15.2 Transport phenomena in polymer membranes

Polymeric membranes are key in separating substances. They work through solution-diffusion, pore-flow, or Knudsen diffusion, depending on the membrane type. These mechanisms allow for selective transport of molecules, making membranes useful in various applications.

Membrane performance hinges on material properties, thickness, and operating conditions. The polymer's structure, crystallinity, and functional groups play crucial roles. Thinner membranes boost permeability, while thicker ones improve selectivity. Temperature and pressure also impact performance significantly.

Transport Mechanisms in Polymeric Membranes

Transport mechanisms in polymeric membranes

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• Solution-diffusion mechanism involves permeants dissolving into the membrane material and diffusing through the polymer matrix driven by a concentration gradient across the membrane, applicable to dense, non-porous membranes (reverse osmosis membranes)
• Pore-flow mechanism involves permeants flowing through pores or channels in the membrane driven by a pressure gradient across the membrane, applicable to porous membranes with pore sizes larger than the permeant molecules (ultrafiltration membranes)
• Knudsen diffusion occurs when the pore size is smaller than the mean free path of the permeant molecules, collisions between permeant molecules and pore walls dominate the transport process, separation is based on the differences in molecular weights of the permeants (gas separation membranes)

Factors Affecting Membrane Performance

Factors affecting membrane performance

• Membrane material factors include the chemical structure and composition of the polymer, degree of crystallinity and crosslinking, presence of functional groups that interact with permeants (polyamide, cellulose acetate)
• Membrane thickness affects performance, with thinner membranes generally exhibiting higher permeability but lower mechanical stability, while thicker membranes provide better selectivity but lower permeability
• Operating conditions impact membrane performance:
  1. Higher temperatures increase permeability but may reduce selectivity
  2. Higher pressure differences across the membrane enhance permeation rates
  3. Feed composition, such as the presence of contaminants or competing species, can affect permeability and selectivity (water, salts, organic compounds)

Mathematical Modeling of Mass Transfer

Mathematical models for mass transfer

• Solution-diffusion model describes permeability coefficient

  $P$

  as the product of diffusion coefficient

  $D$

  and solubility coefficient

  $S$

  :

  $P = D \times S$

  , flux

  $J$

  is proportional to the pressure difference

  $\Delta p$

  across the membrane:

  $J = P \times \Delta p$

  , selectivity

  $\alpha$

  is the ratio of permeability coefficients for two different permeants:

  $\alpha = P_A / P_B$

• Pore-flow model describes flux

  $J$

  as proportional to the pressure gradient

  $\Delta p / l$

  and the pore size

  $r$

  :

  $J = (r^2 / 8\eta) \times (\Delta p / l)$

  , where

  $\eta$

  is the viscosity of the permeant, selectivity is determined by the relative sizes of the permeant molecules and the membrane pores (Hagen-Poiseuille equation)

Structure-Property Relationships

Membrane structure vs transport properties

• Polymer chain flexibility and free volume impact transport properties, with higher chain flexibility and free volume facilitating permeant diffusion, controlled by polymer composition, molecular weight, and crosslinking density (PDMS, PVA)
• Pore size distribution affects separation performance, with narrow pore size distribution enhancing selectivity, tailored by controlling the membrane fabrication process and post-treatment methods (phase inversion, stretching)
• Surface properties, such as hydrophilicity or hydrophobicity of the membrane surface, affect the interaction with permeants, surface modification techniques can be used to improve selectivity and fouling resistance (plasma treatment, grafting)