59th Annual Report on Research 2014

1. Quantitative image analysis software

We have developed fully automated image analysis software in MATLAB R2012b to obtain structural properties of NP clusters from experimental SEM images of NP assembly in polymer thin films. The software utilizes various algorithms to process a set of raw SEM images of the film taken at intermittent time points during assembly to identify individual NPs and their clusters in each processed image. The software then computes and outputs a number of structural characteristics of the NP assemblies in an unbiased, rigorous manner, including their size, radius of gyration, shape anisotropy, fractal dimension, and backbone length as a function of time (Fig. 1). The software also gathers distributions in each computed property. Application of the software to multiple assembly experiments involving different NP shapes (Silver nanocubes, nanospheres, and Gold nanorods) and different sizes (13 nm, 30 nm, 80 nm) revealed a striking universality in the growth and overall morphology of NP cluster across all experiments despite strong variations in the sizes and shapes of NPs examined. In particular, all experiments exhibited exponential-like growth, fractal dimensions D_F in the range 1.35–1.45, and anisotropy ratios of 5–5.5 for NP clusters containing >20 NPs.

Figure 1: Overall scheme for image analysis. The raw SEM images are first pre-processed to determine their size and scale and to improve their contrast and remove noise. The images are then subjected to a number of morphological (erosion and dilation) and segmentation procedures to yield the final processed image that allows identification of individual NPs and NP aggregates. These processed images allow determination of various structural properties of NP aggregates as function of assembly time.

2. Kinetics of NP assembly from experiments

We have developed a computational strategy to infer directly from NP assembly experiments the underlying kinetic mechanisms governing the growth and morphology of NP clusters. The strategy involves iterative adjustment of specific parameters related to the diffusion and binding of NP/NP clusters within a lattice Monte Carlo model of NP assembly until the model reproduces a set of structural properties of NP clusters and their time evolution extracted from experiments via image analysis. Application of this strategy to the different assembly experiments confirms the universality in assembly mechanism seen from image analysis. In particular, NP cluster size distributions from the different assembly experiments at all intermediate to large times during the assembly collapse onto a single master curve obtained from a cluster-cluster aggregation model (Fig. 2A). Furthermore, our strategy uncovers intriguing similarities and differences in the diffusion-mass scaling and NP binding probabilities across the five examined systems (Fig. 2B).

Figure 2: (A) Reduced cluster size distributions obtained from five different assembly experiments carried out with different NP shapes and sizes showing remarkable collapse of data onto a single master curve. (B) Comparing of the degree of mismatch between experimental cluster size distributions and those computed from simulations for different diffusivity-mass scaling coefficient g and NP binding probability P suggests that the large Silver nanocubes exhibit similar diffusivity-mass scalings but much larger probabilities of binding as compared to the smaller Silver nanospheres (as labeled by black squares). 

3. Viscoelastic properties of polymer/NP composites

We have investigated how the addition of polymer-grafted NPs to polymers alters their viscoelastic properties. Specifically, we used molecular dynamics simulations of coarse-grained models of polymer/NP composites to compute their frequency-dependent storage G′ and loss modulus G′′ (Fig. 3A). The simulations showed that grafted NPs strongly enhance the G′ and G′′ of the host polymer, significantly more than bare NPs (Fig. 3B). Further analyses revealed that this enhancement arises due to shear-distortion effects and due to slower relaxation times of grafted polymer chains, as compared to free chains. We also elucidated the role of various NP-associated parameters on the viscoelasticity of the composites, namely: NP size and loading; length and tethering density of the grafted chains; and strength of interactions between the grafted and host polymer (Fig. 3C-F). We also developed a simple model based on Rouse theory to quickly estimate the viscoelastic properties of such polymer/NP composites. The model quantitatively captures, to within a constant multiplicative factor, the observed dependence of G′ and G′′ with the above attributes of the grafted NPs.

Figure 3: (A) Snapshot of a coarse-grained model of a polymer/NP composite captured from molecular dynamics simulations. Purple: NP, green: grafted polymer chains, grey: polymer matrix. (B-F) Loss modulus G′′(w) of the composites computed as a function of frequency w for varying system parameters, highlighting the sensitivity of viscoelastic properties to NP grafting, NP loading, and various properties of the grafted polymer.

The above research has been presented at four conferences and invited talks. Two manuscripts based on this work have been submitted for publication and another one is currently being prepared for publication. The PRF award has provided funds to support a postdoctoral researcher and allowed the involvement of four other students (2 PhD and 2 undergraduate students). The award also contributed towards the PI′s promotion to Associate Professor.