Diffusion gases into polymers

A.3 Diffusion of Gas into Polymer Droplets and Fibers. Consider a molten polymer blend with the minor component in the form of small spheres of radius 5 pm. Calculate the time it takes for the diffusion of these spheres from the major component to reach 90% equilibrium. Repeat the same calculations when the minor component is in the form of long fibers with the same radius as the spherical droplets. D = 10 cm /s. 

Most polymers that have been of interest as membrane materials for gas or vapor separations are amorphous and have a single phase structure. Such polymers are converted into membranes that have a very thin dense layer or skin since pores or defects severely compromise selectivity. Permeation through this dense layer, which ideally is defect free, occurs by a solution-diffusion mechanism, which can lead to useful levels of selectivity. Each component in the gas or vapor feed dissolves in the membrane polymer at its upstream surface, much like gases dissolve in liquids, then diffuse through the polymer layer along a concentration gradient to the opposite surface where they evaporate into the downstream gas phase. In ideal cases, the sorption and diffusion process of one gas component does not alter that of another component, that is, the species permeate independently. 

A recently developed technique, i.e. solid-phase microextraction (SPME), which collects vapors on a micro-liber coated with a gas chromatographic polymer phase (Chai and Pawliszyn, 1995 Grote and Pawliszyn, 1997), may be more promising than typical PSDs for long-term sampling as it permits the entire collected sample to be analyzed. The SPME liber can be exposed directly for rapid assessment of air quality or withdrawn into a tube that controls diffusion to the fiber for longterm sampling. 

Applying the law, the change in concentration of CO2 and low molecular compounds in molten polymer could be monitored by measuring the NIR absorbance on-line at the autoclave. Fig. 5 shows the NIR measured diffusion coefficients of CO2 alone, and those of CO2 as well as propanol, of their mixture to LDPE (MI = 8.0g/10min Mw = 1.05 x lO g/mol Mw/Mn = 6.94) at 175°C by changing the pressure from 0.1 MPa to a specified level. As can be seen in Fig. 5, both propanol (PrOH) and CO2 of mixture could diffuse into the polymer even under the critical pressure of CO2, i.e., 7.38 MPa. Since the propanol is volatile, it mixes with CO2 in gas phase at 175°C. Therefore, the propanol could diffuse into polymer even at the low pressure. It could be worthwhile to note that the diffusivity of propanol was lower than that of CO2 at low-pressure level, but it increased close to that of CO2 over the critical pressure. 

Consider the diffusion of a gas into an underlying layer of a non-volatile liquid such as heavy oil or polymer (Upreti and Mehrotra, 2000 Tendulkar et al., 2009) inside a closed vessel of uniform cross-section area A (Figure 1.6). As the gas penetrates the liquid layer, the pressure inside the vessel goes down. The system is at constant temperature throughout the duration tf of this process with negligible change in the thickness L of the polymer layer. The mass concentration c of gas in the layer at any time t and depth z is given by... 

The initial fuel cell response to changes in load show is rapid with a time constant 1 s this corresponds to the convective flow into the fuel cell and the diffusion across the gas diffusion layer, ti and T2. Diffusion across the polymer membrane from the cathode/electrolyte interface to the anode, T3, is evident in Figure 3.9B, where the relative humidity change at the anode lags the change at the cathode by 100 s. 

The required diffusion time (to) for the dissolution of gas into a molten polymer can be approximated from the striation thickness and the diffusivity of the gas, using the Fourier criterion, expressed as... 

As indicated earlier, the limiting effect of the diffusion of a gas into a molten or thermally softened polymer is its solution. Further, such behavior can be expressed in the form of Henry s law [Eq. (5-5)]. 

The formation of a gas/polymer solution depends on gas absorption and diffusion into the polymer matrix, which can be affected by the nature of the polymer matrix (amorphous versus semicrystalline), gas type, saturation pressure, and temperature [44, 45]. The sorption behaviors of gas in polymers can be explained by Henry s law (gas solubility) and Pick s law (gas diffusivity), as shown in the following equations [46] ... 

Equation 17.4 shows that the concentration of gas in the polymer is directly proportional to the gas pressure. Increasing the pressure can increase the gas absorption and diffusion to facilitate the formation of a gas/polymer single-phase solution. Increasing the saturation temperature increases the gas diffusion rate into the polymer. However, this decreases the gas concentration at a specific pressure. 

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