A molecular dynamics simulation study of nanoparticle interactions in a model polymer-nanoparticle composite
Introduction
Particles are important additives for altering and enhancing the properties of polymers [1]. A well-known example is the addition of carbon black to rubbers that is responsible for increased strength and durability [2], [3]. Because of their very high surface area to volume ratio, the effect of nanoscopic particles (nanoparticles) on the properties of a polymer matrix and the resulting properties of the polymer–nanoparticle composite, or PNPC, can be much more dramatic than is observed in conventional polymer–particle composites. Such PNPCs exhibit promising properties for a wide variety of applications [4], [5], [6], [7], [8]. The properties of PNPCs are strongly influenced by nanoparticle size and filler fraction, nanoparticle shape, nanoparticle distribution, polymer molecular weight and the nature of the interactions between the nanoparticle and polymer matrix. There is a great need for insight that can be provided by theory and simulation regarding factors controlling the dispersion of nanoparticles and the properties of the PNPCs as a function of these parameters.
The application of theory and simulation methods to PNPCs is much less mature than in the related field of colloidal suspensions. Theoretical efforts that have been successful for colloid-polymer solutions (e.g., [9], [10], [11], [12], [13], [14], [15], [16]) have not been fully extended to the dense polymer melts typical of a PNPC. Furthermore, until quite recently [15] theoretical studies of colloid-polymer solutions have dealt almost exclusively with cases where the radius of the colloidal particle is large compared to the radius of gyration of the polymer. The number of molecular simulation studies [17], [18], [19] that have been performed on PNPCs in order to gain insight in their structure and dynamics is also quite limited. These simulations revealed that the presence of nanoparticles as well as the strength of nanoparticle–polymer interactions strongly influence the dynamics, viscosity, and dynamic shear modulus of the polymer matrix and PNPC. Balazs et al. have shown in a series of lattice Monte Carlo and self-consistent field simulations [20], [21], [22], [23], [24] of diblock copolymer/nanoparticle mixtures that nanoparticle-polymer interactions strongly influence the dispersion of nanoparticles. In the present work molecular dynamics (MD) simulations have been employed to examine the polymer-induced interactions between nanoparticles in a dense polymer matrix as a function of polymer molecular weight and the strength of the nanoparticle-polymer interaction, and to correlate polymer matrix effects with the dispersion of nanoparticles in a model PNPC. Here we concentrate on the regime where the radius of the particle, the radius of gyration of the polymer and the statistical segment length of the polymer are comparable which is particularly difficult to address theoretically [15], [16].
Section snippets
Coarse-grained polymer–nanoparticle composites
MD simulations as described below were performed on PNPCs consisting of two or five nanoparticles in a melt of 400, 800 and 1600 bead-necklace chains of length 20, 10, or 5 beads, respectively. The systems with two nanoparticles were utilized to determine the potential of mean force between the nanoparticles which was subsequently used to calculate second virial coefficient. These results were qualitatively compared with the dispersion/aggregation behavior of nanoparticles in the five
Role of the polymer–nanoparticle interaction potential on effective nanoparticle interactions
The potential of mean force V(r) obtained from MD simulations as a function of nanoparticle separation is shown for εnp=1.0, 2.0 and 3.0 for chain lengths n=20, 10 and 5 in Fig. 1a, b and c, respectively. The influence of the polymer matrix on the nanoparticle potential of mean force can be determined by subtracting the bare nanoparticle–nanoparticle interaction [Eq. (1a)], shown in Fig. 2a, from V(r), i.e., Vmatrix(r)=V(r)−Unn(r), where Vmatrix(r) is the effective nanoparticle–nanoparticle
Conclusions and future work
MD simulation studies of matrix-induced interaction between nanoparticles were conducted for model PNPCs where the radius of the nanoparticle, the radius of gyration of the polymer and the statistical segment length of the polymer are comparable. Our simulations reveal that the matrix-induced interaction between nanoparticles in a model PNPC is longer-range than the bare nanoparticle–nanoparticle interaction employed in the simulations and is dependent upon both the molecular weight of the
Acknowledgements
Support for this work came from NASA Langley through grant NAG-12319 and the Department of Energy through grant DEFG0301ER45914.
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