Thermal analysis of microwave assisted bonding of poly(methyl methacrylate) substrates in microfluidic devices
Introduction
Microfluidic devices are finding numerous applications in areas such as analytical chemistry, microbiology, drug development and chemical synthesis [1], [2], [3], [4], [5], [6], [7]. These devices have many advantages such as compact size, disposability, increased functionality and reliability, reduced analysis time and accuracy. In microfluidic devices, glass substrates have been used as the preferred material of choice due to its low cost. However, fabrication process for glass microdevice is very challenging especially for complex device. Moreover, optical characteristics of glass substrates are not suitable for many lab-on-a-chip devices [8]. In recent years, polymers are found to effectively replace glass as substrate materials in microfluidic device fabrication. Polymers possess wide range of physical and chemical properties suitable for chemical and biological analysis, offer low manufacturing cost, provide good optical clarity etc. Different polymers such as polydimethylsiloxane (PDMS), polymethyl methacrylate (PMMA), cyclic olefin copolymer (COC), polycarbonates (PC) are widely used for microfluidic device fabrication [9], [10].
In microfabrication process the polymer substrates, with or without patterned micro feature, need to be bonded to effectively make a functional microchannel. The bonding process is a very challenging issue as it should be carried out without changing or destroying the integrity of the patterned microstructure. Bonding techniques such as adhesive bonding, thermal bonding, solvent bonding and resin-gas injection bonding have been reported in the literatures [11], [12], [13], [14]. However, these techniques either cause geometric deformation of the substrate or induce a chemical reaction that affects the patterned micro channel. Therefore, it is necessary to develop an alternative technique to bond polymer based microfluidic devices.
Recently, the use of microwave technology has been reported to achieve bonding, and it has been found that this technique is especially very effective for bonding PMMA substrates in microfluidic devices without causing any change or destruction to the patterned microstructures [15], [16], [17], [18], [19]. In microwave assisted bonding, a very thin layer of dielectric material is placed between two layers of PMMA as shown in Fig. 1, and the ability of material selective heat generation resulted from microwave radiation is used for bonding purpose. Since PMMA layers are transparent to microwave radiation, the temperature rise in PMMA is not as high as in the sandwiched dielectric layer. This high temperature at the interface results in a localized melting of the PMMA substrates which is the main reason for irreversible bonding of PMMA layers.
The microwave bonding of PMMA microfluidic devices using highly dielectric materials such as ethanol, methanol and isopropyl alcohol as a thin sacrificial layer were examined experimentally [17]. Recently, polymers such as poly-aniline and poly-thiophene have evolved as a new class of sacrificial materials for PMMA bonding. However, the amount of sacrificial material required for effective bonding of the PMMA substrate has been a major issue and requires fundamental understanding for perfect bonding [16], [18]. For instance, bonding would be very weak, if the thickness of the sacrificial layer is less than optimum. On the other hand, there will be significant distortion of the channel feature if the thickness of the interfacial sacrifice layer is very thick. Also microwave exposure time and intensity are very crucial for successful bonding process. Yussuf et al. [16] experimented with poly-aniline to bond PMMA substrates under microwave power and found to achieve strong bonding at the interface that could withstand a pressure up to 1.18 MPa. Lately, Holmes et al. [19] experimented with varying widths and depths of the poly-aniline layer to bond PMMA substrates for defect free seals.
Although there are numerous experimental studies on the use of sacrificial layer for bonding PMMA substrates using microwave radiation, no theoretical study has been reported to understand the fundamental mechanism of PMMA–PMMA bonding. A detail thermal analysis can reveal the local temperature distribution within materials as a function of time, which can explain the microwave assisted bonding process. Moreover, a theoretical analysis can provide the desired correlation between the characteristics of electromagnetic wave and geometric, dielectric, and thermo-physical properties of materials subjected to microwave heating.
The rest of the paper is organized as follows. First the theory and governing equations for electromagnetic heating are provided followed by underlying assumptions for this analytic study. Then an analysis to find the electromagnetic heat generation is presented for each layer. Next, the temperature distribution within each layer is obtained from the energy equation using linear decomposition and separation of variables techniques. This is followed by a discussion on polymer bonding by analyzing the temperature distribution in PMMA and poly-aniline materials at various times for different thicknesses of poly-aniline and PMMA. Finally, we present our conclusions on this analytic work.
Section snippets
Theory
Microwave heating is generally very effective for dielectric materials which contains either permanent or induced dipoles. When electromagnetic radiation with alternating electric field is applied across the dielectric material, the positive and negative charges of the dipole get aligned towards the electric field and result in polarization of the medium. Due to the alternating nature of electric field, dipoles rotate as they try to align with the electric field of the incident electromagnetic
Electromagnetic power
Maxwell’s equations can be simplified by using the assumptions mentioned above and by applying following material constitutive relations [25]where σ′ is the electrical conductivity, ε is the permittivity, and μ is the magnetic permeability. The expression for permittivity can be written as [20]:If electromagnetic incident rays are propagating in the x-direction (Fig. 1), thenTherefore, for a uniform plane wave, the simplified equation for
Results and discussion
The schematic representation of electromagnetic heating of three layered solid is shown in Fig. 1, where poly-aniline is sandwiched between two PMMA layers. Here our goal is to heat poly-aniline via microwave processing to above 105 °C, which is the glass transition temperature of PMMA. The volumetric heat generated in poly-aniline layer is transferred to PMMA by thermal conduction, and eventually heat is dissipated from PMMA surface to the surrounding by convection. The high temperature of
Summary and conclusions
Closed form analytical solutions are obtained for power and temperature distribution in PMMA and poly-aniline under microwave heating. The electromagnetic heat generation is obtained from Maxwell’s equation using temperature dependent dielectric properties which is then used in the energy equation to find the temperature distribution. The temperature distribution is presented as a function of poly-aniline thickness, PMMA thickness and heat transfer coefficient for various microwave exposure
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