Swelling Effects on the Conductivity of Graphene/PSS/PAH Composites

Graphene/poly-(sodium-4-styrene sulfonate)(PSS)/poly-(allylamine hydrochloride) (PAH) composite is a frequently adopted system for fabricating polyelectrolyte multilayer films. Swelling is the bottleneck limiting its applications, and its effects on the conductivity is still controversial. Herein, we report successful swelling of a graphene/PSS/PAH composite in a vapor atmosphere, and the relation with the mass fraction of water is uncovered. The composite was prepared via a layer-by-layer assembly technique and systematically characterized. The results indicated that the average thickness for each bilayer was about 0.95 nm. The hardness and modulus were 2.5 ± 0.2 and 68 ± 5 GPa, respectively, and both were independent of thickness. The sheet resistance decreased slightly with the prolongation of immersion time, but was distinct from that of the water mass fraction. It reduced from 2.44 × 105 to 2.34 × 105 ohm/sq, and the change accelerated as the water mass fraction rose, especially when it was larger than 5%. This could be attributing to the lubrication effect of the water molecules, which sped up the migration of charged groups in the polyelectrolytes. Moreover, molecular dynamics simulations confirmed that a microphase separation occurred when the fraction reached an extreme value owing to the dominated interaction between PSS and PAH. These results provide support for the structural stability of this composite material and its applications in devices.


Introduction
Polyelectrolyte multilayer (PEM) films have been extensively explored in the last decade due to their high chemical and physical stability and their high permeability and selectivity. They have shown great promise in applications such as fabricating ultrathin conducting layers, permeation-selective membranes, protective coatings, sensors, and materials for nonlinear optics [1]. For example, poly-(ethylene)-based delivery systems, such as polyelectrolyte composites (PECs), poly-(ethylene)-coated nanocarriers, and poly-(ethylene) (PE) multilayers, were designed to protect peptides and proteins from degradation and facilitate their absorption. These delivery systems are especially effective when administered orally or intranasally [2]. The K + /Li + selectivity can reach ∼60 through poly(allylamine hydrochloride)/poly-(sodium-4-styrene sulfonate)-coated Nafion membranes, which are much larger than the uncoated Nafion membranes with a K + /Li + selectivity of <3. This because the swelling of poly(allylamine hydrochloride)/poly-(sodium-4-styrene sulfonate) (PAH/PSS) multilayers may open cation-exchange sites that preferentially bind K + to enable highly selective transport [3]. In addition, PPE-SO 3− molecules exhibit interesting optoelectronic properties, making graphene-based materials potentially useful in a variety of optoelectronic device applications [4].
The PAH/PSS was the first system where the stratified nature of linearly growing multilayers was established, and now, it is a widely used polyelectrolyte combination for by Sinopharm Chemical Reagent CO., Ltd. (Tianjin, China). All chemicals and reagents were used directly as received. Deionized water (DI, >18 MΩ) was produced with a Milli-Q Plus system (Millipore) (Tianjin, China).

Preparation of PSS-Stabilized Graphene Sheets (rGO-PSS)
Graphene sheets are usually subject to large van der Waals forces, which cause them to stack together. One of the major challenges in fabricating them is to disperse the graphene sheets without using covalent chemistries or other harsh conditions, which could lower their electrical conductivity. To achieve this purpose, graphene oxide sheets with negatively charged carboxylate groups were re-dispersed in PSS (1.00 mg/mL, pH = 6.15) solution. The π-like stacking of benzene rings of PSS benefits the binding of PSS and graphene sheets, leading to a high fraction of individualized graphene after dispersion and reduction. Details: Graphene oxide was synthesized by Hummer's method [15]. Graphene oxide (0.1250 g) was firstly dissolved in ultrapure water (250 mL), followed by ultrasound treatment at 500 W of power for 50 min. After vacuum suction filtration, the filtrate was taken as liquid sample A. PSS (2.000 g) was dissolved in ultrapure water (250 mL), followed by addition of 2 mL of 0.5 mol/L sodium hydroxide solution drop by drop to adjust the solution pH to 8, and the obtained solution was taken as liquid sample B. Liquid sample A was poured into liquid sample B under stirring, and then filtrated with vacuum suction filtration. Finally, hydrazine hydrate (500 µL) was added into the filtrate, followed by stirring and reflux for 24 h at 90 • C, and then cooled to room temperature.

Preparing (rGO-PSS/PAH) n Multilayer Films (n: Number of Deposition Cycles)
Reduced graphene oxide composite was assembled on glass following the schematic shown in Figure 1a. All supporters were ultrasonically cleaned in absolute ethyl alcohol, propone, and isopropyl alcohol in sequence, and then cleaned with a mixed solution of H 2 SO 4 /H 2 O 2 (v/v: 3/1) at 80 • C for 1 h [16]. Generally, multilayer deposited on surfaces was not thermodynamically favored, and so it seemed unavoidable, as strong interlayer mixing and chain removal, and would be triggered upon exposure to a deposition solution containing one of the polyelectrolytes [17]. Hence, the substrate was preferred to be firstly immersed into PEI (1.00 mg/mL, pH = 7.25) solution for 10 min, followed by rinsing with DI water to generate a cationic surface, which ensured that the surface charge was uniformly decorated to improve the adhesion strength. Since the binding of polyelectrolytes on the substrate surface was prior to the dissolution step, removal of the previously adsorbed polymer chain was inhibited when the pure buffer was used instead of the polymer solution at the early stage of desorption. Subsequently, a rinsing process was conducted to follow each cycle with an alternative dipping, rinsing, and drying procedure with the PAH (1.00 mg/mL, pH = 7.26) and PSS-rGO (0.5 mg/mL) solutions. Additional bilayers were added using identical procedures. For each cycle, a bilayer of PAH/PSS-graphene was prepared; the UV-visible spectra of the growing bilayers were recorded in air after each five assembly cycles. The inset in Figure 1b shows the self-supporting 100-bilayer-thick assembled film transferred to a glass sheet after being peeled off as a result of hydrogen fluoride corrosion. (a) Schematic diagram of one layer-by-layer assembly cycle. The black solid line represents the changed and reduced graphene oxide. The symbols "⊖" and "⊕" represent the negative and positive charges, respectively. The red-colored solution is PAH and the blue-colored solution is rGO-PSS. (b) The sheet resistance affected by H2O concentrations was tested with a four-probe method.

Swelling and Sheet Resistance Tests
The traditional method, which involves immersing the assembled film in electrolyte solution for a certain amount of time, followed by washing and drying, leads, no doubt, to mass loss, especially for the polyelectrolytes in the film. Disruption of inter-polyelectrolyte binding also lies in the heart of salt-induced and pH-induced dissolution of multilayers. So as to avoid an erosion phenomenon in pure water, we swelled the composite film with water vapor at room temperature. The prepared composite films were immersed in water vapor for 24 h to complete the swelling, and then were dried in the air to reach a target mass (or target H2O mass fraction). After that, the sheet resistance was measured using a four-probe method.

Molecular Dynamics Simulations
The cuboid simulation cells were sized 14.76 Å × 14.76 Å × 25.00 Å. There were four monomer units for PSS and PAH in each cell. The element compositions and densities are listed in Table 1. The volume fraction of the reduced graphene oxide sheet was about 7.46%. All dynamics simulations (MDs) were performed using a COMPASS force field. Both energy and geometrical optimization were performed, and a spherical cutoff value of 12.5 Å was chosen to calculate the non-bond interactions. All calculations were carried out at 300 K in an NPT ensemble, which was controlled by Andersen's method. Periodic boundary conditions along all three directions were used. Based on the convergence of potential, kinetic, non-bond, and total energy, the MD simulation ran for 1000 ps to relax and reach an equilibrium state with a time step of 1 fs.

Swelling and Sheet Resistance Tests
The traditional method, which involves immersing the assembled film in electrolyte solution for a certain amount of time, followed by washing and drying, leads, no doubt, to mass loss, especially for the polyelectrolytes in the film. Disruption of inter-polyelectrolyte binding also lies in the heart of salt-induced and pH-induced dissolution of multilayers. So as to avoid an erosion phenomenon in pure water, we swelled the composite film with water vapor at room temperature. The prepared composite films were immersed in water vapor for 24 h to complete the swelling, and then were dried in the air to reach a target mass (or target H 2 O mass fraction). After that, the sheet resistance was measured using a four-probe method.

Molecular Dynamics Simulations
The cuboid simulation cells were sized 14.76 Å × 14.76 Å × 25.00 Å. There were four monomer units for PSS and PAH in each cell. The element compositions and densities are listed in Table 1. The volume fraction of the reduced graphene oxide sheet was about 7.46%. All dynamics simulations (MDs) were performed using a COMPASS force field. Both energy and geometrical optimization were performed, and a spherical cutoff value of 12.5 Å was chosen to calculate the non-bond interactions. All calculations were carried out at 300 K in an NPT ensemble, which was controlled by Andersen's method. Periodic boundary conditions along all three directions were used. Based on the convergence of potential, kinetic, non-bond, and total energy, the MD simulation ran for 1000 ps to relax and reach an equilibrium state with a time step of 1 fs. The spectroscopic properties were investigated using the UV-Vis spectra (Hitachi U-4100 UV-Vis near-FTIR spectrometer, Hitachi, Tokyo, Japan) with a scanning range of 200-800 nm and a scanning speed of 300 nm·min −1 . Raman spectra (Renishaw micro-Raman 1000 spectrometers, Renishaw, British, Gloucestershire, UK) and FT-IR spectra (Fourier-Transform Infrared Spectrometer 3100) were assessed under a laser wavelength of 532 nm and an intensity of 1.5 mW. The wave number range was 4000-400 cm −1 . A minimum of 16 scans signal-averaged with a resolution of 2 cm −1 was employed.

Morphology Characterizations
The morphologies were investigated with an atomic force microscope (AFM, Bruker, Karlsruhe, Germany) on a Veeco Icon in the taping mode, and scanning electron microscopy (SEM, FEI, Hillsboro, OR, USA,) was performed on a HITACHI S4300 system at the accelerated voltage of 20 kV. Transmission electron microscopy measurements were performed on a Tecnai G2 F30 microscope (Thermo Scientific, Eindhoven, Netherlands) at 80 kV.

Mechanical Tests
The mechanical properties were tested by using nano-indentation experiments on a Nano Indenter XP system after a standard calibration. The Poisson ratio was set to 0.25, the surface-approach velocity was 10 nm/s, the strain rate target was 0.05/s, and the frequency target was 45 Hz.

Sheet Resistance Evaluations
Keithley S4200 (Tektronix, Beaverton, WA, USA) was used to measure the sheet resistances with a four-probe method under different levels of humidity at room temperature (30 • C). Because of the changes in the light absorbance properties, the color of the solution became black after a chemical reduction. The small aggregations at the bottom indicate that the reduced graphene oxide sheets were stabilized by PSS molecules. The rGO-PSS sheet had a lamellar structure with a size of tens of microns according to the optical microscope view in Figure 2b and the AFM images in Figure 2c. Figure 2d shows a low-magnification TEM image of typical rGO-PSS sheets over a copper grid. They exhibited typical wrinkle-like features, which were in good agreement with previous reports [18].

Fabrication of Polyelectrolyte/rGO-PSS Composite via the Layer-by-Layer Assembly Method
Polycations with a high density of primary amino groups and polyanions with SO3groups showed the strongest inter-polyelectrolyte binding, resulting in inhibited chain exchange within PEMs. Prior to the assembly, PEI was first absorbed on the substrate to enhance the binding strength between the film and substrate. The growth of the multilayers was monitored using the UV-Vis spectrum. The UV-Vis curves are shown in Figure  3. The characteristic absorption peak appearing at 225 nm was attributed to the π-π* transitions of aromatic C=C bonds. A progressive increase in absorbance in the range of 200-800 nm was visible when the bilayer number increased. The inset shows that, in the early stage of assembly, the linear relationship between the absorbance and the bilayer numbers indicated a reproducible and uniform LBL assembly process, which provided a feasible scheme for controlling the thickness of the film at the nanometer level. The polyelectrolyte multilayers of PAH and PSS grown from ion-free solution showed a large surface charge density of 2−3 mC m −2 (absolute values). Note that PAH and PSS had the same linear charge density; thus, the surface coverage was the same, and each adsorption step was accompanied by charge overcompensation [18]. During the multilayer preparation, at 60 bilayers, a transition from a linear to a parabolic growth regime occurred. In the linear growth regime, the surface of the film was thought to be electrically neutral. Only upon the decrease in the NaCl concentration below a critical value (50 mM in the literature) was a surface charge observed. At lower salt concentrations, Cl − ions dissolved from the multilayer, which was now positively charged. The surface charge density was again unusually low at 0.62 ± 0.22 mC m −2 . Actually, the uniformity of the composite was key in obtaining excellent mechanical properties.

Fabrication of Polyelectrolyte/rGO-PSS Composite via the Layer-by-Layer Assembly Method
Polycations with a high density of primary amino groups and polyanions with SO 3 − groups showed the strongest inter-polyelectrolyte binding, resulting in inhibited chain exchange within PEMs. Prior to the assembly, PEI was first absorbed on the substrate to enhance the binding strength between the film and substrate. The growth of the multilayers was monitored using the UV-Vis spectrum. The UV-Vis curves are shown in Figure 3. The characteristic absorption peak appearing at 225 nm was attributed to the π-π* transitions of aromatic C=C bonds. A progressive increase in absorbance in the range of 200-800 nm was visible when the bilayer number increased. The inset shows that, in the early stage of assembly, the linear relationship between the absorbance and the bilayer numbers indicated a reproducible and uniform LBL assembly process, which provided a feasible scheme for controlling the thickness of the film at the nanometer level. The polyelectrolyte multilayers of PAH and PSS grown from ion-free solution showed a large surface charge density of 2-3 mC m −2 (absolute values). Note that PAH and PSS had the same linear charge density; thus, the surface coverage was the same, and each adsorption step was accompanied by charge overcompensation [18]. During the multilayer preparation, at 60 bilayers, a transition from a linear to a parabolic growth regime occurred. In the linear growth regime, the surface of the film was thought to be electrically neutral. Only upon the decrease in the NaCl concentration below a critical value (50 mM in the literature) was a surface charge observed. At lower salt concentrations, Cl − ions dissolved from the multilayer, which was now positively charged. The surface charge density was again unusually low at 0.62 ± 0.22 mC m −2 . Actually, the uniformity of the composite was key in obtaining excellent mechanical properties.  Figure 4a shows the transmittance FT-IR spectra of the GO-PSS, rGO-PSS, and composite film. The stretching vibrations of the -OH group were located in the range of 3000 to 3700 cm -1 . The decrease in the peak intensity indicated that most of the -OH groups in graphene oxide were removed after the reduction by N2H4·H2O. The peaks of the C=O group were located between 1650 and 1750 cm −1 owing to asymmetric stretching. The peaks at 1540 and 1182 cm -1 were assigned to C=C bonds and C-O-C groups. The peak at 800 cm -1 was attributed to para-disubstituted benzene rings. The Raman peaks located at 1580 and 1380 cm −1 were G and D bands, respectively [19,20]. The intensity of the D band enhanced the red shift over five units after reduction, revealing the hybridization type transformation of the carbon skeletons: sp 3 to sp 2 .

Morphology Characterizations
A typical AFM test in the taping mode was performed, which indicated an average film thickness of 95 nm on a SiO2/Si substrate (Figure 5a,b). The optical microscope photograph in Figure 5c shows darker spots on the surface of the film, which were aggregated fine particles. The surface morphologies of the 100 bilayers were characterized by SEM, as shown in Figure 5d-f. The SEM images indicate a smooth surface with large numbers of wrinkles at a small scale. In addition, the obvious layered characteristics of the interface cross-section were present.  Figure 4a shows the transmittance FT-IR spectra of the GO-PSS, rGO-PSS, and composite film. The stretching vibrations of the -OH group were located in the range of 3000 to 3700 cm −1 . The decrease in the peak intensity indicated that most of the -OH groups in graphene oxide were removed after the reduction by N 2 H 4 ·H 2 O. The peaks of the C=O group were located between 1650 and 1750 cm −1 owing to asymmetric stretching. The peaks at 1540 and 1182 cm −1 were assigned to C=C bonds and C-O-C groups. The peak at 800 cm −1 was attributed to para-disubstituted benzene rings. The Raman peaks located at 1580 and 1380 cm −1 were G and D bands, respectively [19,20]. The intensity of the D band enhanced the red shift over five units after reduction, revealing the hybridization type transformation of the carbon skeletons: sp 3 to sp 2 .   Figure 4a shows the transmittance FT-IR spectra of the GO-PSS, rGO-PSS, and composite film. The stretching vibrations of the -OH group were located in the range of 3000 to 3700 cm -1 . The decrease in the peak intensity indicated that most of the -OH groups in graphene oxide were removed after the reduction by N2H4·H2O. The peaks of the C=O group were located between 1650 and 1750 cm −1 owing to asymmetric stretching. The peaks at 1540 and 1182 cm -1 were assigned to C=C bonds and C-O-C groups. The peak at 800 cm -1 was attributed to para-disubstituted benzene rings. The Raman peaks located at 1580 and 1380 cm −1 were G and D bands, respectively [19,20]. The intensity of the D band enhanced the red shift over five units after reduction, revealing the hybridization type transformation of the carbon skeletons: sp 3 to sp 2 .

Morphology Characterizations
A typical AFM test in the taping mode was performed, which indicated an average film thickness of 95 nm on a SiO2/Si substrate (Figure 5a,b). The optical microscope photograph in Figure 5c shows darker spots on the surface of the film, which were aggregated fine particles. The surface morphologies of the 100 bilayers were characterized by SEM, as shown in Figure 5d-f. The SEM images indicate a smooth surface with large numbers of wrinkles at a small scale. In addition, the obvious layered characteristics of the interface cross-section were present.

Morphology Characterizations
A typical AFM test in the taping mode was performed, which indicated an average film thickness of 95 nm on a SiO 2 /Si substrate (Figure 5a,b). The optical microscope photograph in Figure 5c shows darker spots on the surface of the film, which were aggregated fine particles. The surface morphologies of the 100 bilayers were characterized by SEM, as shown in Figure 5d-f. The SEM images indicate a smooth surface with large numbers of wrinkles at a small scale. In addition, the obvious layered characteristics of the interface cross-section were present.

Modulus and Hardness
The mechanical properties, e.g., elastic modulus and hardness, were characterized by a nano−indentation method owing to its excellent performance on at the nano−scale. The variations in the hardness and modulus with the indentation depth are shown in Figure  6a, and those with the film thickness are shown in Figure 6b. This demonstrated that the average hardness and modulus were about 2.5 ± 0.2 and 68 ± 5 GPa for the 100−bilayer film, which made the composite film easy to peel off and transfer to an arbitrary target. Furthermore, the relationships between the stiffness and modulus of multilayers with different thicknesses are exhibited in Figure 6b. The stiffness and modulus of the multilayers increased slightly with the thickness, but not significantly.

Sheet Resistances and Theoretical Calculations
The effect of the swelling of thin films on the sheet resistance is the key for further consideration. Figure 7a shows the variations in the curves of sheet resistance with the immersion time. They decreased slightly from 2.45 × 10 5 to 2.38 × 10 5 ohm/sq after immersion for 24 h. The sheet resistance decreased slightly with the prolongation of immersion time; however, the modified value was less than only 10% and was eventually saturated, which should not affect the fundamental properties. The influence of the H2O mass fraction, however, was different. It was reduced from 2.44 × 10 5 to 2.34 × 10 5 ohm/sq, and the rate of change increased with the increase in the H2O mass fraction, especially when the

Modulus and Hardness
The mechanical properties, e.g., elastic modulus and hardness, were characterized by a nano−indentation method owing to its excellent performance on at the nano−scale. The variations in the hardness and modulus with the indentation depth are shown in Figure 6a, and those with the film thickness are shown in Figure 6b. This demonstrated that the average hardness and modulus were about 2.5 ± 0.2 and 68 ± 5 GPa for the 100−bilayer film, which made the composite film easy to peel off and transfer to an arbitrary target. Furthermore, the relationships between the stiffness and modulus of multilayers with different thicknesses are exhibited in Figure 6b. The stiffness and modulus of the multilayers increased slightly with the thickness, but not significantly.

Modulus and Hardness
The mechanical properties, e.g., elastic modulus and hardness, were characterized by a nano−indentation method owing to its excellent performance on at the nano−scale. The variations in the hardness and modulus with the indentation depth are shown in Figure  6a, and those with the film thickness are shown in Figure 6b. This demonstrated that the average hardness and modulus were about 2.5 ± 0.2 and 68 ± 5 GPa for the 100−bilayer film, which made the composite film easy to peel off and transfer to an arbitrary target. Furthermore, the relationships between the stiffness and modulus of multilayers with different thicknesses are exhibited in Figure 6b. The stiffness and modulus of the multilayers increased slightly with the thickness, but not significantly.

Sheet Resistances and Theoretical Calculations
The effect of the swelling of thin films on the sheet resistance is the key for further consideration. Figure 7a shows the variations in the curves of sheet resistance with the immersion time. They decreased slightly from 2.45 × 10 5 to 2.38 × 10 5 ohm/sq after immersion for 24 h. The sheet resistance decreased slightly with the prolongation of immersion time; however, the modified value was less than only 10% and was eventually saturated, which should not affect the fundamental properties. The influence of the H2O mass fraction, however, was different. It was reduced from 2.44 × 10 5 to 2.34 × 10 5 ohm/sq, and the rate of change increased with the increase in the H2O mass fraction, especially when the

Sheet Resistances and Theoretical Calculations
The effect of the swelling of thin films on the sheet resistance is the key for further consideration. Figure 7a shows the variations in the curves of sheet resistance with the immersion time. They decreased slightly from 2.45 × 10 5 to 2.38 × 10 5 ohm/sq after immersion for 24 h. The sheet resistance decreased slightly with the prolongation of immersion time; however, the modified value was less than only 10% and was eventually saturated, which should not affect the fundamental properties. The influence of the H 2 O mass fraction, however, was different. It was reduced from 2.44 × 10 5 to 2.34 × 10 5 ohm/sq, and the rate of change increased with the increase in the H 2 O mass fraction, especially when the mass fraction was larger than 5%. This can be attributed to the lubrication effect of the water overflow in the film, which accelerated the migration of charged groups into the polyelectrolytes. However, when the mass fraction of H 2 O continued to increase, the interaction between PSS and PAH dominated and a microphase separation occurred, which led to restacking of the graphene sheets and, thus, a decrease in sheet resistance. Furthermore, graphene sheets could help to stabilize the polyelectrolyte films and greatly reduce the inner resistance by changing the transport of the electrons from a "point-topoint" mode to a more effective "plane-to-point" mode [21]. mass fraction was larger than 5%. This can be attributed to the lubrication effect water overflow in the film, which accelerated the migration of charged groups in polyelectrolytes. However, when the mass fraction of H2O continued to increase, t teraction between PSS and PAH dominated and a microphase separation occurred, led to restacking of the graphene sheets and, thus, a decrease in sheet resistance. Fu more, graphene sheets could help to stabilize the polyelectrolyte films and greatly r the inner resistance by changing the transport of the electrons from a "point-to-p mode to a more effective "plane-to-point'' mode [21].  Figure 8 shows the atomic configurations of the graphene/PSS/PAH composite different mass fractions of water. Under anhydrous condition, the interaction betwee and graphene based on π-π bonding and that between PSS and PAH was mainly el static. These non-bond interactions were often weak, so the composite structures remain stable. However, when the mass fraction of water increased, water molecule free between the polyelectrolyte molecules and played a special role in lubricatin connecting PSS and PAH molecules through hydrogen bonds and intermolecular in tions. In theory, mixing like−charged macromolecules before compositing should o significant scope for controlling the composition and properties of polyelectrolyte co sites/coacervates [22]. Figure 9 shows the total energy and its contributions to th phene/PSS/PAH composites with different water mass fractions. Remarkably, the v energy changed little with the vibration of the water mass fraction, which was d from the vibration of the non-bond energy. When the mass fraction was zero, the bond energy was positive, which means that the system was metastable. When the fraction was larger than 5%, the non-bond energy became negative. When the wate tent reached a certain degree, the interaction between PAH and PSS was greater tha between PSS and graphene, and microphase separation occurred. The graphene were more properly restacked, and hence, the conductivity was improved.   Figure 8 shows the atomic configurations of the graphene/PSS/PAH composites with different mass fractions of water. Under anhydrous condition, the interaction between PSS and graphene based on π-π bonding and that between PSS and PAH was mainly electrostatic. These non-bond interactions were often weak, so the composite structures could remain stable. However, when the mass fraction of water increased, water molecules were free between the polyelectrolyte molecules and played a special role in lubricating and connecting PSS and PAH molecules through hydrogen bonds and intermolecular interactions. In theory, mixing like−charged macromolecules before compositing should offer a significant scope for controlling the composition and properties of polyelectrolyte composites/coacervates [22]. Figure 9 shows the total energy and its contributions to the graphene/PSS/PAH composites with different water mass fractions. Remarkably, the valence energy changed little with the vibration of the water mass fraction, which was distinct from the vibration of the non-bond energy. When the mass fraction was zero, the non-bond energy was positive, which means that the system was metastable. When the mass fraction was larger than 5%, the non-bond energy became negative. When the water content reached a certain degree, the interaction between PAH and PSS was greater than that between PSS and graphene, and microphase separation occurred. The graphene layers were more properly restacked, and hence, the conductivity was improved.
Nanomaterials 2021, 11, x FOR PEER REVIEW 9 of 11 mass fraction was larger than 5%. This can be attributed to the lubrication effect of the water overflow in the film, which accelerated the migration of charged groups into the polyelectrolytes. However, when the mass fraction of H2O continued to increase, the interaction between PSS and PAH dominated and a microphase separation occurred, which led to restacking of the graphene sheets and, thus, a decrease in sheet resistance. Furthermore, graphene sheets could help to stabilize the polyelectrolyte films and greatly reduce the inner resistance by changing the transport of the electrons from a "point-to-point" mode to a more effective "plane-to-point'' mode [21].  Figure 8 shows the atomic configurations of the graphene/PSS/PAH composites with different mass fractions of water. Under anhydrous condition, the interaction between PSS and graphene based on π-π bonding and that between PSS and PAH was mainly electrostatic. These non-bond interactions were often weak, so the composite structures could remain stable. However, when the mass fraction of water increased, water molecules were free between the polyelectrolyte molecules and played a special role in lubricating and connecting PSS and PAH molecules through hydrogen bonds and intermolecular interactions. In theory, mixing like−charged macromolecules before compositing should offer a significant scope for controlling the composition and properties of polyelectrolyte composites/coacervates [22]. Figure 9 shows the total energy and its contributions to the graphene/PSS/PAH composites with different water mass fractions. Remarkably, the valence energy changed little with the vibration of the water mass fraction, which was distinct from the vibration of the non-bond energy. When the mass fraction was zero, the nonbond energy was positive, which means that the system was metastable. When the mass fraction was larger than 5%, the non-bond energy became negative. When the water content reached a certain degree, the interaction between PAH and PSS was greater than that between PSS and graphene, and microphase separation occurred. The graphene layers were more properly restacked, and hence, the conductivity was improved.

Conclusions
In summary, we report the successful fabrication of a graphene/PSS/PAH composite for swelling studies. The composite was prepared via a layer-by-layer assembly technique and systematically characterized by UV-Vis, Raman, and FT-IR spectra, atomic force microscopy, a nano-indentation procedure, a four-probe method, and a theoretical calculation. An average film thickness of 0.95 nm was found for each bilayer. The average hardness and modulus were about 2.5 ± 0.2 and 68 ± 5 GPa, and both were independent of the thickness, which made the composite film easy to peel off and transfer to an arbitrary target. The sheet resistance decreased slightly with the prolongation of the immersion time. The influence of the H2O mass fraction, however, was different. It was reduced from 2.44 × 10 5 to 2.34 × 10 5 ohm/sq, and the rate of change increased with the increase in the H2O mass fraction, especially when the mass fraction was larger than 5%. This could be attributed to the lubrication effect of the water overflow in the film, which accelerated the migration of charged groups into the polyelectrolytes. When the mass fraction of H2O continued to increase, the interaction between PSS and PAH dominated and a microphase separation occurred. These results provide support for applications of the graphene/PSS/PAH thin films.

Conflicts of Interest:
The authors declare no conflict of interest.

Conclusions
In summary, we report the successful fabrication of a graphene/PSS/PAH composite for swelling studies. The composite was prepared via a layer-by-layer assembly technique and systematically characterized by UV-Vis, Raman, and FT-IR spectra, atomic force microscopy, a nano-indentation procedure, a four-probe method, and a theoretical calculation. An average film thickness of 0.95 nm was found for each bilayer. The average hardness and modulus were about 2.5 ± 0.2 and 68 ± 5 GPa, and both were independent of the thickness, which made the composite film easy to peel off and transfer to an arbitrary target. The sheet resistance decreased slightly with the prolongation of the immersion time. The influence of the H 2 O mass fraction, however, was different. It was reduced from 2.44 × 10 5 to 2.34 × 10 5 ohm/sq, and the rate of change increased with the increase in the H 2 O mass fraction, especially when the mass fraction was larger than 5%. This could be attributed to the lubrication effect of the water overflow in the film, which accelerated the migration of charged groups into the polyelectrolytes. When the mass fraction of H 2 O continued to increase, the interaction between PSS and PAH dominated and a microphase separation occurred. These results provide support for applications of the graphene/PSS/PAH thin films.

Conflicts of Interest:
The authors declare no conflict of interest.