Molecular insights into the physics of polyamidoamine-dendrimer-based supercapacitors Tarun Maity

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Molecular insights into the physics of poly(amidoamine)-dendrimer-based

supercapacitors

Tarun Maity

Center for Condensed Matter Theory, Dept. of Physics,

Indian Institute of Science, Bangalore 560012, India

Mounika Gosika†

Centro de F´ısica de Materiales (CSIC,

UPV/EHU) and Materials Physics Center MPC,

Paseo Manuel de Lardizabal 5,

20018 San Sebasti´an, Spain

Tod A. Pascal

ATLAS Materials Physics Laboratory,

Department of NanoEngineering and Chemical Engineering,

University of California, San Diego, CA 92023

Prabal K. Maiti∗

Centre for Condensed Matter Theory, Department of Physics,

Indian Institute of Science, Bangalore 560012, India

(Dated: October 25, 2022)

Increasing the energy density in electric double-layer capacitors (EDLCs), also known as super-

capacitors, remains an active area of research. Speciﬁcally, there is a need to design and discover

electrode and electrolyte materials with enhanced electrochemical storage capacity. Here, using fully

atomistic molecular dynamics (MD) simulations, we investigate the performance of hyper-branched

‘poly(amidoamine) (PAMAM)’ dendrimer as an electrolyte and an electrode coating material in a

graphene-based supercapacitor. We investigate the performance of the capacitor using two diﬀer-

ent modeling approaches, namely the constant charge method (CCM) and the constant potential

method (CPM). These simulations facilitated the direct calculation of the charge density, electro-

static potential and ﬁeld, and hence the diﬀerential capacitance. We found that the presence of

the dendrimer in the electrodes and the electrolyte increased the capacitance by about 65.25% and

99.15% respectively, compared to the bare graphene electrode-based aqueous EDLCs. Further anal-

ysis revealed that these increases were due to the enhanced electrostatic screening and reorganization

of the double layer structure of the dendrimer based electrolyte.

I. INTRODUCTION

Improving the energy densities of electric double layer

capacitor (EDLC), also known as supercapacitor based

energy devices, is of great practical interest [1–3], as

these devices have higher power densities compared to

conventional energy storage devices such as fuel cells,

electrochemical batteries and even dry/moist electrolytic

capacitors. The improved energy density, in turn,

would increase the commercial viability of EDLCs, thus

spurring large scale, mainstream adoption [4]. To this

end, recent work has focused on engineering advanced

electrode and electrolytes materials. Porous materials,

with high speciﬁc surface areas and good electronic con-

†Center for Condensed Matter Theory, Dept. of Physics,

Indian Institute of Science, Bangalore 560012, India

∗maiti@iisc.ac.in; http://www.physics.iisc.ernet.in/˜maiti/

ductivity, have traditionally been used as electrode mate-

rials in these devices [5, 6]. Room temperature ionic liq-

uids (RTILs) are typically chosen as the electrolyte, ow-

ing to their superior electrochemical properties, including

high operating voltage windows and non-ﬂammability,

compared to aqueous and organic based electrolytes [7].

Yet, despite progress over the years in electrode and

electrolyte optimization, further advances demand direct

knowledge of the interfacial structure and dynamics, and

design principles for unique nanoscale physics therein.

In this work, we consider dendrimers: hyper-branched

synthetic polymers as intriguing potential candidates as

electrolytes in these devices [8]. Dendrimers have well-

deﬁned molecular structure, are ﬂexible in size and shape,

and are responsive to controllable stimuli such as pH [9–

11]. They are also known to undergo structural deforma-

tions at interfaces [12, 13] and their charge densities are

comparable to that of ionic liquids [14]. Moreover, the

pore size of a typical microporous electrode ranges from

0.5 to 5 nm, which matches well with the sizes of poly

arXiv:2210.12414v1 [cond-mat.soft] 22 Oct 2022

amidoamine (PAMAM) dendrimers, which vary from 0.6

nm for generation 0 (G0) to 6 nm (G10) [10, 11, 13, 15].

Experiments and theory have shown that the capacitance

in EDLCs is signiﬁcantly enhanced when the pore size of

the electrode material matches the size of the electrolyte

ions [16, 17].

Interfacial adsorption of dendrimers on electrodes dy-

namically exposes their charge groups to the electrolyte,

which facilitates the formation of unique electric double

layer structures. This has been demonstrated by exper-

iments by Guo et al. [18], who reported that hyper-

branched polymers, like dendrimers, exhibit very low

losses in the dielectric response function, even at high

operational frequencies (∼1 MHz). Freire et al. also

showed that the presence of dendrimer can screen re-

pulsive contacts between diﬀerent counter ion molecules

and favored ionic conductivity [19]. These interesting

properties of dendrimers make them potentially excellent

candidates as electrolytes in EDLCs, however, a thorough

microscopic examination of the interfacial behaviour, and

the resulting eﬀect on electrochemical performance, have

not yet been elaborated.

Computer simulations employing molecular dynamics

(MD) based quantum mechanically derived accurate po-

tentials (force-ﬁelds) is a common tool for elucidating

the microscopic nature of interfacial systems, and would

be well suited for exploring the role of dendrimers in

modulating the EDL structure and ultimately the perfor-

mance of EDLCs. The key here is an accurate description

of the interaction parameters, coarse-grained simulations

revealed signiﬁcant force-ﬁeld dependence in the binding

strength of dendrimers to graphene electrodes, as the sys-

tem’s pH [11] is varied [20]. To more clearly understand

the nature of the interaction of the dendrimer-graphene

composites requires us to go beyond coarse-grained force-

ﬁelds and perform fully atomistic simulations. Yet, fully

atomistic simulations of dendrimers at interfaces, where

the dendrimer is being used as an electrolyte, are rel-

atively rare to the best of our knowledge. In contrast,

there have been several experimental [21, 22] and simula-

tion studies [23, 24] that reported carbon-based electrode

materials and studied the capacitance values with ionic

liquids being the electrolytes [25]. For example, Trigue-

rio et al. [21] reported that the dendrimer functionalised

carbon nanotubes can improve the nanotube’s perfor-

mance as an electrode. Another study by Chandra et al.

[26] reported that dendrimer functionalised nanoparticles

coated on an electrode surface can enhance the surface

area available to the electrolyte atoms, thereby achieving

eﬃcient charge transfer and low contact resistances. In

another experimental work, Liu et al. [27] used den-

drimer functionalized graphene-oxide sheet as a coating

on the sulfur electrode of a Li-S battery and achieved long

cycle life (up to 500 cycles). When considering common

electrolytes in EDLCs, various computational studies on

RTILs have been reported, including work by Yeh et al.

[28] which discussed the eﬀect of periodic boundary con-

ditions (BCs) in EDLC simulations.

Recently, we used atomistic MD simulations to study

the structural deformations [13] and the free-energy of

the binding [29] of PAMAM dendrimers at a charge

neutral graphene/water interface, as a function of the

protonation state of the dendrimer. We found that the

van der Waals interactions play a pivotal role in driv-

ing dendrimer adsorption. We also found that mod-

erately charged (neutral pH) dendrimers achieve maxi-

mum surface wetting as compared to the non-protonated

(high pH) and fully protonated (low pH) dendrimers. We

showed that lower generation dendrimers tended to de-

form and form ﬂat, disk-like architectures, with good sur-

face accessibility, at the graphene/water interface [13].

These observations suggest that the lower generation PA-

MAM at neutral pH condition as an ideal choice for

achieving maximum charge densities in PAMAM-based

supercapacitors. Therefore, in this work, we consid-

ered a G2 PAMAM dendrimer at neutral pH, and eluci-

date the electrochemical performance in graphene/water

based EDLCs. Beyond accurate simulations of dendrimer

based systems, we are also concerned with modelling bi-

ased nanoscale interfaces, as a means of probing elec-

trochemical eﬀects in EDLCs. Here, there are two main

computation methods commonly employed for doing this:

1) the constant charge method (CCM) – the charges of

the electrode atoms are ﬁxed, and 2) the constant poten-

tial method (CPM) – a grand canonical statistical me-

chanical ensemble is deﬁned by means of a ﬁctitious bath

that exchanges electrons with the electrodes to maintain

a constant electrode potential (the number of electrons

and chemical potential are conjugate pairs) [30, 31]. The

CPM approach is generally preferred as it enables simula-

tions that are more directly comparable to experiments.

However, it is somewhat restricted in its applicability due

to signiﬁcant additional computational demands. To this

end, Wang et al. [30] compared both approaches for

a LiClO4-acetonitrile/graphite EDLC and showed that

both the approaches lead to similar ion and solvent den-

sity proﬁles for voltages less than 2V. Comparing the

performance of both approaches for a more complicated

electrode/electrolyte morphology is one of the aims of

this study. Moreover, to address the computational chal-

lenges, Reed and coworkerset al. [32] have developed an

eﬃcient approach for simulating cells within CPM [30] in

the LAMMPS simulation engine, which we employ here.

The manuscript is organized as follows. In section

II, we provide the model building and the simulation

methodologies adopted in this work. In section III, we

present our results on the electrostatic potential, charge

density proﬁles and the capacitance values, obtained

from the CCM and the CPM approaches. Finally, in

section IV, we summarize our ﬁndings and conclude with

the key insights from our study to provide future research

directions.

TABLE I. Details of the electrode-electrolyte combinations

studied. The structure of the dendrimer considered corre-

sponds to a G2 PAMAM at neutral pH in all cases.

System Positive Negative Electrolyte

Electrode(+15e) Electrode(−15e)

BAREGP Graphene Graphene H2O

G2PEL Graphene Graphene H2O +

G2 PAMAM

+ Cl-ions

GPDEN Dendrimer coated Graphene H2O

graphene

II. MODEL AND SIMULATION DETAILS

In this work we focus on an aqueous supercapacitor

simulation cell based on water/water+dendrimer elec-

trolyte and graphene/dendrimer coated graphene elec-

trode (Table I). The initial structure of the PAMAM

dendrimer was built using the Dendrimer Builder Toolkit

(DBT) [15], while VMD [33] was used to build the

graphene sheet. The aromatic carbon atoms of graphene

were described using the AMBER FF10 force ﬁeld (atom-

type CA), as in our earlier works [34, 35], which we

showed captures the water-graphene interactions accu-

rately. Inter-molecular interactions involving dendrimer

atoms were described by GAFF force ﬁeld [36], the wa-

ter molecules were modelled using TIP3P [37, 38] water

model, and the Joung-Cheatham [39] parameters were

used to model the Cl-counter ions. Using the xLEaP

module of AMBER 14 [40], the equilibrated electrolyte

solution was placed in-between two graphene sheets with

dimensions of 32.63 ˚

A×62.50 ˚

A and separated by 150

(b)

(a)

(c)

FIG. 1. Instantaneous snapshot of a simulation box repre-

senting (a) BAREGP (b) G2PEL (c) GPDEN at 0 ns: positive

electrode is on the left and negative is on the right. The den-

drimer is shown in CPK. The graphene sheet is shown in grey.

The protonated amines of the dendrimer are shown in blue

and the Cl-counter ions are coloured green. 15 nm vacuum

slab shown, are not drawn to scale.

We aim to understand how the presence of the den-

drimer modiﬁes the electrochemical charge storage and

the capacitance values of the aqueous supercapacitor

with a graphene electrode. Hence, we performed the sim-

ulations for a system with a two bare graphene electrode

encapsulating a box of TIP3P waters, denoted BAREGP,

as a control. To test the potential of using the den-

drimer as an electrolyte and as an electrode, two addi-

tional systems, namely G2PEL and GPDEN respectively,

were considered. G2PEL comprised a G2 PAMAM den-

drimer at neutral pH, immersed in a pre-equilibrated box

of 10,118 TIP3P water molecules and placed between

two graphene electrodes. We neutralize the system by

adding 16 Cl-counter ions (the charge of the G2 PA-

MAM at neutral pH is +16e) [10]. For the GPDEN

system, we covalently grafted the G2 dendrimer onto the

graphene electrode, using a ”top-binding and grafting-to”

approach, as detailed in our previous work [41]. Here, a

dendrimer grafted graphene was used as a positive elec-

trode while a pristine graphene was used as a negative

electrode. 10,775 TIP3P water molecules were added in

between the two electrodes.

A. Constant Charge Method (CCM)

We employed two diﬀerent computational schemes for

simulating applied bias in our systems. First, we used

the PMEMD module of the AMBER14 [40] MD simu-

lation suite to perform supercapacitor simulations with

the CCM method. As mentioned above, in the GPDEN

case, the net charge of the dendrimer coated graphene

electrode was +15e, where charge of grafted dendrimer

atom was adapted from Gosika et al. [41]. Thus, a charge

of 0.01875ewas distributed on each of the carbon atom

comprising the graphene electrode. In these studies, we

minimized spurious electrode - electrode electrostatic in-

teractions by inserting large 15 nm vacuum slab buﬀer in

z-direction between the simulation cell, as shown in Fig.

1. For the BAREGP and G2PEL cases, we performed

two sets of simulations, where the electrodes are i) dis-

charged (charge on every electrode atom is set to 0e) ii)

oppositely charged (charge on each electrode atom was

set to 0.01875e, to be consistent with the GPDEN system

). We initiated each simulation with 1000 steps of the

steepest descent energy minimization, followed by fur-

ther 1000 steps of conjugate gradient minimization, to re-

move the initial bad contacts. We then gradually heated

the system from 0 K to 300 K using a Langevin ther-

mostat with random friction collision frequency 1 ps−1

in the constant temperature-constant volume (canonical

or NVT) ensemble for 5 ns. During heating, we re-

strained the solute (electrode) atoms with a harmonic

spring, with a force constant of 20 kcal mol-1 ˚

A-2 Equilib-

rium MD simulations were then performed under the con-

stant pressure-constant temperature (isothermal-isobaric

or NPT) ensemble, with a weaker restraint (10 kcal mol-1



A-2) on graphene atoms (no restraint on dendrimer).

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Molecularinsightsintothephysicsofpoly(amidoamine)-dendrimer-basedsupercapacitorsTarunMaityCenterforCondensedMatterTheory,Dept.ofPhysics,IndianInstituteofScience,Bangalore560012,IndiaMounikaGosikayCentrodeFsicadeMateriales(CSIC,UPV/EHU)andMaterialsPhysicsCenterMPC,PaseoManueldeLardizabal5,20018SanS...

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Molecular insights into the physics of polyamidoamine-dendrimer-based supercapacitors Tarun Maity

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