Gas Diffusion through Thin Polystyrene Films
1
Background This work is a continuation of a large project on the physics of thin films, with the purpose of developing a more thorough understanding of how the behavior of a polymer changes under molecular confinement. elastic properties of these delicate films using a simple experiment to generate a wrinkle pattern. The author previously studied the effects of the floating film on wave propagation across the fluid surface. Cerda has developed a theoretical basis for the diffusion of gas through a floating thin film, which these experiments have investigated. Materials and methods The floating film system has been of recent interest to the research group, with notable advances into determining the elastic pr Gas Diffusion through Thin Polystyrene Films Kevin Cunningham, Chemical Engineering Advisors: Thomas Russell, Polymer Science & Engineering; Narayanan Menon, Physics University of Massachusetts Amherst, Amherst, MA 01003 This work was supported by the PSE Research Experience for Undergraduates Program, as part of the MRSEC Program of the National Science Foundation under grant number 0820506. Figure 1: Schematic diagram of the bubble cast under a floating thin film. (Credit: Cerda) Polystyrene films were prepared by spin coating solutions in toluene at 2000 rpm for 60 seconds, followed by thermal annealing at 150° Celsius for one hour to remove residual stresses. The films were floated on the surface of water and a tiny bubble of gas was placed under the film. As the gas diffused through the polymer and into the environment, the volume of the bubble decreased, which could easily be measured with an optical microscope. Images of the bubble were taken using a digital camerawith Data processing The digital photos taken at specified intervals during the bubble shrinking were processed using ImageJ software. The color images were imported as a stack for simplified analysis and converted to 8-bit grayscale. then converted to binary using a brightness threshold filter. Finally, the bubble was isolated by filling holes in the binary image. The “analyze particles” tool was then used to identify and measure the circular particles in each of the images. The scale of the images was determined by photographing a small ruler also floated on the same liquid surface for each trial. Assuming the bubbles to be near-perfect circles, as measured by ImageJ, the radius was plotted against time. Results and analysis One of the most interesting phenomena observed was that, for some trials, the rate of the bubble shrinking fell into distinct regimes. It has been hypothesized that this corresponds to the diffusion of different molecular species in the case of air bubbles; however, this phenomenon was observed even with pure nitrogen bubbles. Values for the permeability of the film (P) were calculated in accordance with theoretical work using Equation 1, and found not to correspond to the literature values for gas diffusion through polystyrene by more than an order of magnitude. Work is continuing with a focus on understanding how the actual and expected values of permeability compare depending on the film thickness. Conclusions and future work The current experimental results indicate the possibility of some fundamental flaw in the assumptions behind the experiment. The first was that the films, after annealing, would be homogeneous in terms of diffusive properties. Contrary to this hypothesis, great variation has been seen between trials performed on the same film, where the bubble is observed to shrink at a different rate in each trial. Another assumption was that the contact angle would remain constant for the duration of the bubble’s shrinking. This should lead to an increase in pressure, following Laplace’s equation for a hemispherical bubble. The observed behavior, in which the bubble stops shrinking at a small radius, may indicate that the curvature is not increasing as expected with the decreasing contact area. But if these assumptions do remain valid, then the data provide valuable insight into the behavior of thin films. If the departure from the expected permeation values only occurs at small vales of thickness, then molecular modeling may show how the confined polymer chains behave to influence gas diffusion. To continue this work, it will be important to gather additional data for a statistical analysis of the diffusion phenomenon. It would also be beneficial to change the experiment design to account for more confounding variables, such as ambient gas, bubble casting technique, and contact angle. References E. Cerda. Notes on the Bubbles Experiment. Aug. 2011. J. Huang et al. Capillary Wrinkling of Floating Thin Polymer Films. Science 317, 650 (2007). S. George et al. Transport Phenomena through Polymeric Systems. Progress in Polymer Science 26, 985 (2001). Acknowledgements Kathleen McEnnis, for getting me started in PSE Bugra Toga and Jiangshui Huang, for teaching me all about the floating film system and mentoring me along the way Professors Russell and Menon, for helping me understand the basics of polymer physics and making me feel confident about graduate study in materials engineering For further information, Please contact [email protected]. Further information on projects in the UMass Amherst MRSEC may be found at http://www.pse.umass.edu/mrsec. The film thickness was measured using an optical profilometer after each trial, using the topography along the circle from which the sample was cut off of the glass slide. The validity of the profilometer measurement has been checked against that of a white light interferometer, and the former is preferred because it does not require the preparation of additional samples on silicon wafers. Figure 5: The stages of image processing, with the raw image at top left, and the final image used for measurement at bottom right. Scale = 1mm. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 20 40 60 80 100 120 140 160 180 200 Radius (mm) Time (s) Raw bubble shrinking data for annealed polystyrene films, M n =99k by film thickness and surrounding environment 49.5nm, air 49.5nm, nitrogen 49.5nm, air 58nm, air 58nm, nitrogen 67.4nm, air 67.4nm, air 67.4nm, nitrogen Figure 7: The bubble shrinking displays interesting behavior as the radius approaches zero, where the size remains constant for a significant time. This conflicts with predictions because the pressure should increase as the bubble shrinks, forcing more gas through the film. Equation 1: Calculation for permeability of films, accounting for thickness. Variables: a = Bubble radius a 0 = Initial bubble radius R = Ideal Gas constant γ = Gas-liquid interfacial tension T = Temperature P = Permeability N = Avogadro’s number P 0 = Ambient pressure h = Film thickness t = Time Figure 6: Topography from profilometer. camera with external time-lapse control. Initial experiments used air bubbles, but later experiments used pure nitrogen. For the later trials, a local nitrogen-rich environment was used surrounding the floated film, and the water was saturated with nitrogen gas by bubbling. Figure 2: Commercial polystyrene. Figure 3: In spin coating, the substrate is held with suction while the plate spins to evaporate the solvent, leaving a film behind. Figure 4: Floating a film on the surface of water. This particular film was damaged in the process of taking the photo, demonstrating how delicate thin films can be. By tracing a circle onto the film and gently submerging the sample, the film easily detaches. Film thickness and annealing time contribute to the ease of floating a film.
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Transcript of Gas Diffusion through Thin Polystyrene Films
Background This work is a continuation of a large project on the physics of thin films, with the purpose of developing a more thorough understanding of how the behavior of a polymer changes under molecular confinement. elastic properties of these delicate films using a simple experiment to generate a wrinkle pattern. The author previously studied the effects of the floating film on wave propagation across the fluid surface. Cerda has developed a theoretical basis for the diffusion of gas through a floating thin film, which these experiments have investigated.
Materials and methods
The floating film system has been of recent interest to the research group, with notable advances into determining the elastic pr
Gas Diffusion through Thin Polystyrene Films Kevin Cunningham, Chemical Engineering
Advisors: Thomas Russell, Polymer Science & Engineering; Narayanan Menon, Physics University of Massachusetts Amherst, Amherst, MA 01003
This work was supported by the PSE Research Experience for Undergraduates Program, as part of the MRSEC Program of the National Science Foundation under grant number 0820506.
Figure 1: Schematic diagram of the bubble cast under a floating thin film. (Credit: Cerda)
Polystyrene films were prepared by spin coating solutions in toluene at 2000 rpm for 60 seconds, followed by thermal annealing at 150° Celsius for one hour to remove residual stresses. The films were floated on the surface of water and a tiny bubble of gas was placed under the film. As the gas diffused through the polymer and into the environment, the volume of the bubble decreased, which could easily be measured with an optical microscope. Images of the bubble were taken using a digital camerawith
Data processing The digital photos taken at specified intervals during the bubble shrinking were processed using ImageJ software. The color images were imported as a stack for simplified analysis and converted to 8-bit grayscale. then converted to binary using a brightness threshold filter. Finally, the bubble was isolated by filling holes in the binary image. The “analyze particles” tool was then used to identify and measure the circular particles in each of the images. The scale of the images was determined by photographing a small ruler also floated on the same liquid surface for each trial. Assuming the bubbles to be near-perfect circles, as measured by ImageJ, the radius was plotted against time.
Results and analysis One of the most interesting phenomena observed was that, for some trials, the rate of the bubble shrinking fell into distinct regimes. It has been hypothesized that this corresponds to the diffusion of different molecular species in the case of air bubbles; however, this phenomenon was observed even with pure nitrogen bubbles. Values for the permeability of the film (P) were calculated in accordance with theoretical work using Equation 1, and found not to correspond to the literature values for gas diffusion through polystyrene by more than an order of magnitude. Work is continuing with a focus on understanding how the actual and expected values of permeability compare depending on the film thickness.
Conclusions and future work The current experimental results indicate the possibility of some fundamental flaw in the assumptions behind the experiment. The first was that the films, after annealing, would be homogeneous in terms of diffusive properties. Contrary to this hypothesis, great variation has been seen between trials performed on the same film, where the bubble is observed to shrink at a different rate in each trial. Another assumption was that the contact angle would remain constant for the duration of the bubble’s shrinking. This should lead to an increase in pressure, following Laplace’s equation for a hemispherical bubble. The observed behavior, in which the bubble stops shrinking at a small radius, may indicate that the curvature is not increasing as expected with the decreasing contact area. But if these assumptions do remain valid, then the data provide valuable insight into the behavior of thin films. If the departure from the expected permeation values only occurs at small vales of thickness, then molecular modeling may show how the confined polymer chains behave to influence gas diffusion. To continue this work, it will be important to gather additional data for a statistical analysis of the diffusion phenomenon. It would also be beneficial to change the experiment design to account for more confounding variables, such as ambient gas, bubble casting technique, and contact angle.
References E. Cerda. Notes on the Bubbles Experiment. Aug. 2011.
J. Huang et al. Capillary Wrinkling of Floating Thin Polymer Films. Science 317, 650 (2007).
S. George et al. Transport Phenomena through Polymeric Systems. Progress in Polymer Science 26, 985 (2001).
Acknowledgements Kathleen McEnnis, for getting me started in PSE Bugra Toga and Jiangshui Huang, for teaching me all about the floating film system and mentoring me along the way Professors Russell and Menon, for helping me understand the basics of polymer physics and making me feel confident about graduate study in materials engineering
For further information, Please contact [email protected]. Further information on projects in the UMass Amherst MRSEC may be found at http://www.pse.umass.edu/mrsec.
The film thickness was measured using an optical profilometer after each trial, using the topography along the circle from which the sample was cut off of the glass slide. The validity of the profilometer measurement has been checked against that of a white light interferometer, and the former is preferred because it does not require the preparation of additional samples on silicon wafers.
Figure 5: The stages of image processing, with the raw image at top left, and the final image used for measurement at bottom right. Scale = 1mm.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 20 40 60 80 100 120 140 160 180 200
Rad
ius
(mm
)
Time (s)
Raw bubble shrinking data for annealed polystyrene films, Mn=99k by film thickness and surrounding environment
49.5nm, air
49.5nm, nitrogen
49.5nm, air
58nm, air
58nm, nitrogen
67.4nm, air
67.4nm, air
67.4nm, nitrogen
Figure 7: The bubble shrinking displays interesting behavior as the radius approaches zero, where the size remains constant for a significant time. This conflicts with predictions because the pressure should increase as the bubble shrinks, forcing more gas through the film.
Equation 1: Calculation for permeability of films, accounting for thickness. Variables: a = Bubble radius a0 = Initial bubble radius R = Ideal Gas constant γ = Gas-liquid interfacial tension T = Temperature P = Permeability N = Avogadro’s number P0 = Ambient pressure h = Film thickness t = Time
Figure 6: Topography from profilometer.
camera with external time-lapse control. Initial experiments used air bubbles, but later experiments used pure nitrogen. For the later trials, a local nitrogen-rich environment was used surrounding the floated film, and the water was saturated with nitrogen gas by bubbling.
Figure 2: Commercial polystyrene.
Figure 3: In spin coating, the substrate is held with suction while the plate spins to evaporate the solvent, leaving a film behind.
Figure 4: Floating a film on the surface of water. This particular film was damaged in the process of taking the photo, demonstrating how delicate thin films can be. By tracing a circle onto the film and gently submerging the sample, the film easily detaches. Film thickness and annealing time contribute to the ease of floating a film.
