetration of grafting and matrix chains. ...
... Even the systems with x<1, has been shown to wet the matrix polymers by varying various other parameters like grafting density of the PGNPs, polydispersity of the grafted layers [30,33,34], stiffness of the grafted chains [35] and the fraction of added polymers [26,36]. The differences in phase behavior with different x values were captured by the variation in the glass transition temperature and the viscosity of the mixtures [25,28]. While a large volume of data exists for PNCs, equivalent studies on PGNP-polymer binary suspensions are clearly lacking except for few recent reports [21,37,38]. ...
... to what is expected from the understanding in the melt state [25,26,28]. This is possibly due to the relatively high grafting density of the PGNPs used in our study. ...
... In recent years, soft nanocolloids have generated significant interest, especially due to their tunable strength and range of interactions. [1][2][3][4][5] Their structural and dynamical phase behavior has been shown to be significantly more diverse and richer than that of corresponding hard sphere colloids. [5][6][7][8][9][10] Star polymers and polymer grafted nanoparticles (PGNPs) constitute an important class of such soft nanocolloidal particles, for which some work has emerged recently where the structure and dynamics of either the pristine colloids or their binary mixtures have been investigated. ...
... despite the fact that they are also widely accepted as a prototypical additive in polymer matrices to create novel functional polymer nanocomposites (PNCs). [1][2][3][4]15,[22][23][24][25][26][27] Understanding the phase behavior of such systems is of paramount importance given their enormous technological relevance. Several groups have reported structural, dynamical, thermal, and mechanical properties of systems with different concentrations of PGNPs in a polymer matrix. ...
... where N chain is the total number of chains for a given mass of the PGNPs, and N core is the total number of cores. N chain and N core can be found using Equations (2) and (3), based on the experimental parameters ...
We present the results of combined experimental and theoretical (molecular dynamics simulations and integral equation theory) studies of the structure and effective interactions of suspensions of polymer grafted nanoparticles (PGNPs) in the presence of linear polymers. Due to the absence of systematic experimental and theoretical studies of PGNPs, it is widely believed that the structure and effective interactions in such binary mixtures would be very similar to those of an analogous soft colloidal material—star polymers. In our study, polystyrene-grafted gold
nanoparticles with functionality f = 70 were mixed with linear polystyrene (PS) of two different molecular weights for obtaining two PGNP:PS size ratios, ξ = 0.14 and 2.76 (where, ξ = Mg
/Mm
, Mg
and Mm
being the molecular weights of grafting and matrix polymers, respectively). The experimental structure factor of PGNPs could be modeled with an effective potential (Model-X), which has been found to be widely applicable for star polymers. Similarly, the structure factor of the blends with ξ = 0.14 could be modeled reasonably well, while the structure of blends with ξ = 2.76 could not be captured, especially for high density of added polymers. A model (Model-Y) for effective interactions between PGNPs in a melt of matrix polymers also failed to provide good agreement with the experimental data for samples with ξ = 2.76 and high density of added polymers. We tentatively attribute this anomaly in modeling the structure factor of blends with ξ = 2.76 to the questionable assumption of Model-X in describing the added polymers as star polymers with functionality 2, which gets manifested in both polymer-polymer and polymer-PGNP interactions especially at higher fractions of added polymers. The failure of Model-Y may be due to the neglect of possible many-body interactions among PGNPs mediated by matrix polymers when the fraction of added polymers is high. These observations point to the need for a new framework to understand not only the structural behavior of PGNPs but also possibly their dynamics and thermo-mechanical properties as well.
... In recent years, soft nanocolloids have generated significant interest, especially due to their tunable strength and range of interactions. [1][2][3][4][5] Their structural and dynamical phase behavior has been shown to be significantly more diverse and richer than that of corresponding hard sphere colloids. [5][6][7][8][9][10] Star polymers and polymer grafted nanoparticles (PGNPs) constitute an important class of such soft nanocolloidal particles, for which some work has emerged recently where the structure and dynamics of either the pristine colloids or their binary mixtures have been investigated. ...
... despite the fact that they are also widely accepted as a prototypical additive in polymer matrices to create novel functional polymer nanocomposites (PNCs). [1][2][3][4]15,[22][23][24][25][26][27] Understanding the phase behavior of such systems is of paramount importance given their enormous technological relevance. Several groups have reported structural, dynamical, thermal, and mechanical properties of systems with different concentrations of PGNPs in a polymer matrix. ...
... where N chain is the total number of chains for a given mass of the PGNPs, and N core is the total number of cores. N chain and N core can be found using Equations (2) and (3), based on the experimental parameters ...
