A mesoscale strength model for silica-filled PDMS
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A mesoscale strength model for silica-filled PDMS D. E. Hanson Theoretical Division, Los Alamos National Laboratory Los Alamos, NM, 87545 Abstract We present a mesoscale model that describes the tensile stress of silica-filled polydimethylsiloxane (PDMS) under elongation. Atomistic simulations of a single chain of PDMS, interacting with itself and/or a hydroxylated silica surface provide estimates of the microscopic forces required to stretch or uncoil a chain of PDMS, or detach it from a silica surface Using these results, we develop a mesoscale, inter-particle strength model for uncrosslinked, silica-filled PDMS. The strength model includes these atomistic forces, as determined from the simulations, a small entropic component, and a Gaussian probability distribution to describe the distribution of chain lengths of PDMS strands connecting two silica particles and the chain lengths in the free ends. We obtain an analytic stress/strain expression whose predictions agree with experiment. Introduction Polydimethylsiloxane (PDMS) is a homopolymer with a repeat unit consisting of -[OSi(CH3)2]-. Its resistance to chemical attack and very low glass transition temperature (156 K) make it attractive for many applications. Depending on the molecular weight, pure PDMS can have a consistency ranging from a viscous oil to a semi-solid, like paraffin. Unlike conventional rubber, crosslinking alone does not typically produce a significant increase in strength for PDMS1. To have sufficient strength to be useful, it was found that small (50 - 500 nm) silica particles needed to be added at a volume fraction of ~10-20%. The tensile modulus is also known to be weakly proportional to the filler volume fraction1, and inversely proportional to the size of the filler particle2. Experiments2 also show that the tensile strength of filled and crosslinked PDMS correlates with the molecular weight of the PDMS, peaking at ~1.5 x106 Daltons; for a value of ~0.1 x106, the tensile strength was reduced by an order of magnitude. In another experiment3 using PDMS with a molecular weight of 17,000 Daltons, no increase in tensile modulus was observed with filler. We can therefore conclude that it is both the chain length and the interaction (bonding) of the PDMS polymers with the surfaces of the silica particles that are primarily responsible for the enhancement to tensile strength. One of the earliest and most popular models developed to describe the strength of a filled polymer is that due to Smallwood 4. He applied an expression derived by Einstein, relating the viscosity of a fluid containing a dilute mixture of solid spheres to their volume fraction, and obtained
E = E o (1+ 2.5v ) ,
(1)
where E0 is the modulus of the polymer matrix and ν is the volume fraction of the filler particles. Using a typical value for the filler volume fraction of 15% in Eq. 1 yields an enhancement factor of 1.37. However, experiments1 show that the strength, or modulus, of PDMS increases by a factor of 40 or more when silica particles are added. This increase is obser
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