Model of Local Work Function and PZC for Molecular Self Assembly

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Model of Local Work Function and PZC for Molecular Self Assembly over Nanostructured Metal Electrode Jasmin Kaur, and Rama Kant J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b10696 • Publication Date (Web): 07 Dec 2017 Downloaded from http://pubs.acs.org on December 22, 2017

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The Journal of Physical Chemistry

Model of Local Work function and PZC for Molecular Self Assembly over Nanostructured Metal Electrode Jasmin Kaur and Rama Kant∗ Complex Systems Group, Department of Chemistry, University of Delhi, New Delhi-110007 E-mail: [email protected]

∗

To whom correspondence should be addressed

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ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract The tuning of metal work function (WF) and potential of zero charge (PZC) through molecular self assembly and nanostructuring has been trending. We have developed a generic theoretical approach to address the WF and PZC moderations due to organic molecular dipoles at the surface. Theory quantifies the electronic charge redistribution due to polarization through bonding between the metal/adsorbate and dipoles. The amount of charge reorganization at substrate surface is predicted to depend on the effective dipole moment (µN ) of the adsorbing molecule. The formula obtained for planar surface is used to elaborate experimental observation for WF of Au electrode covered with various DTC (Dithiocarbamate) linked rod shaped organic dipoles (-4.8 to 5.5D). The charge reorganization is stronger for the molecules with positive end of net dipole towards metal i.e., 7-22% of electronic charge whereas for negative pole towards metal it is < 4%. The formula for a spherical metal nanoparticle predicts inversion of excess WF, as the orientation of dipole switches from negative to positive pole towards metal. The slope of the linear dependence of the nanoparticle excess WF on µN is predicted to be size dependent. Further the generic formula for an arbitrary curved geometry shows the effect of shape anisotropy (ellipsoidal particle) in combination with dipole moment on the surface WF. We also theorize creation of Janus type particle with a net giant dipole, assemblies having two halves of the surface capped with differently oriented dipoles, rendering inversion in excess WF. Finally, it is concluded that WF and PZC of metal nanoparticles can be tailored through size, shape and chemical modifications.

Keywords: Excess work function, potential of zero charge, charge redistribution, nanocapping, shape anisotropy, giant dipoles

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Introduction Charge transport across organic/inorganic interfaces is a key phenomena determining their capacitive and electrochemical performance. The efficiency of charge transport at such interfaces is controlled by the relative alignment of work function of electrode and highest occupied or lowest unoccupied molecular orbitals of redox molecules. 5,6 Tuning of work function has been targeted through optimization of size and shape, deposition of thin films, adsorption of or electron transfer from or adsorbates, 7,8 covalently linked self assembled monolayers (SAMs) 9–11 and so on. Modification of electrode work function through such structural and compositional means has been explicitly practiced and applied to myriad of applications, viz. sensing, electrocatalysis, electronics, energy conversion/storage devices. Since the discovery of disulfide adsorption on the Au surface by Nuzzo and Allara in 1983, 12 SAMs of alkanethiols and their derivatives have been widely used in various research fields, viz. electrochemistry, 13 molecular electronics, biomimetics 3 and nanomaterials. The affinity of sulfur for coinage metals has resulted in the most common self-assembly system used to modify electrodes being alkyl/arylthiols 14–16 among other organic adsorbates. 17 Their use has paved the way to simplified customization of efficient organic electronic technologies through electrode work function. Several illustrative reviews on various prospects of metal surface interaction with monolayers of organic assemblies are available. 18–20 Work function tuning has been accomplished by using polar molecules that can self assemble on the metal and form a highly ordered, thin two dimensional layer which has a dipole in the desired direction. 21 Alkanethiols and per fluorinated thiols are known to form such SAMs on group Ib and group VIII metals. 22 Since they have opposite dipoles they can be used to respectively increase or decrease the work function of metals. Also conjugated mono and dithiols are known to form highly ordered SAM which make them particularly useful for optoelectronic applications. 23 Electronic structure calculations have demonstrated the complex interplay between intrinsic dipoles and dipoles induced by bond formation as the reason leading to large work function shifts 9,21 in metal substrates. The packing and 4


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molecular orientation in two dimensional assemblies has also been studied through molecular mechanics calculations of alkanethiolates on gold, 24 molecular dynamics simulations of alkanethiolates on gold 25,26 of lipid membranes, and of Langmuir monolayers (molecular assemblies at the air-water interface) 27,28 and Brownian dynamics of Langmuir monolayers. 29 Employing DFT calculations, Heimel and coworkers 30,31 have analyzed different mechanisms of dipole formation at the interface, which govern the work function change. The theoretical result by Fischer et al. 32 is suggestive of a significant degree of charge transfer to sulfur in thiolates. The work function change arises due to the modification of the respective surface potentials of the two phases in contact, which further modifies due to substrate size/shape or surface adsorption. It is the additional dipole barrier that forms at the interface, that modifies the work function of the metal substrate. The surface dipole of the physically adsorbed layer depends on the intrinsic field of metal substrate, dipole moment of the molecules and their electrostatic interactions. 34 Whereas for chemisorbed layers, the dipole at the interface due to charge transfer between the molecules and the surface is the contributing factor. Beside these attributes, assembly of organic molecules renders stabilization to the nucleated nanocrystals by reducing the free energy and hence the reactivity of the surface. 36 In-fact the concentration ratio of such capping agents to the metal precursors are known to control the size 37 and shape 38 of the resulting nanoparticles. Although the capping groups render structural stabilization, the properties of the resultant assembly over metal nanostructure is also controlled by the curvature at such interfaces. By far the theoretical details of the interface between metals and the monolayers are mostly understood in qualitative terms at planar surfaces. 1,39,40 However, types of substrates can range from planar surfaces (glass or silicon slabs supporting thin films of metal, metal foils, single crystals) to highly curved nanostructures (colloids, nanocrystals, nanorods). Polycrystalline metal substrates manifest structural patterning comprising intergrain boundaries, faceting, occlusions, and other structural irregularities. Also, metal substrates have

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a varying atomic steps density, that affects the structures and defects of adsorbed dipolar molecules. Infact, defects in the adsorbed organic monolayer arising due to rotation of the molecular backbone and changes in the configuration of the tail group are known to significantly affect the electronic work function. 41 Therefore, the ordering of molecular dipoles and the consequent change in work function are manifested by the interplay of structural attributes of substrate and the adsorbing dipole. We intend to theoretically address the work function moderations by quantifying the charge reorganization at planar and curved metal substrates due to covalently linked organic dipoles. The experimentally reported work function change of Au metal substrate, due to adsorption of Dithiocarbamate (DTC) linked alkyl/aryl assembly, 9 is used to estimate the extent of electronic reorganization at the metal surface, based on our recent theory of work function of metal with planar and arbitrary structure in immersed state. 34 The size dependent change in nanoparticle work function as a function of changing dipole moment of adsorbing molecules is illustrated to emphasize the interplay between substrate structure and dipole characteristics. The electronic work function acquired by isotropic (spherical) and anisotropic (ellipsoidal) nanoparticles with changing dipole moment of the adsorbing molecule in the range of -4.8 to 5.5D is also studied. In the last section we theorize Janus type particle assemblies rendering a wide work function distribution over the same structure based on our analytical predictions.

Metal work function and electrostatic self capacitance In vacuum The electronic work function as the electrostatic self-capacitive energy of the circular disc of radius lT F , the Thomas-Fermi electronic screening length, has been recently obtained 42 as, φ0E =

e2 2π0 m lT F 6


(1)

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where, r lT F =

20 m Ef 3n0 e2

(2)

0 is the permittivity of the free space (=8.85×10−12 F/m), m is the metal dielectric constant (listed in supporting information in Ref. 42 ), Ef is the Fermi energy, e is the electronic charge and n0 is the number density of electrons. Based on the curvature dependent electronic capacitance of metal through multiple scattering expansion in curvature terms, 43,44 a generalized definition of work function has been obtained for arbitrary nanostrutured surfaces. 42 So, the electronic threshold energy for randomly nanostructured surfaces, characterized in terms of mean (H) and Gaussian (K) curvatures has been obtained as, 34,42

φE =

φ0E

1 + H lT F

(3H 2 − K) lT2 F + 2

(3)

The validity of equation 3 has been ascertained from the experimental variation of work function of rough spherical nanoparticles. 42

In presence of molecular dipoles Work function being a surface property is highly sensitive to any type of surface modifications through contamination, texturing or adsorption. The coverage (θ) dependent work function for planar and nanostructured metal surface in contact with physisorbed dipoles has been recently defined by Kant et al. 34 The orientational ordering of the adsorbing dipoles is predicted as an attribute of the characteristic intrinsic electric field (ε) of metal that lies between ∼0.6-1.5 V/nm. 34 As during physisorption the adsorbate is not firmly attached to the surface, the ensemble averaged dipole moment, as the function of field, over all possible thermal energy driven orientations has been obtained using Langevin function. Meanwhile, the polarity of the adsorbing molecule manifest redistribution of surface charge at the metal ˜ surface denoted as δe/Fermi disc. The work function obtained here is the operative electron ejection energy of electrode in an electrochemical system and is directly related to another 7



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M useful quantity the potential of zero charge ( Epzc ). The relation between the measured

potential of zero charge and metal work function is given as, 33,34

M Epzc = φch + Eref

(4)

where φch is the work function of metal electrode with adsorbed dipoles, Eref is a constant term including the potential drop at the reference electrode/solution interface and is -4.78V in vacuum and -3.44V in solution corresponding to NHE. 35 For chemisorbed adsorbate, the attachment of dipole molecule to the surface is of chemical nature due to the bond between the two. However, despite the bonding, the electronic redistribution manifest some residual charge at the binding site. Based on the contributions from dipolar molecule and consequent electronic reorganization at the metal surface, the electronic work function for the planar metal surface in contact with chemisorbed dipolar molecules has been defined as, 34 θN0 µN φ0ch = φ0E [1 + θ(2δ˜ + δ˜2 )] − 0 m

(5)

where, φ0E is planar surface work function defined in equation 3, N0 is the number of oriented dipoles per unit area, µN is the normal component of the dipole moment of adsorbing moiety and δ˜ is the amount of reorganized electronic charge at the surface. The second and third terms in equation 5 denote the contributions from the modified surface potentials of the metal and the adsorbing dipolar molecule to the work function. The metal surface potential gets modified due to charge exchange or electronic redistribution at the surface, wherein the adsorbate contribution is effectively accounted through the effective dipole moment it bears at a given temperature. While in the case of physisorbed molecules the thermal driven disorder in molecular orientation is prevalent (estimated through Langevin function 34 ), it plays a lesser role in chemisorbed molecular arrangement that is established through a covalent link with the substrate. However, both these contribution tend to get 8


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modified as the substrate surface tend to deviate form planar structure. The curvature modified electronic work function for the metal surface in contact with non bonding dipolar molecules is obtained as, 34

φch =

φ0ch

+

φ0E

H lT F

(3H 2 − K) lT2 F ˜ − g s θ[2Hrd + Kr2 ] + (1 + 2δθ) 0 d 2

(6)

where φ0ch is the molecular dipole modified work function of planar surface defined in equation 5, g0s = N0 µN /0 m and lT F is defined in equation 2. In equation 6, the structural information of the substrate is incorporated in terms of the mean (H) and Gaussian curvatures (K), and that of adsorbate through a circular projection disc of radius rd .

Electronic reorganization due to chemisorbed dipoles Unlike physisorbed molecular dipoles on metal surface, the organic dipolar molecules anchor through effective charge transfer across the interface forming chemical bonds. 21,23,45 The link between the metal surface and organic adsorbate can be a covalent bond (alkyltrichlorosilanes on hydroxylated surfaces), 46 a slightly polar covalent bond (alkanethiolates on gold), 23 or an ionic bond. 47 Due to stronger chemical link to the surface, dipole’s molecular orientation is primarily controlled by the structure/flexibility of the intermediate and tail groups. 10,48 However, since the adsorbing molecule possess an effective dipole moment, the electron density at the metal substrate is subjected to reorganization. As the work function corresponds to the electrostatic self capacitive energy of the Thomas-Fermi disc, 42 the charge reorgani˜ at this disc due to adsorption contributes to the changes metal work function, zation (δe) see figure 1. However, the amount of charge reorganization is dependent on the polarity of the dipolar end facing the metal and the effective dipole moment of adsorbate. We present a case study wherein the work function variation of Au substrate in contact with the covalently linked DTC (Dithiocarbamate) anchored organic dipoles is considered, as presented by Ford et al. 9 In their study the dipoles are designed as the rod-shaped molecular 9



Figure 1: Schematic illustration of positive and negative dipole molecules anchored over a circular disc of radius of Thomas-Fermi length at the metal surface.

structures having a DTC-piperazine/piperidine-R components, where R is an aryl or alkyl substituent. 9 The molecular structure of the various organic dipoles are listed in table 1. The present study is focused on the local work function changes subject to chemisorption of molecules bearing an effective dipole moment. No account of intra-adsorbate interactions are taken (which is why the rod shaped structures of DTC linked organic structures are appropriate). Considering the substrate as a plane metal surface, the DTC anchored dipole molecules attachment over it is schematically depicted through figure 1. The end groups in the molecular dipole are detrimental of the direction of net dipole moment as shown in figure 1. Since the dipolar head is not under the influence of thermal driven disorder, due to stronger covalent metal adsorbate link, 9 the effective dipole moment values computed along the molecular axis from gas-phase DFT calculations of single molecules 9 are considered. The aromatic backbone of the adsorbed monolayer is known to increase monolayer packing. 49 The molec˚2 /molecule. 50 Considering this to be ular area for densely packed DTC monolayers is ∼ 23A the area of the circular disc projection of molecule over the surface, it corresponds to the packing density of nearly 4.34 molecules/nm2 . Also, as the molecules possess rod shaped structure, the influence of adsorbate deformities such as chain entanglement or disorder are 10


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˜ at the Au surface (φ0 =5.12 Table 1: Estimated values of the redistributed electronic charge (δ) E eV, lT F =0.12 nm and m =4.52) due to assembly of DTC anchored organic dipoles (DTC1-DTC9) and n-Octanethiol, using equation 5. The values are estimated with monolayer coverage, θ=1, corresponding to N0 =4.3nm−2 .

A Dipole Molecule

.

B Label

C µN (D) 9

D E F 9 0 ∆φch (eV) φch (eV) δ˜ (e− )

G charge/Au atom 9

DTC-1

5.54

-1.90

3.22

0.008

-

DTC-2

4.76

-1.89

3.23

-0.018

-

DTC-3

3.85

-1.54

3.58

-0.015

-

DTC-4

3.67

-1.68

3.44

-0.036

-

DTC-5

3.52

-1.60

3.52

-0.033

-0.085

DTC-6

-0.06

-0.69

4.43

-0.072

-0.095

DTC-7

-0.21

-0.79

4.33

-0.088

-

DTC-8

-1.48

-0.61

4.51

-0.118

-

DTC-9

-4.76

-0.37

4.75

-0.228

-

Octanethiol

0.82

-1.0

4.12

-0.071

-0.102

δ˜ denotes the reduction in electronic charge per Thomas-Fermi disc as the negatively charged sulfur head approach the metal (column F).

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insignificant. Using equation 5 and the work function variation listed in table 1, we have estimated the charge redistribution at the metal surface corresponding to DTC anchored dipoles, see table 1. The negative values of redistributed charge δ˜ (table 1), denotes the decrease of that much charge per Thomas-Fermi disc as it encounters the negatively charged sulfur heads of DTC anchor. It corresponds to the extent of electronic charge redistribution at the gold surface beside electronic exchange between the surface and adsorbate (leading to the anchoring of DTC at the metal surface). It is to be noted that the values of the partial charge at metal atom estimated through DFT analysis 9 (column F table 1) is based on a single atom consideration, i.e. influence of a molecular adsorption at just one metal atom. However, the substrate surface in reality is a continuum arrangement of atoms and the charge at each atom due to molecular adsorption is likely to get delocalized over the surface. The partial charge per Au atom due to adsorption of listed molecules, as reported through computational estimate is represented as the consequent charge displaced per Au atom in column G.

Results and discussions WF of spherical nanoparticles with organic monolayer Several characteristics of adsorbing monolayer such as dielectric constant, 10 head and tail group, 31 number of layers in coating 51 etc. are known to influence the electronic properties of the underlying substrate. It is the charge exchange/redistribution at the substrate adsorbate interface that is transmitted to the adsorbing molecular chain thereby influencing its properties. On this basis the layer wise oscillatory work function fluctuation for nanoparticles by Carrara et al. 51 can be attributed to interface induced modifications in dipole moment of first layer and so on. The extraordinary properties of nanostructures can be effectively related to the curvature that they acquire at nano-length scales. The maximum influence of curvature on the electronic properties however prevail for surface features, comparable 12


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to the electronic screening length. So, with reducing size of the surface features, curvature effects gets pronounced thereby exhibiting profound variations in surface properties. The most straightforward illustration can be made through the spherical metal particles. With reducing particle size, the work function of the metal is known to increase, 42 relative to the planar surface, however, the extent of variation differs if the surface is in contact with the dipolar layer. 34 Here we demonstrate the influence of dipole moment of chemisorbed organic layer on the work function change as the function of particle size. Using equation 6, the work function of a spherical particle of radius r, in contact with a dipolar monolayer is, 34

∆φch = φch −

φ0ch

=

φ0E

lT F lT2 F 2rd rd2 2 s ˜ ˜ + 2 (1 + (2δ + δ )θ) − g0 θ + 2 r r r r

(7)

δ˜2 has been negligible in the case of physisorbed adsorbate (due to small values of δ˜ e.g. -0.04 for water), 42 however, in chemically linked adlayer this term is also incorporated.

Size dependent WF inversion As is evident from equation 7, the last term renders decrease in WF with increasing magnitude of molecular dipole moment. A monotonous decrease in Au and Ag work function has been reported for the adsorption of molecules with varying dipole moments (-4.8 to 5.5D) of organic dipoles listed in table 1. 9 However, for spherical nanoparticles, particle size (r) is also an essential factor controlling the WF and its influence further strengthens with reducing r. Unlike planar surface, variation in excess work function (∆φch ) for spherical particles is non-monotonous, see figure 2. Therefore, for a fixed particle size, ∆φch (= φch − φ0ch ) can be positive or negative depending on the polarity of the dipolar end facing the surface. As the polarity of the dipolar end facing the metal changes from positive to negative, the molecular dipole of same magnitude exhibits an inversion in the work function change in spherical nanoparticles of same metal (see figure 2). Interestingly, in our earlier theories 34,42 such an inversion was attained through opposite mean curvatures in geometries like spherical

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Figure 2: Size dependent WF variation of spherical Au nanoparticle as the function of monolayer dipole moment (specified along curves) using equation 7, for DTC-2 (purpleblue), DTC-5 (cyan), DTC-7 (yellow) and DTC-9 (red). Parameters used are: θ=1, N0 =4.3nm−2 , rd =0.27nm.

nanoparticle and cavity. Whereas from current study it is inferred that shape is not the only contributing factor, the structure and nature of the capping organic molecules over the metal nanostructures can significantly modify their electronic properties and performance.

Figure 3: Variation in excess work function for Au spherical particle due to different dipole moments of adsorbing molecular dipoles, DTC-1-DTC-9. Parameters used are: θ=1, N0 =4.3nm−2 , rd =0.27nm.

Ford et al. has shown a linear dependence of the WF on the dipole moment for various 14


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DTC derivatives investigated in their study. For a fixed particle size, the linear dependence of the excess work function on the dipole moment of the capping dipolar molecule is shown in figure 3A and 3B. Unlike planar surface, 9 the work function variation spans over the negative and positive change domain. The range of variation however, is dependent on the size and hence the curvature of the particle. Smaller the particle size, sharper is the curvature and broader is the variation in work function change (figure 3B). In accordance with the current model, an intriguing particle design through incorporation of curvature and dipole moment is theorized to manifest a wide work function variation over the same particle surface. As shown in figure 4 the two halves of the chemically homogeneous gold nanoparticle, mimic the structure of that of a Janus particle 4 as if it comprises two different materials altogether. The attachment of organic dipoles with negative and positive poles on the two halves over the particle of r=3nm, two work functions domains with φch = 3.1 and 5.2 eV are created, respectively.

Figure 4: Surface plots for work function variation for spherical Au nanoparticle with two halves covered with positive (DTC-2) and negative (DTC-9) molecular dipoles each, Janus type particle. Parameters used are: θ=1, N0 =4.3nm−2 , rd =0.27nm.

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WF and shape anisotropy Pertaining to high curvature, the poles of a prolate particle (nanoneedle, nanopiller) and edges of an oblate particle (nanoflake, nanodisc) have been predicted as potential sites for oxidation as they exhibit high work function. 34 This section emphasize on the distribution and dipole moment dependent inversion in the work function change over an anisotropic particle. As depicted in figure 5, the area swept across the prolate particle from one pole

Figure 5: Variation in work function change for Au ellipsoidal (prolate) particle due to: curvature only (black) and different dipole moments of adsorbing molecular dipoles, DTC-2 (blue) and DTC9 (red). Parameters used are: θ=1, N0 =4.3nm−2 , rd =0.27nm. Mean and Gaussian curvatures of ellipsoidal particles are defined in appendix.

to other (form 0◦ to 180◦ ), regions of varying curvatures are encountered thereby rendering distribution of work function change. In vacuum state the curvature term manifest positive contribution to the work function, so it increases with increasing curvature. However, in contact with a dipolar molecule the resultant work function is dependent on the contribution of the effective dipole moment of the molecule, surface curvature and the consequent electronic reorganization. As the dipole contribution switches from positive to negative depending on the polarity of the dipolar end facing metal surface, the work function change also spans over a wide distribution over the same surface. Although the overall variation in excess work function is dependent on the type of dipolar molecule attached, the effect gets amplified 16


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at high curvature sites (poles of a prolate and equator of an oblate particle), see figure 5. By tracing over the particle surface with ellipsoidal structure (nanoneedles, nanoflakes, nanodiscs), sites with varying degree of convexity are encountered. Consequently, the local curvature contribution to work function over the same structure are expected to differ. As a result, various sites on the particle surface behave as though the overall particle has locally contrasting work functions. Through above inferences, one can think of various structural optimizations that can render desired local work function. The effect of curvature distribution and adsorbate dipole

Figure 6: Surface plots for work function variation for Au nanostructures: A. Prolate particle with positive dipoles (DTC-2) and B. Prolate particles with negative dipoles (DTC-9). Parameters used are: θ=1, N0 =4.3nm−2 , rd =0.27nm. Mean and Gaussian curvatures of ellipsoidal particles are defined in appendix.

moment, over the local work function of particle, is further illustrated through surface plots of prolate particle geometry in figure 6A and 6B. It is due to the sharp curvature at the poles of the prolate structure that the work function enhancement or suppression is profound. Similar to the isotropic particle structure assembly discussed in figure 4, even broader work function distribution can be obtained through particle shape anisotropy, see figure 7. The assembly thus formed behaves as a bimetallic structure having giant dipole. Owing to such a wide difference in work function, the two poles of the prolate particle would exhibit contrasting electronic, optical and electronic properties. As the nanoparticles (discussed above) behave as structures with net dipole moment bearing the nanoscale curvature, they can be employed for vast number of applications. Usage of biphasic (Janus) particles has been widely reported 17



Figure 7: Surface plots for work function variation for Au prolate particle with two halves covered with positive (DTC-2) and negative (DTC-9) molecular dipoles each, Janus type anisotropic particle. Parameters used are: θ=1, N0 =4.3nm−2 , rd =0.27nm. Mean and Gaussian curvatures of ellipsoidal particles are defined in appendix.

in the field of catalysis and biological sciences. The dipolar superstructures theorized above can effectively align in an electric field thereby exposing a well customized and organized interfaces to carry out various reactions at macroscopic surfaces. The relation between the electrode work function and the potential of zero charge is a vital link from electrochemistry perspective. 34 Measurement of the local work function of the SAM modified metal electrode therefore provides detail of local potential of zero charge. However the extended structures of organic dipoles into the solution, manifest an additional interface at the SAM surface in contact with electrolyte solution. In this case the operative orientation of the solvent molecules is subjective to the effective dipole orientating field at the SAM—electrolyte interface. Consequently, the potential of zero charge has a contribution from the surface potential from this interface as well 2,13 which in turn is sensitive to the structural influences by the substrate.

Conclusions Model for the variation in electronic work function and potential of zero charge of planar and nanostructured metal due to chemisorbed organic dipolar layer is presented. The present analysis identify the electronic charge redistribution at planar substrate surface and molecular dipole moment as the key attributes generating work function variation. The influence of

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substrate size and shape is combination with attachment of several DTC anchored organic dipoles with varying dipole moment are elaborated through spherical and ellipsoidal particle structures. We also theorize some metal nanostructure-dipole layer assemblies that can facilitate a wide work function variation over the same particle structure. The key conclusions from present analysis are as follows: 1. For a given metal, the amount of charge reorganization depends on the effective dipole moment and orientation of the adsorbing molecule. ˜ due to present set of molecules with positive pole towards 2. The charge reorganization, δ, metal (µN 0) towards metal δ˜ is < 4% of electronic charge. 4. Inversion in sign of excess WF is predicted for convex nanoparticles (spherical, ellipsoidal) as the pole of capping molecule facing metal switches from positive to negative polarity. 5. The extent (slope) of the linear dependence of the nanoparticle excess WF on µN of the capping dipolar molecule is predicted to be dependent on the particle size. It increase with decreasing particle size. 6. Shape anisotropy, as in ellipsoidal particles (prolate , oblate), in combination with varying molecular dipole moment is predicted to render work function variation and inversion over the same particle surface. 7. Assembly of nanostructured particle dipoles are theorized, having convex particles with two halves capped by different monolayers, with work function variation from 3-7 eV over the same structure. Owing to such wide work function variation, these assemblies are predicted to exhibit unusual electronic, optical and electronic properties. Such assemblies can be identified as viable 19



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alternatives to the use of metal alloys (e.g. Mg/Ag; WF∼3.7eV) for these applications. Finally, it is concluded that work function and potential of zero charge of a nanostructured electrode can be tailored through its shape and chemical modifications of surface.

Acknowledgement R. K. thanks DST-SERB (Project No. EMR/2016/007779). J. K. thanks UGC, New Delhi for Financial support.

Appendix

For an ellipsoid with rx , ry and rz as its semi-principle axes, the parametric coordinates are: rx Cos[u]Sin[v], ry Sin[u]Sin[v], rz Cos[v]. The mean (H[u, v]) and Gaussian (K[u, v]) curvature are defined as: 52 rx ry rz H[u, v] =

3(rx2 +ry2 )+2rz2 +(rx2 +ry2 −2rz2 )Cos[2v]

−2(rx2 −ry2 )Cos[2u]Sin[v]2

3/2 8 rx2 ry2 Cos[v]2 + rz2 ry2 Cos[u]2 + rx2 Sin[u]2 Sin[v]2

K[u, v] =

rx2 ry2 rz2 2 rx2 ry2 Cos[v]2 + rz2 ry2 Cos[u]2 + rx2 Sin[u]2 Sin[v]2

(8)

(9)

respectively. Where, u ∈(0,2π) and v ∈(0,π).

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Model of Local Work Function and PZC for Molecular Self Assembly

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