2011 IEEE International Conference on Dielectric Liquids
A correlation between dielectric permittivity and wettability for low energy surface (Bismuth Zinc Niobate) on fused silica V. Madhurima*, Debarun Dhar Purkayastha Department of Physics, Mizoram University
K. Sudheendran, K. C. James Raju School of Physics, University of Hyderabad
Aizawl, India
Hyderabad, India
*
[email protected]
Abstract— Theoretical contact angle of Diiodomethane on Bismuth Zinc Niobate thin film on fused silica substrate is calculated and the results are compared with experimental values. The theoretical calculation of contact angle is by the determination of the Hamaker’s constant from the dielectric data and applying Lifshitz-van der Waals dispersive interaction and Young-Dupree equation and the experimental value is found using a contact angle goniometer using the sessile drop method. The results from the experiment were seen to be close to that from the theoretical calculation. Keywords- Hamaker constant, dielectric permittivity, Lifshitzvan der Waals interaction.
I.
INTRODUCTION
Bismuth Zinc Niobate (BZN) exhibits tunable dielectric properties [1] enabling its use in micro electro mechanical system (MEMS) devices using electro wetting on dielectric (EWOD) for droplet manipulation [2], in thin film capacitors [3], tunable coplanar waveguide (CPW) line [4] etc. In MEMS and their natural extension of nano MEMS (called NEMS), certain intermolecular interactions that are insignificant at the bulk level become dominant, especially when the device sizes goes to the nm regime. Such interactions can be either between the same materials or between dissimilar materials. Often the interactions are between a solid substrate and an interacting liquid drop. In the case of dispersive solids and liquids where the dispersive forces are dominant compared to the polar component, Lifshitz-van der Waals theory along with Young-Dupree equation can be used to calculate the theoretical contact angle for a given system. Wetting properties of liquid over a solid depends upon the chemical composition [5], surface roughness [6-7], dielectric properties of solid [8], and liquid respectively etc. Wettability is determined experimentally by the contact angle formed by a drop of the liquid over the substrate using a goniometer. A. El. Ghzaoui et. al., have made a comparative study of theoretical and experimental contact angle of apolar liquid over different polymer substrate [9]. Hamaker constants have been determined from contact angle data, sometimes in addition to other studies, for carbon fibers [10], fibrous solids [11], and polymers [12]. The present studies are on similar lines where the theoretical contact angles and experimental contact angles of Diiodomethane over Bismuth Zinc Niobate (BZN) on fused silica are compared. The theoretical contact angle values are determined from dielectric data since contact is related to surface energy, which is a direct manifestation of
VM and DDP thank Naval Research Board, India for financial assistance through a research project.
978-1-4244-7354-0/11/$26.00 ©2011 IEEE
intermolecular forces that in turn related to the dielectric permittivity of the material. II.
EXPERIMENTAL
RESULTS
Bi1.5Zn1.0Nb1.5O7 (BZN) films were deposited by pulsed laser deposition (PLD) using a KrF excimer laser (248 nm wavelength, Model Compex pro201F of Lambdaphysik, Germany). Laser power density of 3 J/cm2 was used in all cases at a repetition rate of 5 Hz [13]. The film was grown in pure oxygen atmosphere at a pressure of 10 mTorr on amorphous fused silica substrates. The substrate temperature was maintained at ambient temperature during deposition. The dielectric property of the film was measured by an extended cavity perturbation technique using an Agilent 8722ES Vector Network Analyzer and the refractive index of the film was determined from the spectral transmission technique. Contact angles measurements were performed using Rame-Hart contact angle goniometer (Model 250). The surface energy of BZN on fused silica is calculated using multiliquid tool of the Goniometer’s advance drop image program using deionized water, Diiodomethane (Merck) and DMSO (Merck) as probe liquid for contact angle measurement. The sessile drop method was used to measure the contact angle with a drop volume of 2µl. III.
THEORETICAL BACKGROUND
Wettability of the system is characterized by the contact angle ‘ș’ measured between the liquid drop and solid surface. The contact angle ‘ș’ can be related to the three interfacial tensions via Young equation [14]. (1) YSV − YSL YLV Where, YSV=solid-vapor interfacial tension, YSL=solid-liquid interfacial tension and YLV =liquid-vapor interfacial tension. Dupree modified the Young’s equation by introducing the concept of adhesion and it is the work done to separate the two phases as W=YSV+YLV-YSL Comparing the above equation with Young’s equation we get adhesive energy as
cosθ =
Wa = YLV (1+ cosθ)
(2)
This equation is known as Young-Dupree equation [15]. According to Young-Dupree, the energy of adhesion (the freeenergy interaction per unit area) for a liquid in contact with a solid ESL is given by
ESL = YLV (1+ cosθ) §E · cosθ= ¨¨ SL −1¸¸ © YLV ¹
(3)
The energy of adhesion between two identical surfaces is defined as ELVL=2YLV for liquid and ESVS=2YSV for the solid. In the case of dispersive liquids and solids the energy of adhesion equal to Vander Waals free energy. If we consider two plane surfaces separated by a equilibrium distance H then the total energy per unit area can be expressed by the Lifshitz theory as
W=−
A 12πH 2
From the Young-Dupree equation the theoretical contact angle is determined as 2A cos θ = − SVL A LVL
IV.
TABLE I.
YSV = −
(5)
ASVS 2 24πHSVS
(8)
1
RESULTS AND DISCUSSION
Sample
Contact angle (Water)
SURFACE ENERGY OF BZN ON FUSED SILICA
Contact angle (diiodom ethane)
Adhesive Energy (mJ/m2)
S.E using multiliquid tool (mJ/m2) Polar DisperTotal sive
60.41
0.22
(6)
In the present study we have calculated the non-retarded Hamaker constant of BZN on fused silica by using dielectric permittivity and refractive index previously determined [14] which is an indicator of Lifshitz-van der Waals (dispersion) interaction between two bodies of materials at short distance by the following formula.
( (
2
The dispersive and polar component of surface energy of BZN on fused silica along with contact angle of water, Diiodomethane and adhesive energy is given in Table-ȱ. Various physical properties including surface energy components of Diiodomethane are given in Table-II
A LVL 24πH 2LVL
ª H LVL º « » ¬ HSVL ¼
Where ASVL , ALVL and H SVL , H LVL , represent the associated non-retarded Hamaker constants and the equilibrium distance separations for the hetero-interaction and homo-interaction between solid (S) and liquid (L) in a vapour medium.
(4)
Where A is non-retarded Hamaker constant. Now for homogeneous medium such as liquid and solid W=2Y. Then Lifshitz-van der Waals (dispersion) interaction energy of liquid and solid can be related to Hamaker constant as
YLV = −
BZN on fused silica has been found to be 3.3×10-19 J. From the calculated value of Hamaker constant of solid and liquid we have calculated the Hamaker constant and equilibrium distance of separation of interfacial region between solid and liquid by geometric mean of condensed phases A SVL = A LVL A SVS HSVL = H LVL HSVS respectively.
) )
2 2 § ε −1 · 3 3hν n −1 A = KBT ¨ ¸ + 3 4 © ε +1 ¹ 16 2 2 n +1 2
BZN fused silica
99.80
53.49
TABLE II. Liquid
ε
n
33.85
34.07
PHYSICAL PROPERTIES OF DIIODOMETHANE YLV
YLVd
YLVp
ALVL
HLVL
(mJ/m2)
(mJ/m2)
(mJ/m2)
10−20 J
(nm)
50.8
50.8
0
7.51
0.14
2
Diiodom ethane
(7)
Where ε and n are the dielectric constant and the refractive index of the medium, h is Planck’s constant and ν is the mean electronic absorption frequency and which is assumed typically of the order of 3×1015 S-1. Hamaker constant for
5.3
1.74
From the non-retarded Hamaker constant we have calculated theoretical contact angle of Diiodomethane, which is 51.67o over BZN on fused silica. This compares with the experimental value of 51.32o.The approximately identical value of measured and the theoretical contact angle strongly argue the fact that the wettability of apolar liquid is strongly
dependent on the dielectric character of low energy surfaces like BZN on fused silica.
[3]
[4]
V.
CONCLUSION
Surface energy of BZN on fused silica was determined using the multi-liquid method of contact angle measurements. The present BZN on fused silica sample is found to have low surface energy with a dominant dispersive component. This agrees with the experimentally determined low dielectric permittivity of BZN on fused silica (εr =11). Dielectric permittivity and refractive index µ=2.36 (at wavelength of 750 nm) data of BZN were used to determine the Hamaker constant. Hamaker constant is related to the surface energy through the Lifshitz-van der Waals equation and the surface energy is related to the contact angle as given by the YoungDupree equation. Hence the theoretical contact angle of diiodomethane over BZN was calculated to be 51.67o.This agrees with the experimental value of 51.32 o. In conclusion it is seen that for apolar substrates interacting with apolar dielectric liquids, the dispersive forces of interaction, which are of importance at micro and nano scales, can be estimated from contact angle experiments and dielectric measurements of the substrate. REFERENCES [1]
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