Sorption and surface diffusion in porous glass

Sorption, gas-phase diffusion in the region of molecular streaming, and surface diffusion in very dilute adsorbed films have been studied quantitatively for a number of gases in membranes of porous glass. The sorption of oxygen, nitrogen, argon, sulphur dioxide and ammonia near their liquefying temperatures resulted in type IV isotherms with very characteristic hysteresis loops. From the isotherms porosity, surface area and mean pore radius were evaluated. Heats of sorption, Δ H , have been obtained in very dilute adsorbed films and in films where v/v m approaches or exceeds one. These heats showed the porous glass to be an energetically non-uniform sorbing surface. The Henry’s law region of sorption was studied and Henry’s law sorption constants evaluated at 273, 290, 323 and 343° K for the most dilute adsorbed films of oxygen, nitrogen, argon, krypton, methane and ethane. Nearly all this information is essential for measurements of surface diffusion by the transient state method of Barrer & Grove (1951). The micropore structure was so fine that non-sorbed gases diffused within the porous glass only by molecular streaming at pressures up to half an atmosphere or more. Effects of sorption upon this diffusion were inappreciable for helium, neon and possibly hydrogen; for oxygen, nitrogen, argon, krypton, methane and ethane the influence of sorption upon timelags and diffusion coefficients became progressively more marked. In the steady state of flow there was little evidence of surface diffusion when, in the most dilute adsorbed films, Henry’s law is obeyed. On the other hand, in the transient state of flow, surface diffusion makes a substantial contribution to flow. Reasons are given for the difference in the extent to which surface mobility can be detected in the two states of flow. Consistent values of the surface diffusion coefficients, D 8 , were obtained for oxygen, nitrogen, argon, krypton, methane and ethane. These values of D 8 were compatible with the Arrheniusequation D 8 = D 0 exp ( – E / RT ) over the temperature range of 273 to 343° K investigated. The ratio of E to Δ H for very dilute adsorbed films lay between 0·5 and 0·6, and should in order of magnitude be characteristic of a heterogeneous sorbing surface. The numerical values of D 8 have been compared with D for liquids, and analyzed in terms of entropy and energy of activation.

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Hygromechanical Analysis of Liquid Crystal Display Panels

Journal of Electronic Packaging ◽

10.1115/1.4025527 ◽

2013 ◽

Vol 135 (4) ◽

Cited By ~ 1

Author(s):

Toru Ikeda ◽

Tomonori Mizutani ◽

Kiyoshi Miyake ◽

Noriyuki Miyazaki

Keyword(s):

Boundary Layer ◽

Liquid Crystal ◽

Numerical Analysis ◽

Diffusion Coefficients ◽

Liquid Crystal Display ◽

Fem Analysis ◽

Contact Condition ◽

Henry's Law ◽

Henry’S Law ◽

The Difference

Liquid crystal displays (LCDs) are getting larger, and the homogeneity of an LCD panel is becoming very important for the quality of the display. Inhomogeneity in an LCD panel can be caused by inhomogeneity of its materials and the defective production process, warpage of the panel due to changes in the temperature and humidity, and so on. In this study, we developed a scheme of hygromechanical analysis to reduce the warpage of an LCD. First, we measured the diffusion coefficients and Henry's law coefficients of the respective components of an LCD using a thermogravimetric analyzer (TGA) under controlled humidity. We then measured the coefficients of moisture expansion (CME) of the components using a humidity-controlled thermomechanical analyzer (TMA). We analyzed the hygromechanical deformations of the respective components, a polarizing plate and an LCD panel using the finite element method (FEM) with measured diffusion coefficients, Henry's law coefficients and the CMEs of the respective components. The analyzed deformations of the respective components corresponded quantitatively with the deformations measured experimentally. However, the analyzed deformation of the polarizing plate did not correspond with the measured deformation perfectly. A polarizing plate is made by sandwiching a polarizer between two sheets of protection film. We ignored the effect of the thin boundary layer between the polarizer and its protecting film in this analysis, and the effect of this boundary layer on the diffusion of moisture may have caused the difference between the analysis and the measurement. The expected warpage of the analyzed LCD corresponded qualitatively with the measured warpage. However, the numerical analyzed strains near the edge of the LCD panel strongly shifted to the compression side compared to the experimental measured strains. A possible reason for this shift was the difference in the boundary condition at the edge of the LCD panel between the numerical analysis and the experimental measurement. The actual edge of the LCD panel was fastened by a bezel, and the contact condition between the LCD panel and the bezel was ambiguous. To perform a quantitative analysis, we will need to investigate the contact condition between the LCD panel and the bezel and introduce it to the numerical analysis. This is left for a future study. We qualitatively investigated the warpage of LCDs with two types of protecting film and different directions of polarizing plates using the developed technique of FEM analysis.

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Hygro-Mechanical Analysis of LCD Panels

ASME 2009 InterPACK Conference, Volume 1 ◽

10.1115/interpack2009-89267 ◽

2009 ◽

Cited By ~ 1

Author(s):

Toru Ikeda ◽

Tomonori Mizutani ◽

Noriyuki Miyazaki

Keyword(s):

Boundary Layer ◽

Diffusion Coefficients ◽

Fem Analysis ◽

Mechanical Analysis ◽

Protective Film ◽

Henry's Law ◽

Pressure Sensitive Adhesive ◽

Moisture Expansion ◽

Henry’S Law ◽

Glass Plates

Liquid crystal displays (LCDs) are getting larger, and the homogeneity of an LCD panel is becoming very important for the quality of the display. Inhomogeneity in an LCD panel can be caused by inhomogeneity of its materials and the defective production process, warpage of the panel due to changes in the temperature and humidity, and so on. In this study, we developed a scheme of hygro-mechanical analysis to reduce the warpage of an LCD. First, we measured the diffusion coefficients and Henry’s law coefficients of the respective components of an LCD using a thermo-gravimetric analyzer (TGA) under controlled humidity. We then measured the coefficients of moisture expansion (CME) of the componenets using a humidity-controlled thermo-mechanical analyzer (TMA). We analyzed the hygro-mechanical deformations of the respective components, a polarizing plate and an LCD panel using the finite element method (FEM) with measured diffusion coefficients, Henry’s law coefficients and the CMEs of the respective components. The analyzed deformations of the respective components corresponded quantitatively with the deformations measured experimentally. However, the analyzed deformation of the polarizing plate did not correspond with the measured deformation perfectly. A polarizing plate is made by sandwiching a polarizer by two sheets of protective film; the effect of the thin boundary layer between the polarizer and its protecting film was ignored in this analysis. The effect of this boundary layer on the diffusion of moisture may have caused the difference between the analysis and the measurement. The expected warpage of the analyzed LCD corresponded qualitatively with the measured warpage. In LCD panels, glass plates and polarizing plates are bonded using pressure-sensitive adhesive. Slippage between the glass plates and the polarizing plates may occur during the deformation of an LCD. We investigated the warpage of LCDs with two types of protecting film and different directions of polarizing plates using the developed technique of FEM analysis.

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Sorption and surface diffusion in microporous carbon cylinders

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1955.0156 ◽

1955 ◽

Vol 231 (1184) ◽

pp. 52-74 ◽

Cited By ~ 41

Keyword(s):

Surface Diffusion ◽

Diffusion Coefficients ◽

Surface Concentration ◽

Surface Flow ◽

Carbon Powder ◽

Type I ◽

Equilibrium Studies ◽

Type Iv ◽

Internal Surfaces ◽

Helium Neon

An investigation has been made of adsorption and diffusion of helium, neon, hydrogen, argon, nitrogen and krypton in microporous cylinders of carbon compressed to different porosities e, and having very high internal surfaces, A . On the uncompressed carbon powder sorption of argon occurred at 90 and 78° K without hysteresis; in a compressed cylinder with e = 0.64 cm 3 per cm 3 and 2e A = 18.8 Å the isotherms changed from type II to type IV in Brunauer’s classification and a pronounced hysteresis loop appeared. In a highly compressed cylinder with e = 0.37 cm 3 per cm 3 and 2e/ A = 6.5 Å hysteresis again disappeared and the isotherms changed from type IV nearly to type I. The areas A and heats of sorption were measured, and special attention was paid to sorption equilibria involving dilute films of nitrogen, argon and krypton between 273 and 323° K. Surface and volume diffusion were then investigated over the same temperature interval, 273 to 323° K, in the compressed cylinders already carefully characterized by the equilibrium studies. Surface diffusion coefficients, D s , were evaluated for all the gases including helium. The properties of D s indicate that dilute films of helium, neon and hydrogen are best regarded as one- or two-dimensional gases but that argon, nitrogen and krypton still give localized adsorbed films in which surface flow is by jumps, each unit diffusion requiring an energy of activation which was 0.53 to 0.62 of the heat of adsorption. It was further shown that adsorption isotherms in the Henry’s law region can be measured by flow methods, and are in agreement with those obtained by direct measurement. The surface diffusion coefficients increase and the activation energies for diffusion decrease for argon, nitrogen and krypton as the surface concentration of adsorbate increases. In some cases, especially for krypton, surface flow was much the most important mode of transport within the micropore system.

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Sorption and diffusion of simple paraffins in silica-alumina cracking catalyst

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1960.0109 ◽

1960 ◽

Vol 256 (1285) ◽

pp. 267-290 ◽

Cited By ~ 31

Keyword(s):

Surface Diffusion ◽

Diffusion Coefficients ◽

Time Lag ◽

Transient State ◽

Surface Flow ◽

Sorption Data ◽

Silica Alumina ◽

Pore Properties ◽

Permanent Gases ◽

And Diffusion

Sorption and diffusion measurements have been made of methane, ethane and propane in the silica-alumina cracking catalyst previously employed in similar measurements for permanent gases (Barrer & Gabor 1959). The sorption data show no evidence of molecular sieve behaviour in the micropore structure of the catalyst, for the species studied. The ratio of surface to volume flow increases with increasing molecular weight of hydrocarbons and with decreasing porosity. On the other hand, in or near the Henry’s law region of sorption, this ratio decreases as the temperature rises. In a micropore system there are many points where surface flow may be interrupted by roughnesses, blind pores or crevices. A treatment has been given which permits the influence of such pore properties upon surface diffusion to be considered. The procedure developed has been applied to the data obtained in this research, and estimates have been made of some properties of the surface diffusion coefficients which could be expected upon uninterrupted surfaces of the catalyst. Owing to differences in the roles of pores in steady and transient states of flow, transient state (time-lag) diffusion coefficients could depend on time. Some consequences of this have also been examined.

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A comparative structural study of cracking catalyst, porous glass, and carbon plugs by surface and volume flow of gases

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1959.0112 ◽

1959 ◽

Vol 251 (1266) ◽

pp. 353-368 ◽

Cited By ~ 29

Keyword(s):

Steady Flow ◽

Gas Phase ◽

Surface Diffusion ◽

Porous Glass ◽

Diffusion Coefficients ◽

Transient Flow ◽

Time Lag ◽

Surface Flow ◽

Microporous Media ◽

Pore Properties

Transient and steady states of volume and surface flow of gases and vapours in microporous media require for their description four different diffusion coefficients, namely, a surface and a gas-phase coefficient for transient and a surface and gas-phase coefficient for steady flow. The distinction between steady and transient flow arises in part because of the role of blind pores. Similarly, two different porosities ∊ and ∊ 8 and two different surface areas A and A 8 govern transient and steady-state flow respectively. By comparing the two gas-phase and the two surface diffusion coefficients with gas-phase and surface diffusion coefficients in a smooth cylindrical capillary having ∊/ A equal to that for the porous medium, four structure factors can be defined, in terms of which the pore properties of microporous media can be discussed. Data are presented for sorption, transient flow (time lag) and steady flow of He, Ne, A and N 2 in compressed alumina-silica catalyst plugs. These, and previously obtained data for Vycor porous glass (Barrer & Barrie 1952) and Carbolac carbon plugs (Barrer & Strachan 1955) have been analyzed according to the above procedure, and pore properties compared. In this way it was possible to obtain information regarding pore structure which could not have been derived by other methods.

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