The Role of the Topological Constraints in the Chain Dynamics in All-Polymer Nanocomposites

Nonmonotonic Composition Dependence of Viscosity upon Adding Single-Chain Nanoparticles to Entangled Polymers

Well-characterized single-chain nanoparticles (SCNPs), synthesized from a linear polystyrene precursor through an intramolecular [4 + 4] thermal cycloaddition cross-linking reaction in dilute conditions, were added to entangled polystyrene melts at different concentrations. Starting from the pure linear melt, which is much more viscous than the melt of SCNPs, the zero-shear viscosity increased upon the addition of nanoparticles and reached a maximum before eventually dropping to the value of the SCNP melt. Molecular simulations reveal the origin of this unexpected behavior, which is the interplay of the very different compositional dependences of the dynamics of the two components. The SCNPs become much slower than the linear chains as their concentration decreases because they are threaded by the linear chains, reaching a maximum viscosity which is higher than that of the linear chains at a fraction of about 20%. This behavior is akin to that of single-loop ring polymers when added to linear matrices. This finding provides insights into the design and use of SCNPs as effective entropic viscosity modifiers of polymers and contributes to the discussion of the physics of loopy structures.

Disentangling Component Dynamics in an All-Polymer Nanocomposite Based on Single-Chain Nanoparticles by Quasielastic Neutron Scattering

We have investigated an all-polymer nanocomposite (NC) consisting of single-chain nanoparticles (SCNPs) immersed in a matrix of linear chains of their precursors (25/75% composition in weight). The SCNPs were previously synthesized via “click” chemistry, which induces intramolecular cross-links in the individual macromolecules accompanied by a slight shift (5–8 K) of the glass transition temperature toward higher values and a broadening of the dynamic response with respect to the raw precursor material. The selective investigation of the dynamics of the NC components has been possible by using properly isotopically labeled materials and applying quasielastic neutron scattering techniques. Results have been analyzed in the momentum transfer range where the coherent scattering contribution is minimal, as determined by complementary neutron diffraction experiments with polarization analysis. We observe the development of dynamic heterogeneity in the intermediate scattering function of the NC components, which grows with increasing time. Local motions in the precursor matrix of the NC are accelerated with respect to the reference bulk behavior, while the displacements of SCNPs’ hydrogens show enhanced deviations from Gaussian and exponential behavior compared with the pure melt of SCNPs. The resulting averaged behavior in the NC coincides with that of the pure precursor, in accordance with the macroscopic observations by differential scanning calorimetry (DSC) experiments.

Assessing the derivation of time parameters from branched polymer coarse-grain model

The parameterization of rheological models for polymers is often obtained from experiments via the top-down approach. This procedure allows us to determine good fitting parameters for homogeneous materials but is less effective for polymer mixtures. From a molecular simulation point of view, the timescales needed to derive those parameters are often accessed through the use of coarse-grain potentials. However, these potentials are often derived from linear model systems and the transferability to a more complex structure is not straightforward. Here, we verify the transferability of a potential computed from linear polymer simulations to more complex molecular shapes and present a type of analysis, which was recently formulated in the framework of a tube theory, to a coarse-grain molecular approach in order to derive the input parameters for a rheological model. We describe the different behaviors arising from the local topological structure of molecular sub-units. Coarse-grain models and mean-field based tube theory for polymers form a powerful combination with potentially important applications.

Crowded solutions of single-chain nanoparticles under shear flow

Single-chain nanoparticles (SCNPs) are ultrasoft objects obtained through purely intramolecular cross-linking of single polymer chains. By means of computer simulations with implemented hydrodynamic interactions, we investigate for the first time the effect of the shear flow on the structural and dynamic properties of SCNPs in semidilute and concentrated solutions. We characterize the dependence of several conformational and dynamic observables on the shear rate and the concentration, obtaining a set of power-law scaling laws. The concentration has a very different effect on the shear rate dependence of the former observables in SCNPs than in simple linear chains. Whereas for the latter the scaling behaviour is marginally dependent on the concentration, two clearly different scaling regimes are found for the SCNPs below and above the overlap concentration. At fixed shear rate SCNPs and linear chains also respond very differently to crowding. Whereas, at moderate and high Weissenberg numbers the linear chains swell, the SCNPs exhibit a complex non-monotonic behaviour. We suggest that these findings are inherently related to the topological interactions preventing concatenation of the SCNPs, which lead to less interpenetration than for linear chains, and to the limitation to stretching imposed by the permanent cross-links in the SCNPs, which itself limits the ways to spatially arrange in the shear flow.

Collective Motions and Mechanical Response of a Bulk of Single-Chain Nano-Particles Synthesized by Click-Chemistry

We investigate the effect of intra-molecular cross-links on the properties of polymer bulks. To do this, we apply a combination of thermal, rheological, diffraction, and neutron spin echo experiments covering the inter-molecular as well as the intermediate length scales to melts of single-chain nano-particles (SCNPs) obtained through 'click' chemistry. The comparison with the results obtained in a bulk of the corresponding linear precursor chains (prior to intra-molecular reaction) and in a bulk of SCNPs obtained through azide photodecomposition process shows that internal cross-links do not influence the average inter-molecular distances in the melt, but have a profound impact at intermediate length scales. This manifests in the structure, through the emergence of heterogeneities at nanometric scale, and also in the dynamics, leading to a more complex relaxation behavior including processes that allow relaxation of the internal domains. The influence of the nature of the internal bonds is reflected in the structural relaxation that is slowed down if bulky cross-linking agents are used. We also found that any residual amount of cross-links is critical for the rheological behavior, which can vary from an almost entanglement-free polymer bulk to a gel. The presence of such inter-molecular cross-links additionally hinders the decay of density fluctuations at intermediate length scales.

Synthesis of Polymer Single-Chain Nanoparticle with High Compactness in Cosolvent Condition: A Computer Simulation Study

Polymeric single-chain nanoparticles (SCNPs) are soft nano-objects synthesized by intramolecular crosslinking of isolated single polymer chains. Syntheses of such SCNPs usually need to be performed in a dilute solution. In such a condition, the bonding probability of the two active crosslinking units at a short contour distance along the chain backbone is much higher than those which are far away from each other. Such a reaction condition often results in local spheroidization and, therefore, the formation of loosely packed structures. How to inhibit the local spheroidization and improve the compactness of SCNPs is thus a major challenge for the syntheses of SCNPs. In this study, computer simulations are performed and the fact that a precollapse of the polymer chain conformation in a cosolvent condition can largely improve the probability of the crosslinking reactions at large contour distances is demonstrated, favoring the formations of closely packed globular structures. As a result, the formed SCNPs can be more spherical and have higher compactness than those fabricated in ultradilute good solvent solution in a conventional way. It is believed this simulation work can provide a insight into the effective syntheses of SCNPs with spherical conformations and high compactness.

Polymer dynamics under confinement

We review recent neutron scattering work and related results from simulation and complementary techniques focusing on the microscopic dynamics of polymers under confinement. Confinement is either realized in model porous materials or in polymer nanocomposites (PNC). The dynamics of such confined polymers is affected on the local segmental level, the level of entanglements as well as on global levels: (i) at the segmental level the interaction with the surface is of key importance. At locally repulsive surfaces compared to the bulk the segmental dynamics is not altered. Attractive surfaces slow down the segmental dynamics in their neighborhood but do not give rise to dead, glassy layers. (ii) Confinement generally has little effect on the inter-chain entanglements: both for weakly as well as for marginally confined polymers the reptation tube size is not changed. Only for strongly confined polymers disentanglement takes place. Similarly, in PNC at higher NP loading disentanglement phenomena are observed; in addition, at very high loading a transition from polymer caused topological constraints to purely geometrical constraints is observed. (iii) On the more global scale NSE experiments revealed important information on the nature of the interphase between adsorbed layer and bulk polymer. (iv) Polymer grafts at NP mutually confine each other, an effect that is most pronounced for one component NP. (v) Global diffusion of entangled polymers both in weakly and strongly attractive PNC is governed by the ratio of bottle-neck to chain size that characterizes the 'entropic barrier' for global diffusion.

Glass-Transition Dynamics of Mixtures of Linear Poly(vinyl methyl ether) with Single-Chain Polymer Nanoparticles: Evidence of a New Type of Nanocomposite Materials

Single-chain polymer nanoparticles (SCNPs) obtained through chain collapse by intramolecular cross-linking are attracting increasing interest as components of all-polymer nanocomposites, among other applications. We present a dielectric relaxation study on the dynamics of mixtures of poly(vinyl methyl ether) (PVME) and polystyrene (PS)-based SCNPs with various compositions. Analogous dielectric measurements on a miscible blend of PVME with the linear precursor chains of the SCNPs are taken as reference for this study. Both systems present completely different behaviors: While the blend with the linear precursor presents dynamics very similar to that reported for PVME/PS miscible blends, in the PVME/SCNP mixtures there are an appreciable amount of PVME segments that are barely affected by the presence of SCNPs, which nearly vanishes only for mixtures with high SCNP content. Interestingly, in the frame of a simple two-phase system, our findings point towards the existence of a SCNP-rich phase with a constant PVME fraction, regardless of the overall concentration of the mixture. Moreover, the dynamics of the PVME segments in this SCNP-rich phase display an extreme dynamic heterogeneity, a signature of constraint effects.

Facile Access to Completely Deuterated Single-Chain Nanoparticles Enabled by Intramolecular Azide Photodecomposition

Access to completely deuterated single-chain nanoparticles (dSCNPs) has remained an unresolved issue. Herein, the first facile and efficient procedure to produce dSCNPs is reported, which comprises: i) the use of commercially available perdeuterated cyclic ether monomers as starting reagents, ii) a ring-opening copolymerization process performed in bulk to produce a neat dSCNP precursor, iii) a standard azidation reaction to decorate this precursor with azide moieties, and iv) a facile intramolecular azide photodecomposition step carried out under UV irradiation at high dilution providing with highly valuable, completely deuterated soft nano-objects from the precursor. dSCNPs are used to investigate by means of neutron-scattering measurements the form factor (radius of gyration, scaling exponent) of polyethylene oxide (PEO) chains in nanocomposites with different amounts of dSCNPs. Moreover, to illustrate the possibilities offered by the synthetic route disclosed in this communication for potential applications, the significant reduction in viscosity observed in a pure melt of polyether-based single-chain nanoparticles when compared to a melt of the corresponding linear polymer chains is shown.

Intermolecular structural correlations in model globular and unconcatenated ring polymer liquids

We employ the field theoretic polymer integral equation theory to construct a segment-level theory for the thermodynamics and pair structure of dense liquids of interpenetrating ring polymers and a simple globule model. The latter is defined by a fractal mass distribution on all internal length scales with an exponent equal to the spatial dimension (dF = ds = 3). In an isochoric ensemble the dimensionless compressibility and pressure is predicted to vary exponentially with macromolecular volume fraction. An intermolecular correlation hole exists down to small length scales. This model appears to be useful for a recently studied experimental soft nanoparticle suspension, and also serves as a reference system for our analysis of ring liquids. Motivated by simulations, a two-fractal exponent ring model is adopted for the intramolecular structure factor. At smaller lengths it describes chain-like macromolecules, while on larger scales it corresponds to a space-filling object in the sense that dF = ds = 3. The crossover between these two regimes is of order the entanglement length of the linear chain analog. Based on a constant compressibility ensemble, the effective volume fraction grows at intermediate values of degree of polymerization (N), and crosses over to a very slow logarithmic growth at large N. A weaker intermolecular correlation hole is predicted. The number of nearest neighbor rings increases dramatically at small N, akin to linear chain melts, but then tends to saturate at large N, in accord with simulations. The tools developed may be relevant for other partially interpenetrating soft objects such as core-shell nanogels or microgels.

Computational investigation of microgels: synthesis and effect of the microstructure on the deswelling behavior

We present computer simulations of a realistic model of microgels. Unlike the regular network frameworks usually assumed in the simulation literature, we model and simulate a realistic and efficient synthesis route, mimicking cross-linking of functionalized chains inside a cavity. This model is inspired, e.g., by microfluidic fabrication of microgels from macromolecular precursors and is different from standard polymerization routes. The assembly of the chains is mediated by a low fraction of interchain crosslinks. The microgels are polydisperse in size and shape but globally spherical objects. In order to deeply understand the microgel structure and eventually improve the synthesis protocol we characterize their conformational properties and deswelling kinetics, and compare them with the results found for microgels obtained via underlying regular (diamond-like) structures. For the same molecular weight, monomer concentration and effective degree of cross-linking, the specific microstructure of the microgel has no significant effect on the locus of the volume phase transition (VPT). However, it strongly affects the deswelling kinetics, as revealed by a consistent analysis of the domain growth during the microgel collapse. Though both the disordered and the regular networks exhibit a similar early growth of the domains, an acceleration is observed in the regular network at the late stage of the collapse. Similar trends are found for the dynamic correlations coupled to the domain growth. As a consequence, the fast late processes for the domain growth and the dynamic correlations in the regular network are compensated, and the dynamic correlations follow a power-law dependence on the growing length scale that is independent of the microgel microstructure.

Effect of chain stiffness on the structure of single-chain polymer nanoparticles

Polymeric single-chain nanoparticles (SCNPs) are soft nano-objects synthesized by purely intramolecular cross-linking of single polymer chains. By means of computer simulations, we investigate the conformational properties of SCNPs as a function of the bending stiffness of their linear polymer precursors. We investigate a broad range of characteristic ratios from the fully flexible case to those typical of bulky synthetic polymers. Increasing stiffness hinders bonding of groups separated by short contour distances and increases looping over longer distances, leading to more compact nanoparticles with a structure of highly interconnected loops. This feature is reflected in a crossover in the scaling behaviour of several structural observables. The scaling exponents change from those characteristic for Gaussian chains or rings in θ-solvents in the fully flexible limit, to values resembling fractal or 'crumpled' globular behaviour for very stiff SCNPs. We characterize domains in the SCNPs. These are weakly deformable regions that can be seen as disordered analogues of domains in disordered proteins. Increasing stiffness leads to bigger and less deformable domains. Surprisingly, the scaling behaviour of the domains is in all cases similar to that of Gaussian chains or rings, irrespective of the stiffness and degree of cross-linking. It is the spatial arrangement of the domains which determines the global structure of the SCNP (sparse Gaussian-like object or crumpled globule). Since intramolecular stiffness can be varied through the specific chemistry of the precursor or by introducing bulky side groups in its backbone, our results propose a new strategy to tune the global structure of SCNPs.

Translational and rotational dynamics of an ultra-thin nanorod probe particle in linear polymer melts

Translational and rotational dynamics of a single rigid ultra-thin nanorod probe particle in linear polymer melts are investigated using coarse-grained molecular dynamics (CG-MD) simulations.

Tunable synthetic control of soft polymeric nanoparticle morphology

With a growing variety of nanoparticles available, research probing the influence of particle deformability, morphology, and topology on the behavior of all polymer nanocomposites is also increasing. In particular, the behavior of soft polymeric nanoparticles in polymer nanocomposites has displayed unique behavior, but their precise performance depends intimately on the internal structure and morphology of the nanoparticle. With the goal of providing guidelines to control the structure and morphology of soft polymeric nanoparticles, we have examined monomer starved semi-batch nano-emulsion polymerizations that form organic, soft nanoparticles, to correlate the precise structure of the nanoparticle to the rate of monomer addition and crosslinking density. The synthesis method produces 5-20 nm radii polystyrene nanoparticles with tunable morphologies. We report small angle neutron scattering (SANS) results that correlate synthetic conditions to the structural characteristics of soft polystyrene nanoparticles. These results show that the measured molecular weight of the nanoparticles is controlled by the monomer addition rate, the total nanoparticle radius is controlled by the excess surfactant concentration, and the crosslinking density has a direct effect on the topology of each nanoparticle. These studies thus provide pathways to control these 3 structural characteristics of the nanoparticle. This research, therefore provides a conduit to thoroughly investigate the effect of structural features of soft nanoparticles on their individual properties and those of their polymer nanocomposites.

In Silico Synthesis of Microgel Particles

Microgels are colloidal-scale particles individually made of cross-linked polymer networks that can swell and deswell in response to external stimuli, such as changes to temperature or pH. Despite a large amount of experimental activities on microgels, a proper theoretical description based on individual particle properties is still missing due to the complexity of the particles. To go one step further, here we propose a novel methodology to assemble realistic microgel particles in silico. We exploit the self-assembly of a binary mixture composed of tetravalent (cross-linkers) and bivalent (monomer beads) patchy particles under spherical confinement in order to produce fully bonded networks. The resulting structure is then used to generate the initial microgel configuration, which is subsequently simulated with a bead-spring model complemented by a temperature-induced hydrophobic attraction. To validate our assembly protocol, we focus on a small microgel test case and show that we can reproduce the experimental swelling curve by appropriately tuning the confining sphere radius, something that would not be possible with less sophisticated assembly methodologies, e.g., in the case of networks generated from an underlying crystal structure. We further investigate the structure (in reciprocal and real space) and the swelling curves of microgels as a function of temperature, finding that our results are well described by the widely used fuzzy sphere model. This is a first step toward a realistic modeling of microgel particles, which will pave the way for a careful assessment of their elastic properties and effective interactions.

Effects of precursor topology and synthesis under crowding conditions on the structure of single-chain polymer nanoparticles

By means of molecular dynamics simulations, we investigate the formation of single-chain nanoparticles through intramolecular cross-linking of polymer chains, in the presence of their precursors acting as purely steric crowders in concentrated solution. In the case of linear precursors, the structure of the resulting SCNPs is weakly affected by the density at which the synthesis is performed. Crowding has significant effects if ring precursors are used: higher concentrations lead to the formation of SCNPs with more compact and spherical morphologies. Such SCNPs retain in the swollen state (high dilution) the crumpled globular conformations adopted by the ring precursors in the crowded solutions. Increasing the concentration of both the linear and ring precursors up to 30% leads to faster formation of the respective SCNPs, prior to deceleration expected at higher densities. The results presented here propose promising new routes for the synthesis of globular SCNPs, which are usually elusive by conventional methods.