Ashutosh Sharma - Academia.edu (original) (raw)

Papers by Ashutosh Sharma

Research paper thumbnail of A unified model for flux prediction during batch cell ultrafiltration

Journal of Membrane Science, 1996

An analysis of the flux decline encountered during ultrafiltration (UF) in a batch cell is presen... more An analysis of the flux decline encountered during ultrafiltration (UF) in a batch cell is presented by including the combined influence of the osmotic pressure and the gel layer. A predictive model for the flux decline in unstirred and stirred batch cell UF processes is developed by unifying the osmotic pressure and gel layer models. UF experiments were performed in a batch cell with polymeric solutes (PEG, dextran and PVA) and a protein (BSA), ranging widely in molecular weights and physico-cbemical properties, under various operating conditions (pressure, solution pH, and stirrer speed). The present unified model predictions match closely with the experimental flux behaviour for all cases, while individual osmotic pressure and gel layer models are found to be inadequate.

Research paper thumbnail of Generalized integral and similarity solutions of the concentration profiles for osmotic pressure controlled ultrafiltration

Journal of Membrane Science, 1997

A mathematical model describing the concentration polarization phenomenon during osmotic pressure... more A mathematical model describing the concentration polarization phenomenon during osmotic pressure controlled ultrafiltration is presented. Generalized integral and similarity solutions of the concentration profile in the mass transfer boundary layer are obtained. The parameters governing the shape of the concentration profile vary with time in case of a batch cell and axial distance in a cross flow cell. The model is used to predict the permeate flux and the solute rejection simultaneously during unstirred batch cell and cross flow UF. The results obtained by integral and similarity solutions are compared with the results of detailed numerical solution of the governing equations for both the systems. The predictions of permeate flux from the generalized integral method are also compared with some approximate solutions in order to assess the limitations of the various approximations. UF experiments were performed with Dextran (T-20) in cross flow system and with PEG-6000 and Dextran (T-40 and T-20) in unstirred batch cell. Predictions of the model are in remarkably good agreement with detailed simulation as well as experimental results. Moreover, the integral solution can also account for the variation of diffusivity with solute concentration. Comparisons show that (a) while the generalized integral method is much simpler than the detailed numerical solutions, it is much more general and accurate than other analytical and semi-analytical solutions, and, (b) the proposed solution predicts the osmotic pressure controlled flux decline accurately over a wide range of operating conditions. The expression for gel layer governed UF (constant membrane surface concentration) is found to be an asymptotic case of the present solution.

Research paper thumbnail of Pulse Electroplating of Ultrafine Grained Tin Coating

Electroplating of Nanostructures, 2015

In the electronic packaging industries, soldering materials are essential in joining various micr... more In the electronic packaging industries, soldering materials are essential in joining various microelectronic networks. Solders assure the reliability of joints and protect the microelectronic packaging devices. They provide electrical, thermal, and mechanical continuity among various interconnections in an electronic device. The service performance of all the electronic appliances depends on high strength and durable soldering materials. Lead-containing solders are in use for years, resulting in an extensive database for the reliability of these materials. However, due to toxicity and legislations, lead-free solders are now being developed. As tin (Sn) is the major component of solders, this chapter presents the detailed results and discussion about the metallurgical overview of Sn, synthesis, and characterization of pulse electrodeposited pure tin finish from different aqueous solution baths. The experiments on pulse electrodeposition such as common tin plating baths employed, their chemical compositions, rationale behind their selection and their characterization by bath conductivity and cathodic current efficiency, microstructures, and tin whisker growth are discussed. Further, the effect of pulse electrodeposition parameters such as current density, additive concentration, pH, duty cycle, frequency, temperature, and stirring speed on microstructural characteristics of the coating obtained from sulfate bath and their effect on grain size distribution have been presented.

Research paper thumbnail of Influence of different acids on the transport of CdSe quantum dots from polymer nanocomposites to food simulants

Environmental science & technology, Jan 13, 2018

We fabricated polymer nanocomposites (PNCs) from low density polyethylene and CdSe quantum dots (... more We fabricated polymer nanocomposites (PNCs) from low density polyethylene and CdSe quantum dots (QDs) and used these materials to explore potential exposure after long term storage in different acidic media that could be encountered in food contact applications. While low level release of QD-associated mass into all the food simulants was observed, exposure to dilute acetic acid resulted in more than double the mass transfer than occurred during exposure to dilute hydrochloric acid at the same pH. Conversely, exposure to citric acid resulted in a suppression of QD release. Permeation experiments and confocal microscopy were used to reveal mechanistic details underlying these mass transfer phenomena. From this work, we conclude that permeation of undissociated acid molecules into the polymer, limited by partitioning of the acids into the hydrophobic polymer, plays a larger role than pH in determining exposure to nanoparticles embedded in plastics. Although caution must be exercised w...

Research paper thumbnail of Microfluidic Immuno-Biochip for Detection of Breast Cancer Biomarkers Using Hierarchical Composite of Porous Graphene and Titanium Dioxide Nanofibers

ACS Applied Materials & Interfaces, 2016

We report on a label-free microfluidic immunosensor with femtomolar sensitivity and high selectiv... more We report on a label-free microfluidic immunosensor with femtomolar sensitivity and high selectivity for early detection of epidermal growth factor receptor 2 (EGFR2 or ErbB2) proteins. This sensor utilizes a uniquely structured immunoelectrode made of porous hierarchical graphene foam (GF) modified with electrospun carbon-doped titanium dioxide nanofibers (nTiO 2) as an electrochemical working electrode. Due to excellent biocompatibility, intrinsic surface defects, high reaction kinetics, and good stability for proteins, anatase nTiO 2 are ideal for electrochemical sensor applications. The three-dimensional and porous features of GF allow nTiO 2 to penetrate and attach to the surface of the GF by physical adsorption. Combining GF with functional nTiO 2 yields high charge transfer resistance, large surface area, and porous access to the sensing surface by the analyte, resulting in new possibilities for the development of electrochemical immunosensors. Here, the enabling of EDC−NHS chemistry covalently immobilized the antibody of ErbB2 (anti-ErbB2) on the GF−nTiO 2 composite. To obtain a compact sensor architecture, the composite working electrode was designed to hang above the gold counter electrode in a microfluidic channel. The sensor underwent differential pulse voltammetry and electrochemical impedance spectroscopy to quantify breast cancer biomarkers. The two methods had high sensitivities of 0.585 μA μM −1 cm −2 and 43.7 kΩ μM −1 cm −2 in a wide concentration range of target ErbB2 antigen from 1 × 10 −15 M (1.0 fM) to 0.1 × 10 −6 M (0.1 μM) and from 1 × 10 −13 M (0.1 pM) to 0.1 × 10 −6 M (0.1 μM), respectively. Utilization of the specific recognition element, i.e., anti-ErbB2, results in high specificity, even in the presence of identical members of the EGFR family of receptor tyrosine kinases, such as ErbB3 and ErbB4. Many promising applications in the field of electrochemical detection of chemical and biological species will derive from the integration of the porous GF−nTiO 2 composite into microfluidic devices.

Research paper thumbnail of Janus silica film with hydrophobic and hydrophilic surfaces grown at an oil–water interface

Journal of Materials Chemistry, 2008

We report a new methyltrimethoxysilane (MTMS) based route to growing a Janus silica film at the o... more We report a new methyltrimethoxysilane (MTMS) based route to growing a Janus silica film at the oil-water interface, which upon drying shows anisotropic wetting by water on its two surfaces. The contact angle of water on the surface grown in contact with the oil-side is found to be 150,butitismuchsmaller,150 , but it is much smaller, 150,butitismuchsmaller,65 , on the side which grew in contact with the aqueous phase. This large difference in the contact angle is found to be primarily because of two reasons: (i) orientation of hydrophobic methyl groups towards the oil-side of the film as confirmed by micro-Raman spectroscopy, and (ii) microstructural differences in the oil and water-side surfaces of the film. The inherently hydrophobic silica cluster network on the oil-side surface also exhibits larger pores that provide an air cushion for the water droplet and engenders a large contact angle. Effects of oil-water interfacial tension on the film growth and on its wetting and microstructural properties are also investigated by addition of cationic and anionic surfactants in the aqueous subphase. Static and dynamic wetting properties of the oil-side surface indicate that these do not change significantly due to variations in either the microstructure or chemical nature of the surface alone, but is a combined effect of both. Interestingly, the Janus films showing asymmetric surface properties can also be grown directly and thus integrated with a variety of porous surfaces like cotton, paper, hydrogel and ceramic substrates by having these surfaces straddle an oil-water interface.

Research paper thumbnail of Patterned growth and differentiation of neural cells on polymer derived carbon substrates with micro/nano structures in vitro

Carbon, 2013

The growth of neuroblastoma (N2a) and Schwann cells has been explored on polymer derived carbon s... more The growth of neuroblastoma (N2a) and Schwann cells has been explored on polymer derived carbon substrates of varying micro and nanoscale geometries: resorcinol-formaldehyde (RF) gel derived carbon films and electrospun nanofibrous ($200 nm diameter) mat and SU-8 (a negative photoresist) derived carbon micro-patterns. MTT assay and complementary lactate dehydrogenase (LDH) assay established cytocompatibility of RF derived carbon films and fibers over a period of 6 days in culture. The role of length scale of surface patterns in eliciting lineage-specific adaptive response along, across and on the interspacing between adjacent micropatterns (i.e., ''on'', ''across'' and ''off'') has been assayed. Textural features were found to affect 3 0 ,5 0-cyclic AMP sodium salt-induced neurite outgrowth, over a wide range of length scales: from 200nm(carbonfibers)to200 nm (carbon fibers) to 200nm(carbonfibers)to60 lm (carbon patterns). Despite their innate randomness, carbon nanofibers promoted preferential differentiation of N2a cells into neuronal lineage, similar to ordered micro-patterns. Our results, for the first time, conclusively demonstrate the potential of RF-gel and SU-8 derived carbon substrates as nerve tissue engineering platforms for guided proliferation and differentiation of neural cells in vitro.

Research paper thumbnail of One-step maskless grayscale lithography for the fabrication of 3-dimensional structures in SU-8

Sensors and Actuators B-Chemical, 2011

We propose a novel and simplified method to fabricate complex 3-dimensional structures in SU-8 ph... more We propose a novel and simplified method to fabricate complex 3-dimensional structures in SU-8 photoresist using maskless grayscale lithography. The proposed method uses a Digital Micro-mirror Device (DMD ®) to modulate the light intensity across a single SU-8 photoresist layer. Top and backside exposure are implemented in the fabrication of original structures such as cantilevers, covered channels with embedded features and arrays of microneedles. The fabrication of similar structures in SU-8 with other techniques often requires complex physical masks or the patterning of several stacked layers. The effects of critical process parameters such as software mask design, exposure and developing conditions on the quality of 3-D structures are discussed. A number of applications using bridges, cantilevers and micromixers fabricated using this methodology are explored.

Research paper thumbnail of Kinetics of spinodal phase separation in unstable thin liquid films

Physical Review E, 2010

We study universality in the kinetics of spinodal phase separation in unstable thin liquid films,... more We study universality in the kinetics of spinodal phase separation in unstable thin liquid films, via simulations of the thin film equation. It is shown that, in addition to morphology and free energy, the number density of local maxima in the film profile can also be used to identify the early, late and intermediate stages of spinodal phase separation. A universal curve between the number density of local maxima and rescaled time describes the kinetics of the early stage in d = 2, 3. The Lifshitz-Slyozov exponent of −1/3 describes the kinetics of the late stage in d = 2 even in the absence of coexisting equilibrium phases.

Research paper thumbnail of Instability of Thin Liquid Films by Density Variations: A New Mechanism that Mimics Spinodal Dewetting

Physical Review Letters, 2002

Based on the linear stability analysis and nonlinear simulations, conditions are established unde... more Based on the linear stability analysis and nonlinear simulations, conditions are established under which instability and dewetting of a thin liquid film can be engendered solely by the density variations (for example, due to confinement, layering, defects, and restructuring) related to changes in the local film thickness. An increase in the density with the increasing film thickness can stabilize a thermodynamically unstable film, and, equally interesting, a decrease in the density with increasing film thickness can render a thermodynamically stable film unstable. Morphological characteristics of this novel density variation induced instability closely resemble the well-known spinodal dewetting.

Research paper thumbnail of Combinatorial Block Copolymer Ordering on Tunable Rough Substrates

Macromolecules, 2012

Morphology control of block copolymer (BCP) thin films through substrate interaction via controll... more Morphology control of block copolymer (BCP) thin films through substrate interaction via controlled roughness parameters is of significant interest for numerous hightech applications ranging from solar cells to high-density storage media. While effects of substrate surface energy (SE) and roughness (R) on BCP morphology have been individually investigated, their synergistic effects have not been explored in any systematic manner. Interestingly, orientation response of BCP to changes in SE can be similar to what can be accomplished with variations in R. Here we present a novel approach for orienting lamellar BCP films of poly(styrene)-blockpoly(methyl methacrylate) (PS−PMMA) on spin-coated xerogel (a dried gel of silica nanoparticle network) substrate with simultaneously tunable surface energy, γ s ∼ 29−53 mJ/m 2 , by UVO exposure and roughness, R rms ∼ 0.5−30 nm, by sol−gel processing steps of regulating the catalyst concentration and sol aging time. As in previous BCP orientation studies on 20 nm diameter monodisperse silica nanoparticle coated surface, we find a similar but broadened oscillatory BCP orientation behavior with film thickness due to the random rather than periodic rough surfaces. We also find that higher random roughness amplitude is not the necessary criteria for obtaining a vertical orientation of BCP lamellae. Rather, a high surface fractal dimension (D f > 2.4) of the rough substrate in conjunction with an optimal substrate surface energy γ s ∼29 mJ/m 2 results in 100% vertically oriented lamellar microdomains. The AFM measured film surface microstructure correlates well with the internal 3D BCP film structure probed by grazing incidence small-angle X-ray scattering (GISAXS) and rotational small-angle neutron scattering (SANS). In contrast to tunable self-assembled monolayer (SAM)-coated substrates, the xerogel films are very durable and retain their chemical properties over period of several months. These results also highlight importantly that BCP orientation control for nanotechnology is possible not only on specially prepared patterned substrates but also on industrially viable sol−gel substrates.

Research paper thumbnail of Pervaporation from a Dense Membrane:  Roles of Permeant−Membrane Interactions, Kelvin Effect, and Membrane Swelling

Langmuir, 2004

Dense polymeric membranes with extremely small pores in the form of free volume are used widely i... more Dense polymeric membranes with extremely small pores in the form of free volume are used widely in the pervaporative separation of liquid mixtures. The membrane permeation of a component followed by its vaporization on the opposite face is governed by the solubility and downstream pressure. We measured the evaporative flux of pure methanol and 2-propanol using dense membranes with different free volumes and different affinities (wettabilities and solubilities) for the permeant. Interestingly, the evaporative flux for different membranes vanished substantially (10-75%) below the equilibrium vapor pressure in the bulk. The discrepancy was larger for a smaller pore size and for more wettable membranes (higher positive spreading coefficients). This observation, which cannot be explained by the existing (mostly solutiondiffusion type) models of pervaporation, suggests an important role for the membrane-permeant interactions in nanopores that can lower the equilibrium vapor pressure. The pore sizes, as estimated from the positron annihilation, ranged from 0.2 to 0.6 nm for the dry membranes. Solubilities of methanol in different composite membranes were estimated from the Flory-Huggins theory. The interaction parameter was obtained from the surface properties measured by the contact angle goniometry in conjunction with the acid-base theory of polar surface interactions. For the membranes examined, the increase in the "wet" pore volume due to membrane swelling correlates almost linearly with the solubility of methanol in these membranes. Indeed, the observations are found to be consistent with the lowering of the equilibrium vapor pressure on the basis of the Kelvin equation. Thus, a higher solubility or selectivity of a membrane also implies stronger permeant-membrane interactions and a greater retention of the permeant by the membrane, thus decreasing its evaporative flux. This observation has important implications for the interpretation of existing experiments and in the separation of liquid mixtures by pervaporation.

Research paper thumbnail of Instability of the interface between thin fluid films subjected to electric fields

Journal of Colloid and Interface Science, 2004

The effect of an externally applied electric field on the stability of the interface between two ... more The effect of an externally applied electric field on the stability of the interface between two thin leaky dielectric fluid films of thickness ratio β and viscosity ratio µ r is analyzed using a linear stability analysis in the long-wave limit. A systematic asymptotic expansion is employed in this limit to derive the coupled nonlinear differential equations describing the evolution of the position of the interface between the fluids and the interfacial free charge distribution. The linearized stability of these equations is determined and the effect of the ratio of the conductivities, dielectric constants, thicknesses, and viscosities on the wavenumber of the fastest growing mode, k max , and the growth rate of the most unstable mode, s max , is examined in detail. Specific configurations considered in previous studies, such as a perfect dielectric-air interface, leaky dielectric-air interface, etc., emerge as limiting cases from the general formulation developed in this paper. Our results show that the viscosity ratio, µ r , does not have any significant effect on k max for the interface between perfect and leaky dielectric fluids. In marked contrast, however, µ r is shown to have a significant effect on the interface between two leaky dielectrics. Increasing µ r from 0.1 to 10 could decrease k max up to a factor of 5. In general, our results show that the presence of nonzero conductivity in either one or both of the fluids has a profound influence on the length-scale characteristic of the linear instability: a reduction even by a factor of 1/50 in the length scale can be effected when compared to the interface between two perfect dielectrics. These predictions could have important implications in pattern formation applications in thin fluid films that employ electric fields. The variation of k max and s max on the thickness ratio, β, indicates in general that k max ∝ β −α , and s max ∝ β −θ , where the exponents α and θ (both > 0) are found to depend only on the ratio of conductivities, and are largely independent of other system parameters.

Research paper thumbnail of Confinement-induced instability and adhesive failure between dissimilar thin elastic films

The European Physical Journal E, 2006

When two thin soft elastomeric films are separated from each other, an elastic instability develo... more When two thin soft elastomeric films are separated from each other, an elastic instability develops at the interface. Although similar instability develops for the case of a soft film separating from a rigid adherent, there are important differences in the two cases. For the single-film case, the wavelength of instability is independent of any material properties of the system, and it scales only with thickness of the film. For the two-film case, a cooperative instability mode develops, which is a non-linear function of the thicknesses and the elastic moduli of both films. We investigate the development of such instability by energy minimization procedures. Understanding the nature of this instability is important, as it affects the adhesive compliance of the system and thus the energy release rate in the debonding of soft interfaces.

Research paper thumbnail of PZT–PDMS composite for active damping of vibrations

Composites Science and Technology, 2013

A Lead Zirconate-Titanate (PZT)/poly-dimethylsiloxane (PDMS) based flexible composite is synthesi... more A Lead Zirconate-Titanate (PZT)/poly-dimethylsiloxane (PDMS) based flexible composite is synthesized and investigated for its potential in significantly enhancing the vibration damping capability along with its tunable properties. Rheologically and functionally different PZT/PDMS composites are prepared by dispersing different volume fractions of piezoelectric soft/hard PZT and Fe particles in a cross-linked PDMS matrix. It is observed that passive damping increases with increase in the soft PZT volume fraction from 0 to 0.32. This effect becomes more prominent after poling the composite at optimum conditions. The loss factor depends on the viscoelastic properties of the PDMS, homo and hetero-particle connectivity in the composite, and polarization and localization of the PZT particles in composite. Rheological analysis of the composite shows that the material loss factor (tan d) increases linearly from $0.3 to 0.75 along with a broadening of the peak when the PZT volume fraction is increased from 0 to 0.32. Maximum structural damping (g) is obtained at 0.32 (V/V) of the soft-PZT as measured by the Oberst beam technique. This effect becomes more pronounced after a poling treatment. The X-ray diffraction results indicate that the dispersed PZT particles in PDMS matrix have the lattice parameters of a = 5.84 Å, c = 14.41 Å and (0 0 1) orientation. Further, after poling treatment, the dielectric constant and the piezoelectric coefficient (d 33) for soft (submicron) PZT filler particles in PDMS matrix tend to be higher than those for hard PZT. The soft PZT/PDMS composite shows better performance as a damper than the hard, PZT composite.

Research paper thumbnail of Fabrication and electrical conductivity of suspended carbon nanofiber arrays

Carbon, 2011

We demonstrate a simple, efficient and novel self-assembly based method to fabricate arrays of su... more We demonstrate a simple, efficient and novel self-assembly based method to fabricate arrays of suspended polymeric nanofibers of polyacrylonitrile and SU-8 negative photoresist by electrospinning on micro-fabricated posts of resorcinol-formaldehyde (RF) gel. The suspended electrospun nanofibers together with the RF gel posts were subsequently pyrolyzed in an inert atmosphere to yield large area monolithic structures of suspended glassy carbon nanofibers (CNF) integrated on RF gel derived carbon posts. The electrospun nanofibers self-assemble to connect the posts owing to a stronger electric field on their tips, obviating the need for positioning and integration of carbon nanowires with the underlying microstructures and paving the way for fabricating novel carbon based micro and nanoscale devices. The fabrication technique also allowed measurements of electrical conductivity of a single suspended CNF between carbon electrodes using I-V characteristics and comparison of the carbon nanowire conductivities for the CNF derived from different polymer precursors.

Research paper thumbnail of Resorcinol-formaldehyde based carbon nanospheres by electrospraying

Bulletin of Materials Science, 2009

Carbon nanospheres were synthesized using sol-gel processing of organic and aqueous resorcinol fo... more Carbon nanospheres were synthesized using sol-gel processing of organic and aqueous resorcinol formaldehyde (RF) sols combined with electrospraying technique. RF sol was electrosprayed to form nanodroplets which were collected on a Si wafer. After oven drying at 60°C for 12 h, RF nano-droplets were pyrolyzed at 900°C in an inert atmosphere to yield the carbon nanospheres. This study reports the optimization of various process parameters including needle diameter, applied electric potential and liquid flow rate in order to get spherical, mono-disperse particles. For the organic RF sol, the optimized parameters, needle diameter 0⋅241 mm, electric potential, 1⋅5 kV/cm and a flow rate of 0⋅8 ml/h, enabled the synthesis of nearly monodispersed carbon nano-spheres with diameter of 30⋅2 ± 7⋅1 nm. With the same conditions, aqueous RF sol produced irregularly shaped nanoparticles with a smaller mean diameter and much higher variance (17⋅4 ± 8⋅0 nm). The surface properties were significantly influenced by the surface morphologies as demonstrated by the water contact angle (WCA) studies. The surface covered with the RF derived carbon nano-spheres was extremely hydrophilic (WCA 10⋅1°) as compared to a much weaker hydrophilicity of the RF derived carbon films (WCA 83⋅3°). The hydrophilic carbon nanospheres reported here may have potential applications as adsorbents and in controlled drug delivery, biosensors and carbon-based microelectromechanical systems (C-MEMS) including bio-MEMS.

Research paper thumbnail of Electric-Field-Controlled Surface Instabilities in Soft Elastic Films

Research paper thumbnail of Electric Field Induced Morphological Transitions in Polyelectrolyte Multilayers

ACS Applied Materials & Interfaces, 2013

In this work, the morphological transitions in weak polyelectrolyte (PE) multilayers (PEMs) assem... more In this work, the morphological transitions in weak polyelectrolyte (PE) multilayers (PEMs) assembled from linear poly(ethylene imine) (LPEI) and poly(acrylic acid) (PAA) upon application of an electric field were studied. Exposure to an electric field results in the creation of a porous structure, which can be ascribed to local changes in pH from the hydrolysis of water and subsequent structural rearrangements of the weak PE constituents. Depending on the duration of application of the field, the porous transition gradually develops into a range of structures and pore sizes. It was discovered that the morphological transition of the LbL films starts at the multilayer-electrode interface and propagates through the film. First an asymmetrical structure forms, consisting of microscaled pores near the electrode and nanoscaled pores near the surface in contact with the electrolyte solution. At longer application of the field the porous structures become microscaled throughout. The results revealed in this study not only demonstrate experimental feasibility for controlling variation in pore size and porosity of multilayer films but also deepens the understanding of the mechanism of the porous transition. In addition, electrical potential is used to release small molecules from the PEMs.

Research paper thumbnail of Spontaneous surface roughening induced by surface interactions between two compressible elastic films

Physical Review E, 2003

The surfaces of soft thin elastic films bonded to two rigid substrates become spontaneously rough... more The surfaces of soft thin elastic films bonded to two rigid substrates become spontaneously rough due to the attractive intersurface interactions when the intersurface distance declines sufficiently to produce a critical force. The effects of compressibility on the conditions for surface roughening and its length scale are investigated. For highly compressible films (less than 0.25), surface roughening is not possible. The critical force required for the onset of instability and its wave number both decline with increased compressibility. The wavelength of the instability is influenced much more by the properties of the more compliant film ͓compliance equals (1Ϫ2)h/2(1Ϫ)]. There is an abrupt change in the wavelength as the compliances of the two films become nearly equal.

Research paper thumbnail of A unified model for flux prediction during batch cell ultrafiltration

Journal of Membrane Science, 1996

An analysis of the flux decline encountered during ultrafiltration (UF) in a batch cell is presen... more An analysis of the flux decline encountered during ultrafiltration (UF) in a batch cell is presented by including the combined influence of the osmotic pressure and the gel layer. A predictive model for the flux decline in unstirred and stirred batch cell UF processes is developed by unifying the osmotic pressure and gel layer models. UF experiments were performed in a batch cell with polymeric solutes (PEG, dextran and PVA) and a protein (BSA), ranging widely in molecular weights and physico-cbemical properties, under various operating conditions (pressure, solution pH, and stirrer speed). The present unified model predictions match closely with the experimental flux behaviour for all cases, while individual osmotic pressure and gel layer models are found to be inadequate.

Research paper thumbnail of Generalized integral and similarity solutions of the concentration profiles for osmotic pressure controlled ultrafiltration

Journal of Membrane Science, 1997

A mathematical model describing the concentration polarization phenomenon during osmotic pressure... more A mathematical model describing the concentration polarization phenomenon during osmotic pressure controlled ultrafiltration is presented. Generalized integral and similarity solutions of the concentration profile in the mass transfer boundary layer are obtained. The parameters governing the shape of the concentration profile vary with time in case of a batch cell and axial distance in a cross flow cell. The model is used to predict the permeate flux and the solute rejection simultaneously during unstirred batch cell and cross flow UF. The results obtained by integral and similarity solutions are compared with the results of detailed numerical solution of the governing equations for both the systems. The predictions of permeate flux from the generalized integral method are also compared with some approximate solutions in order to assess the limitations of the various approximations. UF experiments were performed with Dextran (T-20) in cross flow system and with PEG-6000 and Dextran (T-40 and T-20) in unstirred batch cell. Predictions of the model are in remarkably good agreement with detailed simulation as well as experimental results. Moreover, the integral solution can also account for the variation of diffusivity with solute concentration. Comparisons show that (a) while the generalized integral method is much simpler than the detailed numerical solutions, it is much more general and accurate than other analytical and semi-analytical solutions, and, (b) the proposed solution predicts the osmotic pressure controlled flux decline accurately over a wide range of operating conditions. The expression for gel layer governed UF (constant membrane surface concentration) is found to be an asymptotic case of the present solution.

Research paper thumbnail of Pulse Electroplating of Ultrafine Grained Tin Coating

Electroplating of Nanostructures, 2015

In the electronic packaging industries, soldering materials are essential in joining various micr... more In the electronic packaging industries, soldering materials are essential in joining various microelectronic networks. Solders assure the reliability of joints and protect the microelectronic packaging devices. They provide electrical, thermal, and mechanical continuity among various interconnections in an electronic device. The service performance of all the electronic appliances depends on high strength and durable soldering materials. Lead-containing solders are in use for years, resulting in an extensive database for the reliability of these materials. However, due to toxicity and legislations, lead-free solders are now being developed. As tin (Sn) is the major component of solders, this chapter presents the detailed results and discussion about the metallurgical overview of Sn, synthesis, and characterization of pulse electrodeposited pure tin finish from different aqueous solution baths. The experiments on pulse electrodeposition such as common tin plating baths employed, their chemical compositions, rationale behind their selection and their characterization by bath conductivity and cathodic current efficiency, microstructures, and tin whisker growth are discussed. Further, the effect of pulse electrodeposition parameters such as current density, additive concentration, pH, duty cycle, frequency, temperature, and stirring speed on microstructural characteristics of the coating obtained from sulfate bath and their effect on grain size distribution have been presented.

Research paper thumbnail of Influence of different acids on the transport of CdSe quantum dots from polymer nanocomposites to food simulants

Environmental science & technology, Jan 13, 2018

We fabricated polymer nanocomposites (PNCs) from low density polyethylene and CdSe quantum dots (... more We fabricated polymer nanocomposites (PNCs) from low density polyethylene and CdSe quantum dots (QDs) and used these materials to explore potential exposure after long term storage in different acidic media that could be encountered in food contact applications. While low level release of QD-associated mass into all the food simulants was observed, exposure to dilute acetic acid resulted in more than double the mass transfer than occurred during exposure to dilute hydrochloric acid at the same pH. Conversely, exposure to citric acid resulted in a suppression of QD release. Permeation experiments and confocal microscopy were used to reveal mechanistic details underlying these mass transfer phenomena. From this work, we conclude that permeation of undissociated acid molecules into the polymer, limited by partitioning of the acids into the hydrophobic polymer, plays a larger role than pH in determining exposure to nanoparticles embedded in plastics. Although caution must be exercised w...

Research paper thumbnail of Microfluidic Immuno-Biochip for Detection of Breast Cancer Biomarkers Using Hierarchical Composite of Porous Graphene and Titanium Dioxide Nanofibers

ACS Applied Materials & Interfaces, 2016

We report on a label-free microfluidic immunosensor with femtomolar sensitivity and high selectiv... more We report on a label-free microfluidic immunosensor with femtomolar sensitivity and high selectivity for early detection of epidermal growth factor receptor 2 (EGFR2 or ErbB2) proteins. This sensor utilizes a uniquely structured immunoelectrode made of porous hierarchical graphene foam (GF) modified with electrospun carbon-doped titanium dioxide nanofibers (nTiO 2) as an electrochemical working electrode. Due to excellent biocompatibility, intrinsic surface defects, high reaction kinetics, and good stability for proteins, anatase nTiO 2 are ideal for electrochemical sensor applications. The three-dimensional and porous features of GF allow nTiO 2 to penetrate and attach to the surface of the GF by physical adsorption. Combining GF with functional nTiO 2 yields high charge transfer resistance, large surface area, and porous access to the sensing surface by the analyte, resulting in new possibilities for the development of electrochemical immunosensors. Here, the enabling of EDC−NHS chemistry covalently immobilized the antibody of ErbB2 (anti-ErbB2) on the GF−nTiO 2 composite. To obtain a compact sensor architecture, the composite working electrode was designed to hang above the gold counter electrode in a microfluidic channel. The sensor underwent differential pulse voltammetry and electrochemical impedance spectroscopy to quantify breast cancer biomarkers. The two methods had high sensitivities of 0.585 μA μM −1 cm −2 and 43.7 kΩ μM −1 cm −2 in a wide concentration range of target ErbB2 antigen from 1 × 10 −15 M (1.0 fM) to 0.1 × 10 −6 M (0.1 μM) and from 1 × 10 −13 M (0.1 pM) to 0.1 × 10 −6 M (0.1 μM), respectively. Utilization of the specific recognition element, i.e., anti-ErbB2, results in high specificity, even in the presence of identical members of the EGFR family of receptor tyrosine kinases, such as ErbB3 and ErbB4. Many promising applications in the field of electrochemical detection of chemical and biological species will derive from the integration of the porous GF−nTiO 2 composite into microfluidic devices.

Research paper thumbnail of Janus silica film with hydrophobic and hydrophilic surfaces grown at an oil–water interface

Journal of Materials Chemistry, 2008

We report a new methyltrimethoxysilane (MTMS) based route to growing a Janus silica film at the o... more We report a new methyltrimethoxysilane (MTMS) based route to growing a Janus silica film at the oil-water interface, which upon drying shows anisotropic wetting by water on its two surfaces. The contact angle of water on the surface grown in contact with the oil-side is found to be 150,butitismuchsmaller,150 , but it is much smaller, 150,butitismuchsmaller,65 , on the side which grew in contact with the aqueous phase. This large difference in the contact angle is found to be primarily because of two reasons: (i) orientation of hydrophobic methyl groups towards the oil-side of the film as confirmed by micro-Raman spectroscopy, and (ii) microstructural differences in the oil and water-side surfaces of the film. The inherently hydrophobic silica cluster network on the oil-side surface also exhibits larger pores that provide an air cushion for the water droplet and engenders a large contact angle. Effects of oil-water interfacial tension on the film growth and on its wetting and microstructural properties are also investigated by addition of cationic and anionic surfactants in the aqueous subphase. Static and dynamic wetting properties of the oil-side surface indicate that these do not change significantly due to variations in either the microstructure or chemical nature of the surface alone, but is a combined effect of both. Interestingly, the Janus films showing asymmetric surface properties can also be grown directly and thus integrated with a variety of porous surfaces like cotton, paper, hydrogel and ceramic substrates by having these surfaces straddle an oil-water interface.

Research paper thumbnail of Patterned growth and differentiation of neural cells on polymer derived carbon substrates with micro/nano structures in vitro

Carbon, 2013

The growth of neuroblastoma (N2a) and Schwann cells has been explored on polymer derived carbon s... more The growth of neuroblastoma (N2a) and Schwann cells has been explored on polymer derived carbon substrates of varying micro and nanoscale geometries: resorcinol-formaldehyde (RF) gel derived carbon films and electrospun nanofibrous ($200 nm diameter) mat and SU-8 (a negative photoresist) derived carbon micro-patterns. MTT assay and complementary lactate dehydrogenase (LDH) assay established cytocompatibility of RF derived carbon films and fibers over a period of 6 days in culture. The role of length scale of surface patterns in eliciting lineage-specific adaptive response along, across and on the interspacing between adjacent micropatterns (i.e., ''on'', ''across'' and ''off'') has been assayed. Textural features were found to affect 3 0 ,5 0-cyclic AMP sodium salt-induced neurite outgrowth, over a wide range of length scales: from 200nm(carbonfibers)to200 nm (carbon fibers) to 200nm(carbonfibers)to60 lm (carbon patterns). Despite their innate randomness, carbon nanofibers promoted preferential differentiation of N2a cells into neuronal lineage, similar to ordered micro-patterns. Our results, for the first time, conclusively demonstrate the potential of RF-gel and SU-8 derived carbon substrates as nerve tissue engineering platforms for guided proliferation and differentiation of neural cells in vitro.

Research paper thumbnail of One-step maskless grayscale lithography for the fabrication of 3-dimensional structures in SU-8

Sensors and Actuators B-Chemical, 2011

We propose a novel and simplified method to fabricate complex 3-dimensional structures in SU-8 ph... more We propose a novel and simplified method to fabricate complex 3-dimensional structures in SU-8 photoresist using maskless grayscale lithography. The proposed method uses a Digital Micro-mirror Device (DMD ®) to modulate the light intensity across a single SU-8 photoresist layer. Top and backside exposure are implemented in the fabrication of original structures such as cantilevers, covered channels with embedded features and arrays of microneedles. The fabrication of similar structures in SU-8 with other techniques often requires complex physical masks or the patterning of several stacked layers. The effects of critical process parameters such as software mask design, exposure and developing conditions on the quality of 3-D structures are discussed. A number of applications using bridges, cantilevers and micromixers fabricated using this methodology are explored.

Research paper thumbnail of Kinetics of spinodal phase separation in unstable thin liquid films

Physical Review E, 2010

We study universality in the kinetics of spinodal phase separation in unstable thin liquid films,... more We study universality in the kinetics of spinodal phase separation in unstable thin liquid films, via simulations of the thin film equation. It is shown that, in addition to morphology and free energy, the number density of local maxima in the film profile can also be used to identify the early, late and intermediate stages of spinodal phase separation. A universal curve between the number density of local maxima and rescaled time describes the kinetics of the early stage in d = 2, 3. The Lifshitz-Slyozov exponent of −1/3 describes the kinetics of the late stage in d = 2 even in the absence of coexisting equilibrium phases.

Research paper thumbnail of Instability of Thin Liquid Films by Density Variations: A New Mechanism that Mimics Spinodal Dewetting

Physical Review Letters, 2002

Based on the linear stability analysis and nonlinear simulations, conditions are established unde... more Based on the linear stability analysis and nonlinear simulations, conditions are established under which instability and dewetting of a thin liquid film can be engendered solely by the density variations (for example, due to confinement, layering, defects, and restructuring) related to changes in the local film thickness. An increase in the density with the increasing film thickness can stabilize a thermodynamically unstable film, and, equally interesting, a decrease in the density with increasing film thickness can render a thermodynamically stable film unstable. Morphological characteristics of this novel density variation induced instability closely resemble the well-known spinodal dewetting.

Research paper thumbnail of Combinatorial Block Copolymer Ordering on Tunable Rough Substrates

Macromolecules, 2012

Morphology control of block copolymer (BCP) thin films through substrate interaction via controll... more Morphology control of block copolymer (BCP) thin films through substrate interaction via controlled roughness parameters is of significant interest for numerous hightech applications ranging from solar cells to high-density storage media. While effects of substrate surface energy (SE) and roughness (R) on BCP morphology have been individually investigated, their synergistic effects have not been explored in any systematic manner. Interestingly, orientation response of BCP to changes in SE can be similar to what can be accomplished with variations in R. Here we present a novel approach for orienting lamellar BCP films of poly(styrene)-blockpoly(methyl methacrylate) (PS−PMMA) on spin-coated xerogel (a dried gel of silica nanoparticle network) substrate with simultaneously tunable surface energy, γ s ∼ 29−53 mJ/m 2 , by UVO exposure and roughness, R rms ∼ 0.5−30 nm, by sol−gel processing steps of regulating the catalyst concentration and sol aging time. As in previous BCP orientation studies on 20 nm diameter monodisperse silica nanoparticle coated surface, we find a similar but broadened oscillatory BCP orientation behavior with film thickness due to the random rather than periodic rough surfaces. We also find that higher random roughness amplitude is not the necessary criteria for obtaining a vertical orientation of BCP lamellae. Rather, a high surface fractal dimension (D f > 2.4) of the rough substrate in conjunction with an optimal substrate surface energy γ s ∼29 mJ/m 2 results in 100% vertically oriented lamellar microdomains. The AFM measured film surface microstructure correlates well with the internal 3D BCP film structure probed by grazing incidence small-angle X-ray scattering (GISAXS) and rotational small-angle neutron scattering (SANS). In contrast to tunable self-assembled monolayer (SAM)-coated substrates, the xerogel films are very durable and retain their chemical properties over period of several months. These results also highlight importantly that BCP orientation control for nanotechnology is possible not only on specially prepared patterned substrates but also on industrially viable sol−gel substrates.

Research paper thumbnail of Pervaporation from a Dense Membrane:  Roles of Permeant−Membrane Interactions, Kelvin Effect, and Membrane Swelling

Langmuir, 2004

Dense polymeric membranes with extremely small pores in the form of free volume are used widely i... more Dense polymeric membranes with extremely small pores in the form of free volume are used widely in the pervaporative separation of liquid mixtures. The membrane permeation of a component followed by its vaporization on the opposite face is governed by the solubility and downstream pressure. We measured the evaporative flux of pure methanol and 2-propanol using dense membranes with different free volumes and different affinities (wettabilities and solubilities) for the permeant. Interestingly, the evaporative flux for different membranes vanished substantially (10-75%) below the equilibrium vapor pressure in the bulk. The discrepancy was larger for a smaller pore size and for more wettable membranes (higher positive spreading coefficients). This observation, which cannot be explained by the existing (mostly solutiondiffusion type) models of pervaporation, suggests an important role for the membrane-permeant interactions in nanopores that can lower the equilibrium vapor pressure. The pore sizes, as estimated from the positron annihilation, ranged from 0.2 to 0.6 nm for the dry membranes. Solubilities of methanol in different composite membranes were estimated from the Flory-Huggins theory. The interaction parameter was obtained from the surface properties measured by the contact angle goniometry in conjunction with the acid-base theory of polar surface interactions. For the membranes examined, the increase in the "wet" pore volume due to membrane swelling correlates almost linearly with the solubility of methanol in these membranes. Indeed, the observations are found to be consistent with the lowering of the equilibrium vapor pressure on the basis of the Kelvin equation. Thus, a higher solubility or selectivity of a membrane also implies stronger permeant-membrane interactions and a greater retention of the permeant by the membrane, thus decreasing its evaporative flux. This observation has important implications for the interpretation of existing experiments and in the separation of liquid mixtures by pervaporation.

Research paper thumbnail of Instability of the interface between thin fluid films subjected to electric fields

Journal of Colloid and Interface Science, 2004

The effect of an externally applied electric field on the stability of the interface between two ... more The effect of an externally applied electric field on the stability of the interface between two thin leaky dielectric fluid films of thickness ratio β and viscosity ratio µ r is analyzed using a linear stability analysis in the long-wave limit. A systematic asymptotic expansion is employed in this limit to derive the coupled nonlinear differential equations describing the evolution of the position of the interface between the fluids and the interfacial free charge distribution. The linearized stability of these equations is determined and the effect of the ratio of the conductivities, dielectric constants, thicknesses, and viscosities on the wavenumber of the fastest growing mode, k max , and the growth rate of the most unstable mode, s max , is examined in detail. Specific configurations considered in previous studies, such as a perfect dielectric-air interface, leaky dielectric-air interface, etc., emerge as limiting cases from the general formulation developed in this paper. Our results show that the viscosity ratio, µ r , does not have any significant effect on k max for the interface between perfect and leaky dielectric fluids. In marked contrast, however, µ r is shown to have a significant effect on the interface between two leaky dielectrics. Increasing µ r from 0.1 to 10 could decrease k max up to a factor of 5. In general, our results show that the presence of nonzero conductivity in either one or both of the fluids has a profound influence on the length-scale characteristic of the linear instability: a reduction even by a factor of 1/50 in the length scale can be effected when compared to the interface between two perfect dielectrics. These predictions could have important implications in pattern formation applications in thin fluid films that employ electric fields. The variation of k max and s max on the thickness ratio, β, indicates in general that k max ∝ β −α , and s max ∝ β −θ , where the exponents α and θ (both > 0) are found to depend only on the ratio of conductivities, and are largely independent of other system parameters.

Research paper thumbnail of Confinement-induced instability and adhesive failure between dissimilar thin elastic films

The European Physical Journal E, 2006

When two thin soft elastomeric films are separated from each other, an elastic instability develo... more When two thin soft elastomeric films are separated from each other, an elastic instability develops at the interface. Although similar instability develops for the case of a soft film separating from a rigid adherent, there are important differences in the two cases. For the single-film case, the wavelength of instability is independent of any material properties of the system, and it scales only with thickness of the film. For the two-film case, a cooperative instability mode develops, which is a non-linear function of the thicknesses and the elastic moduli of both films. We investigate the development of such instability by energy minimization procedures. Understanding the nature of this instability is important, as it affects the adhesive compliance of the system and thus the energy release rate in the debonding of soft interfaces.

Research paper thumbnail of PZT–PDMS composite for active damping of vibrations

Composites Science and Technology, 2013

A Lead Zirconate-Titanate (PZT)/poly-dimethylsiloxane (PDMS) based flexible composite is synthesi... more A Lead Zirconate-Titanate (PZT)/poly-dimethylsiloxane (PDMS) based flexible composite is synthesized and investigated for its potential in significantly enhancing the vibration damping capability along with its tunable properties. Rheologically and functionally different PZT/PDMS composites are prepared by dispersing different volume fractions of piezoelectric soft/hard PZT and Fe particles in a cross-linked PDMS matrix. It is observed that passive damping increases with increase in the soft PZT volume fraction from 0 to 0.32. This effect becomes more prominent after poling the composite at optimum conditions. The loss factor depends on the viscoelastic properties of the PDMS, homo and hetero-particle connectivity in the composite, and polarization and localization of the PZT particles in composite. Rheological analysis of the composite shows that the material loss factor (tan d) increases linearly from $0.3 to 0.75 along with a broadening of the peak when the PZT volume fraction is increased from 0 to 0.32. Maximum structural damping (g) is obtained at 0.32 (V/V) of the soft-PZT as measured by the Oberst beam technique. This effect becomes more pronounced after a poling treatment. The X-ray diffraction results indicate that the dispersed PZT particles in PDMS matrix have the lattice parameters of a = 5.84 Å, c = 14.41 Å and (0 0 1) orientation. Further, after poling treatment, the dielectric constant and the piezoelectric coefficient (d 33) for soft (submicron) PZT filler particles in PDMS matrix tend to be higher than those for hard PZT. The soft PZT/PDMS composite shows better performance as a damper than the hard, PZT composite.

Research paper thumbnail of Fabrication and electrical conductivity of suspended carbon nanofiber arrays

Carbon, 2011

We demonstrate a simple, efficient and novel self-assembly based method to fabricate arrays of su... more We demonstrate a simple, efficient and novel self-assembly based method to fabricate arrays of suspended polymeric nanofibers of polyacrylonitrile and SU-8 negative photoresist by electrospinning on micro-fabricated posts of resorcinol-formaldehyde (RF) gel. The suspended electrospun nanofibers together with the RF gel posts were subsequently pyrolyzed in an inert atmosphere to yield large area monolithic structures of suspended glassy carbon nanofibers (CNF) integrated on RF gel derived carbon posts. The electrospun nanofibers self-assemble to connect the posts owing to a stronger electric field on their tips, obviating the need for positioning and integration of carbon nanowires with the underlying microstructures and paving the way for fabricating novel carbon based micro and nanoscale devices. The fabrication technique also allowed measurements of electrical conductivity of a single suspended CNF between carbon electrodes using I-V characteristics and comparison of the carbon nanowire conductivities for the CNF derived from different polymer precursors.

Research paper thumbnail of Resorcinol-formaldehyde based carbon nanospheres by electrospraying

Bulletin of Materials Science, 2009

Carbon nanospheres were synthesized using sol-gel processing of organic and aqueous resorcinol fo... more Carbon nanospheres were synthesized using sol-gel processing of organic and aqueous resorcinol formaldehyde (RF) sols combined with electrospraying technique. RF sol was electrosprayed to form nanodroplets which were collected on a Si wafer. After oven drying at 60°C for 12 h, RF nano-droplets were pyrolyzed at 900°C in an inert atmosphere to yield the carbon nanospheres. This study reports the optimization of various process parameters including needle diameter, applied electric potential and liquid flow rate in order to get spherical, mono-disperse particles. For the organic RF sol, the optimized parameters, needle diameter 0⋅241 mm, electric potential, 1⋅5 kV/cm and a flow rate of 0⋅8 ml/h, enabled the synthesis of nearly monodispersed carbon nano-spheres with diameter of 30⋅2 ± 7⋅1 nm. With the same conditions, aqueous RF sol produced irregularly shaped nanoparticles with a smaller mean diameter and much higher variance (17⋅4 ± 8⋅0 nm). The surface properties were significantly influenced by the surface morphologies as demonstrated by the water contact angle (WCA) studies. The surface covered with the RF derived carbon nano-spheres was extremely hydrophilic (WCA 10⋅1°) as compared to a much weaker hydrophilicity of the RF derived carbon films (WCA 83⋅3°). The hydrophilic carbon nanospheres reported here may have potential applications as adsorbents and in controlled drug delivery, biosensors and carbon-based microelectromechanical systems (C-MEMS) including bio-MEMS.

Research paper thumbnail of Electric-Field-Controlled Surface Instabilities in Soft Elastic Films

Research paper thumbnail of Electric Field Induced Morphological Transitions in Polyelectrolyte Multilayers

ACS Applied Materials & Interfaces, 2013

In this work, the morphological transitions in weak polyelectrolyte (PE) multilayers (PEMs) assem... more In this work, the morphological transitions in weak polyelectrolyte (PE) multilayers (PEMs) assembled from linear poly(ethylene imine) (LPEI) and poly(acrylic acid) (PAA) upon application of an electric field were studied. Exposure to an electric field results in the creation of a porous structure, which can be ascribed to local changes in pH from the hydrolysis of water and subsequent structural rearrangements of the weak PE constituents. Depending on the duration of application of the field, the porous transition gradually develops into a range of structures and pore sizes. It was discovered that the morphological transition of the LbL films starts at the multilayer-electrode interface and propagates through the film. First an asymmetrical structure forms, consisting of microscaled pores near the electrode and nanoscaled pores near the surface in contact with the electrolyte solution. At longer application of the field the porous structures become microscaled throughout. The results revealed in this study not only demonstrate experimental feasibility for controlling variation in pore size and porosity of multilayer films but also deepens the understanding of the mechanism of the porous transition. In addition, electrical potential is used to release small molecules from the PEMs.

Research paper thumbnail of Spontaneous surface roughening induced by surface interactions between two compressible elastic films

Physical Review E, 2003

The surfaces of soft thin elastic films bonded to two rigid substrates become spontaneously rough... more The surfaces of soft thin elastic films bonded to two rigid substrates become spontaneously rough due to the attractive intersurface interactions when the intersurface distance declines sufficiently to produce a critical force. The effects of compressibility on the conditions for surface roughening and its length scale are investigated. For highly compressible films (less than 0.25), surface roughening is not possible. The critical force required for the onset of instability and its wave number both decline with increased compressibility. The wavelength of the instability is influenced much more by the properties of the more compliant film ͓compliance equals (1Ϫ2)h/2(1Ϫ)]. There is an abrupt change in the wavelength as the compliances of the two films become nearly equal.