Steric and bridging interactions between two plates induced by grafted polyelectrolytes

If colloidal particles are grafted with a polymer, then the grafted chains can provide steric repulsion between them. If some of the grafted polymer chains are also adsorbed to a second particle, then a bridging force is generated as well. For uncharged plates and polymer, the following contributions to the free energy of the system have been taken into account in the calculation of the interaction force: (i) the Flory-Huggins expression for the mixing free energy of the grafted chains with the liquid; (ii) the entropy loss due to the connectivity of the polymeric segments; (iii) the van der Waals interactions between the segments and the plates; and (iv) the free energy of adsorption of the polymer segments of the grafted chains on the other plate. For charged plates, the electrostatic free energy as well as the free energy of the electrolyte are included in the total free energy of the system. By minimizing the free energy with respect to the segment concentration and, when it is the case, with respect to the electrical potential, equations for the segment number density distribution and for the electrical potential are obtained, on the basis of which the interactions between two plates grafted with polymer chains that can be also adsorbed on the other plate were calculated. The interaction thus obtained includes steric and bridging forces.     

Effect of bidispersity in grafted chain length on grafted chain conformations and potential of mean force between polymer grafted nanoparticles in a homopolymer matrix

In efforts to produce polymeric materials with tailored physical properties, significant interest has grown around the ability to control the spatial organization of nanoparticles in polymer nanocomposites. One way to achieve controlled particle arrangement is by grafting the nanoparticle surface with polymers that are compatible with the matrix, thus manipulating the interfacial interactions between the nanoparticles and the polymer matrix. Previous work has shown that the molecular weight of the grafted polymer, both at high grafting density and low grafting density, plays a key role in dictating the effective inter-particle interactions in a polymer matrix. At high grafting density nanoparticles disperse (aggregate) if the graft molecular weight is higher (lower) than the matrix molecular weight. At low grafting density the longer grafts can better shield the nanoparticle surface from direct particle-particle contacts than the shorter grafts and lead to the dispersion of the grafted particles in the matrix. Despite the importance of graft molecular weight, and evidence of non-trivial effects of polydispersity of chains grafted on flat surfaces, most theoretical work on polymer grafted nanoparticles has only focused on monodisperse grafted chains. In this paper, we focus on how bidispersity in grafted chain lengths affects the grafted chain conformations and inter-particle interactions in an implicit solvent and in a dense homopolymer polymer matrix. We first present the effects of bidispersity on grafted chain conformations in a single polymer grafted particle using purely Monte Carlo (MC) simulations. This is followed by calculations of the potential of mean force (PMF) between two grafted particles in a polymer matrix using a self-consistent Polymer Reference Interaction Site Model theory-Monte Carlo simulation approach. Monte Carlo simulations of a single polymer grafted particle in an implicit solvent show that in the bidisperse polymer grafted particles with an equal number of short and long grafts at low to medium grafting density, the short grafts are in a more coiled up conformation (lower radius of gyration) than their monodisperse counterparts to provide a larger free volume to the longer grafts so they can gain conformational entropy. The longer grafts do not show much difference in conformation from their monodisperse counterparts at low grafting density, but at medium grafting density the longer grafts exhibit less stretched conformations (lower radius of gyration) as compared to their monodisperse counterparts. In the presence of an explicit homopolymer matrix, the longer grafts are more compressed by the matrix homopolymer chains than the short grafts. We observe that the potential of mean force between bidisperse grafted particles has features of the PMF of monodisperse grafted particles with short grafts and monodisperse grafted particles with long grafts. The value of the PMF at contact is governed by the short grafts and values at large inter-particle distances are governed by the longer grafts. Further comparison of the PMF for bidisperse and monodisperse polymer grafted particles in a homopolymer matrix at varying parameters shows that the effects of matrix chain length, matrix packing fraction, grafting density, and particle curvature on the PMF between bidisperse polymer grafted particles are similar to those seen between monodisperse polymer grafted particles.     

Effect of solvent quality on the dispersibility of polymer-grafted spherical nanoparticles in polymer solutions

In this work, lattice-based self consistent field theory is used to study the structural properties of individual polymer-grafted spherical nanopartices and particle-particle interactions in polymer melts and solutions under variable solvent conditions. Our study has focused on the depth of the minimum in the potential of mean force between the two brush-coated nanoparticles, if such a minimum occurs, and we have also addressed the corresponding radial density profiles of free and grafted chains around a single nanoparticle, in an attempt to clarify the extent of correlation between the depth of the minimum, W(min), and the parameter δ characterizing the interpenetration between the profiles of free and grafted chains. Although one cannot establish a simple one-to-one correspondence between W(min) and δ, we do find common trends, in particular, if the solvent conditions for free and grafted chains differ: varying the volume fraction of the free chains, δ typically exhibits a broad minimum, corresponding to a region where the magnitude of W(min) exceeds thermal energy k(B)T, leading to particle aggregation.     

Nanoparticle stability in semidilute and concentrated polymer solutions

The wetting of PDMS-grafted silica spheres (PDMS- g-silica) is connected to their depletion restabilization in semidilute and concentrated PDMS/cyohexane polymer solutions. Specifically, we found that a wetting diagram of chemically identical graft and free homopolymers predicts stability of hard, semisoft, and soft spheres as a function of the bulk free polymer volume fraction, graft density, and the graft and free polymer chain lengths. The transition between stable and aggregated regions is determined optically and with dynamic light scattering. The point of demarcation between the regions occurs when the graft and free polymer chains are equal in length. When graft chains are longer than free chains, the particles are stable; in contrast, the particles are unstable when the opposite is true. The regions of particle stability and instability are corroborated with theoretical self-consistent mean-field calculations, which not only show that the grafted brush is responsible for particle dispersion in the complete wetting region but also aggregation in the incomplete wetting region. Ultimately, our results indicate that depletion restabilization depends on the interfacial properties of the nanoparticles in semidilute and concentrated polymer solutions.     

Polymer modified colloidal dispersions

The effect of added polyvinyl alcohol (PVA) and polyvinyl pyrrolidone (PVP) on a dispersion of polystyrene particles stabilised with grafted methoxy PEG chains is discussed. PVA adsorbed more strongly on the particles compared to PVP. Polymer addition led to stable mixtures in the case of PVA compared to depletion phase separation observed in the case of PVP. Rheological measurements showed thickening of the dispersion and absence of any structure in the case of PVA, in contrast to structure formation in the case of PVP due to depletion phase separation. A weak gel state was reached for ca. 7% w/w PVP. The observed behaviour is in accord with the relative propensity of PVA and PVP to interact with the particle surface, the grafted chains and their solubility in water. The solvency of the free polymer chains dominated the overall behaviour while the contribution from the incompatibility between free and grafted chains was conterbalanced by differences in the free polymer adsorption on the particles.     

Adsorption of enantiomeric poly(lactide)s on surface-grafted poly(L-lactide)

We show that resistance of densely grafted polymer layers to adsorption of chemically identical free chains, which is known to be caused by entropic expulsion of free chains from the grafted layer, can be suppressed using the grafted and free chains of opposite stereoconfiguration. Specifically, we study adsorption of poly(L-lactide) (PLLA) and its enantiomer poly(D-lactide) (PDLA) onto layers of surface-grafted PLLA in acetonitrile and chloroform by infrared spectroscopy (IR). The grafted layers with thicknesses ranging from 7 to 35 nm are produced by ring-opening polymerization of L-lactide from hydroxyl end-groups of a self-assembled monolayer on gold. The IR data indicate that adsorption on the bare gold surface is the same for the L- and D-form of the polymer. However, covering the gold with the surface-grafted PLLA produces a significant decline in the adsorption of free PLLA and, by contrast, a strong enhancement in the adsorption of free PDLA. In addition, the IR data indicate that the adsorbed PDLA chains are stereocomplexed with the grafted PLLA chains. Thus, entropic expulsion of free chains from the grafted layer, which is responsible for the resistance of surface-grafted PLLA to adsorption of free PLLA, is suppressed in the case of free PDLA by stereocomplexation between the grafted and free chains.     

Curvature effects upon interactions of polymer-grafted nanoparticles in chemically identical polymer matrices

We study the interactions between polymer-grafted nanoparticles immersed in a chemically identical polymer melt using a numerical implementation of polymer mean-field theory. We focus on the interpenetration width between the grafted and free chains and its relationship to the polymer-mediated interparticle interactions. To this end, we quantify the interpenetration width as a function of particle curvature, grafting density, and the relative molecular weights of the grafted and free chains. We show the onset of wetting and dewetting as a function of these quantities and explain our results through simple scaling arguments to include the effects of curvature. Subsequently, we show that the interparticle potentials correlate quantitatively with the trends displayed by the interpenetration widths.     

Nanoparticle Dispersion and Glass Transition Behavior of Polyimide-grafted Silica Nanocomposites

How to control the spatial distribution of nanoparticles to meet different performance requirements is a constant challenge in the field of polymer nanocomposites.Current studies have been focused on the flexible polymer chain systems.In this study,the rigid polyimide(PI) chain grafted silica particles with different grafting chain lengths and grafting densities were prepared by "grafting to" method,and the influence of polymerization degree of grafted chains(N),matrix chains(P),and grafting density(a) on the spatial distribution of nanoparticles in the PI matrix was explored.The glass transition temperature(Tg) of PI composites was systematically investigated as well.The results show that silica particles are well dispersed in polyamic acid composite systems,while aggregation and small clusters appear in PI nanocomposites after thermal imidization.Besides,the particle size has no impact on the spatial distribution of nanoparticles.When σ·N0.5<<(N/P)2,the grafted and matrix chains interpenetrate,and the frictional resistance of the segment increases,resulting in restricted relaxation kinetics and Tg increase of the PI composite system.In addition,smaller particle size and longer grafted chains are beneficial to improving Tg of composites These results are all propitious to complete the microstructure control theory of nanocomposites and make a theoretical foundation for the high performance and multi-function of PI nanocomposites.     

Phase behavior of a blend of polymer-tethered nanoparticles with diblock copolymers

Using the self-consistent field theory (SCFT), we investigate the phase behavior of a mixture of diblock copolymers and nanoparticles with monodisperse polymer chains tethered to their surfaces. We assume the size of the nanoparticles to be much smaller than that of the attached polymer chains and therefore model the particles with their grafted polymer "shell" as star polymers. The polymer chains attached to the particles are of the same species as one of the blocks of the symmetric diblock copolymer. Of primary interest is how to tune the shell of the particle by changing both the length and number of tethered polymers in order to achieve higher loading of nanoparticles within an ordered structure without macrophase separation occurring. We find that the phase behavior of the system is very sensitive to the size of the particle including its tethered shell. The region of microphase separation is increased upon decreasing the star polymer size, which may be achieved by shortening and/or removing tethered polymer chains. To explore the possible structures in these systems we employ SCFT simulations that provide insight into the arrangement of the different species in these complex composites.     

The influence of PEG macromonomers on the size and properties of thermosensitive aqueous microgels

We describe the preparation and thermal response of aqueous microgels based on poly(N-vinyl caprolactam) containing grafted poly(ethylene glycol) (PEG) chains. These microgels were synthesized by free radical copolymerization of vinyl caprolactam and acetoacetoxyethyl methacrylate in the presence of methoxy-capped poly(ethylene glycol)methacrylate macromonomers. We show that variation of the amount of PEG macromonomer or the length of the PEG chain provides effective control of the microgel diameter in the range 60–220 nm. The presence of the grafted PEG chains improves the colloidal stability of the microgels. The incorporation of the PEG macromonomers into microgel structure decreases the swelling degree and induces a shift of the volume phase transition to higher temperatures. This paper is dedicated to Professor Haruma Kawaguchi in honor of his many contributions to the field of polymer particle synthesis and applications.     

Electrohydrodynamics of spherical polyampholyte‐grafted nanoparticles: Multiscale simulations by coupling of molecular dynamics and lattice‐boltzmann method

We perform multiscale simulations based on the coupling of molecular dynamics and lattice‐Boltzmann (LB) method to study the electrohydrodynamics of a polyampholyte‐grafted spherical nanoparticle. The long‐range hydrodynamic interactions are modeled by coupling the movement of particles to a LB fluid. Our results indicate that the net‐neutral soft particle moves with a nonzero mobility under applied electric fields. We systematically explore the effects of different parameters, including the chain length, grafting density, electric field, and charge sequence, on the structures of the polymer layer and the electrophoretic mobility of the soft particle. It shows that the mobility of nanoparticles has remarkable dependence on these parameters. We find that the deformation of the polyampholyte chains and the ion distribution play dominant roles in modulating the electrokinetic behavior of the polyampholyte‐grafted particle. The enhancement or reduction in the accumulation of counterions around monomers can be attributed to the polymer layer structure and the conformational transition of the chains in the electric field. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1435–1447     

Effect of matrix bidispersity on the morphology of polymer-grafted nanoparticle-filled polymer nanocomposites

We present a simulation study showing the effect of bidispersity in matrix homopolymer length on the wetting/dewetting of homopolymer-grafted nanoparticles and the morphology of polymer nanocomposites where the graft and matrix polymer chemistries are identical. In a bidisperse matrix with equal number of short and long chains and average matrix length greater than the monodisperse graft length, the densely grafted polymer layer is preferentially wet by the short chains and relatively dewet by the long chains. This is driven by a larger gain in entropy of mixing between graft and matrix for short matrix chains than long matrix chains. Despite the preferential wetting of the short and dewetting of long chains, matrix length bidispersity does not significantly change the overall wetting of the grafted layer. Unlike graft length bidispersity that significantly improves particle dispersion, matrix length bidispersity slightly increases particle aggregation in the polymer matrix. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1661–1668     

Mean‐field theoretical analysis of brush‐coated nanoparticle dispersion in polymer matrices

The equilibrium dispersion of nanoparticles with grafted polymer chains into polymer matrices, of the same chemical structure as the brush, is studied through the device of mean‐field theory. Our results show that the disperion of brush‐coated nanoparticles into a matrix polymer is improved with (i) decreasing particle radius and (ii) increasing brush chain length. Both of these aspects can be understood based on the fact that, unlike the case of planar surfaces, homopolymer chains end‐grafted to spherical nanoparticle surfaces tangentially spread away from the surface thus alleviating the packing frustration that is created by the relatively high grafting densities. This permits significant brush/matrix overlap, even at high grafting densities, a regime that has only recently become experimentally available due to advances in polymer synthesis (i.e., the “grafting‐to” methods). © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 351–358, 2008     

Polymer Chain Conformation on Deuterated Polystyrene Nanoparticles Investigated by SANS

We previously reported that grafted polystyrene (PS) chains on silica nanoparticles at a low grafting density show similar conformations to free PS chains in the same solvent, THF (diameter ?50 nm, Colloid.poly.Sci. (2013), 291, 9, 2087–2099). As an extension of our previous study we choose an organic nanoparticle (deuterated polystyrene, dPS) instead of inorganic nanoparticle to see the impact of the substrate material on chain conformation. Additionally, a wider range of molecular weights were prepared to investigate the conformation feature of grafted PS chains more in detail. Small angle neutron scattering (SANS) experiments were performed to characterize PS grafted dPS particles in good solvent condition, with deuterated toluene and deuterated THF as solvent. To get insight into the conformation of the grafted PS layer we apply a scaling law describing the dimension of free PS polymer in good solvent condition to the obtained thickness of the grafted PS layer. We find an overall agreement with the scaling law where the thickness of the grafted PS layer is slightly larger than 2R_g of the free polymer chains in the respective solvent giving hint for semi dilute polymer brush (SDPB) situation.     

Particle monolayer formation at the air–water interface by silica particle with well‐defined grafted polymer

Particle monolayer formation at the air–water interface by polymer‐grafted colloidal silica was investigated. Methyl methacrylate (MMA) was polymerized from initiative bromide groups at colloidal silica surface by atom transfer radical polymerization. We obtained polymer‐grafted silica particle (SiO₂‐PMMA) with relative narrow polydispersity of PMMA. For the polymer‐grafted particle with high graft density, particle monolayer formation was confirmed by π‐A isotherm measurement and SEM observation. Interparticle distance was controllable by surface pressure. Furthermore, grafted polymer chains were suggested to be fairly extended at the air–water interface. However, for the polymer‐grafted particle with low graft density, monolayer structure on substrate showed aggregation and voids. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2789–2797, 2006     

Tethered nanoparticle-polymer composites: phase stability and curvature

Phase behavior of poly(ethylene glycol) (PEG) tethered silica nanoparticles dispersed in PEG hosts is investigated using small-angle X-ray scattering. Phase separation in dispersions of densely grafted nanoparticles is found to display strikingly different small-angle X-ray scattering signatures in comparison to phase-separated composites comprised of bare or sparsely grafted nanoparticles. A general diagram for the dispersion state and phase stability of polymer tethered nanoparticle-polymer composites incorporating results from this as well as various other contemporary studies is presented. We show that in the range of moderate to high grafting densities the dispersion state of nanoparticles in composites is largely insensitive to the grafting density of the tethered chains and chemistry of the polymer host. Instead, the ratio of the particle diameter to the size of the tethered chain and the ratio of the molecular weights of the host and tethered polymer chains (P/N) are shown to play a dominant role. Additionally, we find that well-functionalized nanoparticles form stable dispersions in their polymer host beyond the P/N limit that demarcates the wetting/dewetting transition in polymer brushes on flat substrates interacting with polymer melts. A general strategy for achieving uniform nanoparticle dispersion in polymers is proposed.     

Studies on Mechanism of Grafting of Polystyrene on Elastomer Backbone

The mechanism of grafting of polystyrene on a polybutadiene (PB) backbone during the preparation of impact-resistant polystyrene was studied by withdrawing samples during propolym-erization from beginning of the reaction to about 25% conversion. Good separation of the “elastomer and graft” fraction of the polymer from the free polystyrene part could be achieved by using 0.24 volume fraction of methanol in (MEK + benzene) + methanol solvent-nonsolvent. IR analysis of the grafted fraction showed that the microstructure of the elastomer remained unaltered. The unsaturation of the samples studied through the bromine number as well as by the perbenzoic acid number was also found to remain unchanged. Formation of free polystyrene started with the onset of polymerization and was faster. During prepolymerization, 80% of styrene converted constantly to form free polystyrene and 20% went into the grafted polymer. The results indicate that grafting is initiated through proton abstraction at the α-carbon of butadiene, most probably by initiator radicals. The grafted polystyrene chains possibly are shorter than free polystyrene chains.     

Static and dynamic properties of the interface between a polymer brush and a melt of identical chains

Molecular-dynamics simulations of a short-chain polymer melt between two brush-covered surfaces under shear have been performed. The end-grafted polymers which constitute the brush have the same chemical properties as the free chains in the melt and provide a soft deformable substrate. Polymer chains are described by a coarse-grained bead-spring model, which includes excluded volume and backbone connectivity of the chains. The grafting density of the brush layer offers a way of controlling the behavior of the surface without altering the molecular interactions. We perform equilibrium and nonequilibrium molecular-dynamics simulations at constant temperature and volume using the dissipative particle dynamics thermostat. The equilibrium density profiles and the behavior under shear are studied as well as the interdigitation of the melt into the brush, the orientation on different length scales (bond vectors, radius of gyration, and end-to-end vector) of free and grafted chains, and velocity profiles. The obtained boundary conditions and slip length show a rich behavior as a function of grafting density and shear velocity.     

Control of the Colloidal Stability of Polymer-Grafted-Silica Nanoparticles Obtained by Atom Transfer Radical Polymerization

Polymer chains are grafted from silica nanobeads. The method consists in grafting first the initiator molecules on the silica surface. Then, the polymerization of styrene or n-butyl methacrylate using Atom Transfer Radical Polymerization, is conducted. The nanoparticles are kept in solution during the whole process to avoid irreversible aggregation. The state of dispersion of the grafted silica nanoparticles is followed by Small Angle Neutron Scattering, as well as the quantity and the spatial organisation of the polymer. This is done during the functionalisation and the polymerization, but also after purification where free polymer chains are eliminated. This permits to reach a quantitative level of SANS analysis from these purified particles, which is compared to chemical data given by Size Exclusion Chromatography and Thermogravimetric analysis.