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C: Physical Processes in Nanomaterials and Nanostructures
Shear-Induced Microscopic Structure Damage in Polymer Nanocomposites: A Dynamic Density Functional Theoretical Study Yi Ye, Nanying Ning, Ming Tian, Liqun Zhang, and Jianguo Mi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b03663 • Publication Date (Web): 20 Aug 2019 Downloaded from pubs.acs.org on August 24, 2019
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The Journal of Physical Chemistry
Shear-Induced Microscopic Structure Damage in Polymer Nanocomposites: A Dynamic Density Functional Theoretical Study Yi Yea,b, Nanying Ningb, Ming Tiana,b*, Liqun Zhanga,b, and Jianguo Mia* a State
Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, China
bKey
Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials, Beijing University of Chemical Technology, Beijing, China
ABSTRACT: The dynamic density functional theory has been applied to investigate diffusion dynamics in polymer nanocomposites under shear conditions. According to the time-dependent density relaxations of the test particle and polymer chains, the particle diffusion mode and polymer flow pattern have been quantitatively determined and examined by the reported experimental and computational data. It is shown that a suitable coupling of particle size and particle−polymer interaction can produce the maximum diffusion resistance. More importantly, shear stress can induce the microscopic structure transition in polymer nanocomposites from homogeneous dispersion to microphase separation or ordered layer arrangement. The influence extent of particle size, particle volume fraction, and particle−polymer interaction on the transition has been identified to find the optimum condition to minimize the damage to the overall structure.
Corresponding authors:
[email protected];
[email protected].
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1. Introduction In a shear field, incorporating nanoparticles into a polymer matrix can cause many different properties via homogeneous dispersion, microphase separation, or aligning anisotropic nanostructures.1-6 These properties arise from the changes of spatial structure of polymer nanocomposites due to the relative movement of particles and polymer chains. The influence of shear flow on the structure has received tremendous attention of the scientific and industrial communities.7-9 In order to understand such influence, the relative movement between particles and polymer chains and the structure evolution process should be clarified from microscopic point of view, as it relates to develop polymer nanocomposites with specific applications.10 Fruitful insights were obtained from experimental studies.11-15 For instances, an elongational shear flow could induce the micro cracks and thereby destroyed the self-assembled structure of nanoparticles.13 When the shear rate reached a critical value, the flow-induced necklace or vorticity-aligned structure of particles could be formed.14 Under a suitable shear field, a binary crystal of polymeric micelles and particles was easier to align than the neat micelle crystal, but high shear rates resulted in worse stability of the binary crystal.15 Nevertheless, there are still many problems which require further investigation. Such as: (1) what kinds of shear type can influence the dispersion or aggregation state in polymer nanocomposites? (2) how does the structure form or change under the action of shear flow? (3) what is the essential issue to particle rearrangement in the flow direction? For the microscopic morphologies and dynamics of particles, it is difficult to control the experiment conditions (particle size, particle surface potential, and polymer chain length) and to quantitatively evaluate these effects. Molecular dynamic simulations and statistical mechanic theories provide reliable methods to yield microscopic insights into the diffusion of particles in polymer systems under various shear conditions. In some simulations, the influences of shear flow on particle dispersion states were clearly displayed via particle coordinates.16-18 It was shown that a suitable shear strength can result in particle aggregation, sandwich-like ACS Paragon Plus Environment
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The Journal of Physical Chemistry
structure formation, and homogeneous particle dispersion in polymer matrix with increase of particle−polymer interaction.19 Shear field also played an important role in particle distribution in the cases of symmetric block copolymers but had little effect on the immiscible polymer blend/particle composites.17 In a Brownian suspension, shear thickening resulted in a transition of particle flow from lubricated near-contacting to frictionally contacting.20,21 However, these simulations are computationally intensive, thus only few parameters were considered. On the other hand, the dynamical density functional theory (DDFT) was developed to study particle dynamics in solvents under shear flows. On the basis of Brownian dynamics, different particle regimes in linear shear flows were identified according to the mean square displacement (MSD) exponents.22,23 In the systems of particles near a wall or spherical obstacle under shear flows, DDFT characterized the effects of shear on interfacial distribution of particles around obstacles via the shear-induced transition from non-equilibrium to steady state.24,25 This approach has turned out to be a highly effective tool to characterize different thermodynamic and dynamic behaviors under shear conditions.26-32 In this work, we apply the DDFT to study the dynamics of particles in polymer systems under different shear flows. By integrating the Smoluchowski equation and the test particle method into the theoretical approach, we obtain the time-dependent density relaxations of particles and polymer chains to decipher the molecular mechanism of the accumulation and rearrangement of particles under shear flow. After assess the reliability of the theoretical model, we use it to study particle diffusion mode and polymer flow type, and to clarify the effects of particle size, polymer density, and particle−polymer interaction on the relative motions between particles and polymer chains. Finally, we pay attention to the influence of shear-induced microscopic structure transition on the stability of nanocomposites, and provide the maximum diffusion resistance and minimum structure deformation to sketch out a framework for protecting their overall structure from shear damage.
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2. Theory and equations 2.1 Interaction potentials Here we use model systems to study the diffusion dynamics and structure evolution under in shear fields. The polymer is modeled as the free-joined chain with tangent spheres, and each chain contains 1000 spheres with the diameter of p to ignore the tail effect. The particles are modeled as spheres with diameter n varying from 2 p to 10 p . The interaction potentials of particle−particle and polymer−polymer are given by the Lennard-Jones form 12 6 4 ij ( ij / r ) ( ij / r ) + C vij ( r ) 0
0 r 3 ij
(1)
3 ij c
