Taking a Tailored Approach to Material Design: A Mechanistic Study of the Selective Localization of Phase-Separated Graphene Microdomains

To achieve multifunctional properties using nanocomposites, selectively locating nanofillers in specific areas by tailoring a mixture of two immiscible polymers has been widely investigated. Forming a phase-separated structure from entirely miscible molecules is rarely reported, and the related mechanisms to govern the formation of assemblies from molecules have not been fully resolved. In this work, a novel method and the underlying mechanism to fabricate self-assembling, bicontinuous, biphasic structures with localized domains made up of amine-functionalized graphene nanoplatelets are presented, involving the tailoring of compositions in a liquid processable multicomponent epoxy blend. Kinetics studies were carried out to investigate the differences in reactivity of various epoxy-hardener pairs. Molecular dynamics simulations and in situ optical photothermal infrared spectroscopy measurements revealed the trajectories of different components during the early stages of polymerization, supporting the migration (phase behavior) of each component during the curing process. Confirmed by the phase structure and the correlated chemical maps down to the submicrometer level, it is believed that the bicontinuous phase separation is driven by the change of the miscibility between various building blocks forming during polymerization, leading to the formation of nanofiller domains. The proposed morphology evolution mechanism is based on combining solubility parameter calculations with kinetics studies, and preliminary experiments are performed to validate the applicability of the mechanism of selectively locating nanofillers in the phase-separated structure. This provides a simple yet sophisticated engineering model and a roadmap to a mechanism for fabricating phase-separated structures with nanofiller domains in nanocomposite films.


Differential Scanning Calorimetry (DSC)
In this study, DSC experiments were conducted using a Netzsch DSC 204F1 with aluminium pans as sample holders, and sample masses of ~5 mg (uncured samples) and 5.1 ± 0.5 mg (cured samples).Samples were equilibrated at 25°C for 3 mins before cooled to -50°C immediately and held isothermally for 5 min, then heated to 250 °C at a heating rate of 10°C min -1 under a constant nitrogen flow of 50 cm 3 min -1 .Heat/cool/heat scans, with a cooling rate of 20°C min -1 , were used to evaluate the residual curing exotherms.Heat scans were performed with heating rates of 1, 2, 5, and 10°C min -1 .In addition, to determine the cure degree over time, isothermal tests were performed at 25°C.

Non-isothermal reaction kinetics
Figure S1 shows the DSC thermograms of various reaction pairs of the multi-component amine-cured epoxy resin blends from the dynamic DSC experiments conducted at heating rates of 1, 2, 5 and 10°C /min, respectively.As expected, the exothermic peak shifts to a higher temperature and the peak width is extended with an increased heating rate.Additionally, the total heat release of the cure reaction increases gradually with an increasing heating rate [1].
Cure kinetics were evaluated using the equation that is better suited to an autocatalytic system than an n th -order model [2].Therefore, first-order reaction kinetics are assumed, and the Kissinger method [3] used as a preliminary assessment of the resin kinetics for the three main reaction peaks of each blend.Kissinger method (Equation 1) is used, the activation energy and the pre-exponential factor were calculated as below [4], where β is the heating rate, Tmax is the exothermic peak maximum (K); Ea is the activation energy, which is the energy barrier which the reaction must overcome for the reaction to proceed; A is the pre-exponential factor, which is interpreted as the frequency of collisions between reactant molecules at a standard concentration (leading to a reaction or not) per second; and R is the gas constant (8.314J K -1 mol -1 ).
By plotting lnβ = (Tmax) 2 versus 1/Tmax, the activation energy and pre-exponential factor can be determined from the gradient and y-intercept respectively [4].The Kissinger method also enables the rate constant (k) for the reaction, which is interpreted as the frequency of collisions between molecules that result in a reaction, to be determined, using the Arrhenius equation expressed as [5]: where, k is the rate constant (s -1 ) and T is the temperature of the reaction (here 298 K or 25°C was selected as this was the cure temperature used throughout the study).The calculated values are given in Table S4.

Isothermal reaction kinetics
In dynamic DSC experiments, the Kissinger method is not able to evaluate the degree of cure as the reaction progresses, but rather enables certain cure kinetic parameters to be accessed by assuming first-order cure kinetics [6].Thus, to establish the relationship between phase behaviours and cure behaviours, the isothermal cure kinetics have to be evaluated to investigate the cure behaviour (kinetics) of the resin.Consequently, isothermal DSC measurements were performed to determine the reaction rate and degree of conversion.Assuming that the cure rate of the blending system, /, is proportional to the rate of heat flow, /, the cure rate can be expressed as [7]: The reaction rate versus time for the isothermal cure at the ambient temperature of various combinations is shown in Figure S2.
In addition, the degree of conversion of the resin at a given time could be obtained by integrating the area under the curve of cure rate versus time, which is given as [7]: The degree of cure versus time for the isothermal cure at the ambient temperature of various combinations is shown in Figure S2.

Fourier Transform Infrared Spectroscopy (FTIR)
PerkinElmer Spectrum 100 FTIR spectrometer (Beaconsfield, UK) was employed to acquire the bulk infrared spectra of the A-GNPs and each component of the resin formulation.The spectrum range was 4000-600 cm -1 and 16 scans were acquired and co-added for each measurement.Before conducting measurements, a background scan was run to remove any interferences caused by ambient atmosphere.

Rheological Analysis
Rheological analysis was conducted using a TA Discovery HR-1 hybrid rheometer with a parallel plate fixture, using pairs of disposable aluminium plates (diameter 25 mm, gap 0.3 mm).To determine how the viscosity of various blends changed over time, isothermal tests were performed at 25°C with a shear rate of 5 s -1 .The strain frequency used was 1 Hz, and an oscillation amplitude of 50% was selected to match with linear viscoelastic regime [8].

UV-Visible absorbance
Dispersibility of the amine-functionalized graphene nanoplatelets (A-GNPs) in solvents was confirmed via UV-Vis absorbance spectroscopy using the Bristol-Xi'an Jiaotong approach reported by the Faul group [9].A-GNPs solutions were prepared by placing A-GNPs (5 mg) in different solvents (20 mL), using a sonication probe for over 5 min.After sonication, the solutions were allowed to settle for 1 hour before measurement.A Cary 5000 UV-Vis NIR absorption spectrometer (Varian, USA) was used to confirm the dispersibility of the A-GNPs in each solution by evaluating the absorbance over a wavelength range of 220-800 nm.
To evaluate the solubility of A-GNPs, Hansen solubility parameters (HSPs), provide a useful framework to predict and improve the solubility, compatibility, stability and efficacy between the solvent and the solute [10].The absorbance (  ) of a solution is closely related to the molar concentration (), as expressed by the Beer-Lambert law, where  the molar absorptivity and  is the path length of a cell.
The Beer-Lambert law illustrates that a solution with a higher content of A-GNPs would absorb visible light and thus will become more opaque.An open-source Hansen solubility parameter estimation toolkit, MLoc (version 1.0), which is based on minimising the overall weighted distance between material (M) and solvents in the Hansen space, is used for HSP calculation.The HSP may be separated into three different types of partial solubility parameters related to the specific intermolecular interactions [11][12][13]: where , , and ℎ refer to the dispersion, polar, and hydrogenbonding interactions.The HSP Distance between two molecules, conventionally called , is the measure of how alike they are.The smaller , the more likely they are to be compatible.This well-known equation is expressed as, Hansen solubility parameters for the organic solvents examined, and the distances between the solubility parameters of the A-GNPs and solvents (unit: MPa 1/2 ).The results are summarized in Table S4 and the 3D M Locator plot shown in Figure 4a.

Figure S3 :
Figure S3: Plot of the degree of cure versus time (a) and reaction rate versus time for the isothermal cure at various temperatures.

Figure. S4 .Figure S5 .
Figure.S4.Plots of FTIR spectra of a) chemical components shown plotted as absorbance versus wavenumber, and b) A-GNPs, plotted as transmittance versus wavenumber.