Abstract
Gravimetry is used to study the diffusivity of a homologous series of linear alkanes (Cn, with n = 8, 10, 12, 14 and 16) in amorphous polystyrene at temperatures ranging from 45 °C to 145 °C, i.e. both below and above the polymer glass transition temperature (100 °C). All the mass uptake results obtained are well described by a simple Fickian model (for t < t1/2) and are used to calculate the corresponding diffusion coefficients (D) using the thin-film approximation of the Fickian equation. For all the alkanes considered, the temperature dependency of the diffusion coefficients is non-Arrhenius in character, over the broad temperature intervals considered. For any particular temperature log(D) varies linearly (R2 > 0.993, for all temperatures) with respect to the number of carbon atoms (n) in the alkyl chain, log(D) decreasing when n increases. For each liquid penetrant, over the temperature intervals considered, its log(D) also increases linearly (R2 > 0.996 for all the systems) with the decrease in the penetrant’s liquid viscosity.
Similar content being viewed by others
References
Yampolskii Y, Pinnau I, Freeman BD (eds) (2006) Materials science of membranes for gas and vapor separation. John Wiley & Sons
Vieth WR (1991) Diffusion in and through polymers - principles and applications. Hanser Publishers, Munich
Neogi P (ed) (1996) Diffusion in polymers. Marcel Dekker, Inc., New York
Böddeker KW (2008) Liquid separations with membranes. Springer, Berlin Heidelberg
Snow D et al (2007) Static deflection measurements of cantilever arrays reveal polymer film expansion and contraction. J Colloid Interface Sci 316(2):687–693
Igarashi S et al (2006) Swelling signals of polymer films measured by a combination of micromechanical cantilever sensor and surface plasmon resonance spectroscopy. Sensor Actuat B-Chem 117(1):43–49
Elabd YA et al (2001) Effect of penetrant-polymer interactions on molecular diffusion in conformational isomers of a heterogeneous polymer. Macromolecules 34(18):6268–6273
Zhao TJ, Beckham HW, Gibson HW (2003) Quantitative determination of threading in rotaxanated polymers by diffusion-ordered NMR spectroscopy. Macromolecules 36(13):4833–4837
Cosgrove T et al (2007) Self-diffusion in solutions of carboxylated acrylic polymers as studied by pulsed field gradient NMR. 1. Solvent diffusion studies. J Polym Res 14(3):167–174
Mukherjee M et al (2007) Effect of solvent-polymer interaction in swelling dynamics of ultrathin polyacrylamide films: A neutron and X-ray reflectivity study. Macromolecules 40(4):1073–1080
Wang D, Storey RF, Mauritz KA (1992) Investigation of the diffusion of di-N-hexyl phthalate in rubbery poly(Vinyl chloride) using electrical-impedance spectroscopy. Macromolecules 25(11):2869–2874
Pu Y et al (2001) Probe diffusion in thin PS free-standing films. Macromolecules 34(24):8518–8522
Cherdhirankorn T et al (2009) Fluorescence correlation spectroscopy study of molecular probe diffusion in polymer melts. Macromolecules 42:4858–4866
Morrissey P, Vesely D (2000) Accurate measurement of diffusion rates of small molecules through polymers. Polymer 41(5):1865–1872
Storey RF, Mauritz KA, Cox BD (1989) Diffusion of various Dialkyl Phthalate Plasticizers in PVC. Macromolecules 22(1):289–294
Storey RF, Mauritz KA, Cole BB (1991) Diffusion of Bis(2-Ethylhexyl) phthalate above and below the glass-transition temperature of Poly(Vinyl Chloride). Macromolecules 24(2):450–454
Storey RF, Mauritz KA, Carter ML (1991) Corrected densities and revised coefficients for diffusion of various dialkyl phthalate plasticizers in PVC. Macromolecules 24(25):6784–6785
Manoj KC et al (2010) Aromatic liquid transport through filled EPDM/NBR blends. J Polym Res 17(1):1–9
Mudassir J, Ranjha NM (2008) Dynamic and equilibrium swelling studies: crosslinked pH sensitive methyl methacrylate-co-itaconic acid (MMA-co-IA) hydrogels. J Polym Res 15(3):195–203
Arnould D, Laurence RL (1992) Size effects on solvent diffusion in polymers. Ind Eng Chem Res 31:218–228
Lv H-L, WANG B-G (2006) Prediction of solvent diffusion coefficient in amorphous polymers based on an equation-of-state. J Polymer Sci, Part B: Polymer Phys 44:1000–1009
Vrentas JS, Vrentas CM, Faridi N (1996) Effect of solvent size on solvent self-diffusion in polymer-solvent systems. Macromolecules 29(9):3272–3276
Vrentas JS, Vrentas CM (1994) Solvent self-diffusion in glassy polymer-solvent systems. Macromolecules 27(20):5570–5576
Jiang WH, Han R (2000) Prediction of solvent-diffusion coefficient in polymer by a modified free-volume theory. J Appl Polym Sci 77(2):428–436
Makrodimitri ZA, Economou IG (2008) Atomistic simulation of poly(dimethylsiloxane) permeability properties to gases and n-alkanes. Macromolecules 41:5899–5907
Mozaffari F, Eslami H, Moghadasi J (2010) Molecular dynamics simulation of diffusion and permeation of gases in polystyrene. Polymer 51(1):300–307
Bharadwaj RK, Boyd RH (1999) Small molecule penetrant diffusion in aromatic polyesters: a molecular dynamics simulation study. Polymer 40:4229–4236
Harogoppad SB, Aminabhavi TM (1991) Diffusion and sorption of organic liquids through polymer membranes. 5. Neoprene, Styrene-Butadiene-Rubber, Ethylene-Propylene-Diene Terpolymer, and Natural Rubber versus Hydrocarbons (C8 - C16). Macromolecules 24:2598–2605
Aminabhavi TM, Khinnavar RS (1993) Diffusion and sorption of organic liquids through polymer membranes: 10. Polyurethane, nitrile-butadiene rubber and epichlorohydrin versus aliphatic alcohols (C1-C5). Polymer 34(5):1006–1018
Chen SP, Ferry JD (1968) The diffusion of radioactively tagged n-hexadecane and n-dodecane through rubbery polymers. effects of temperature, cross-linking, and chemical structure. Macromolecules 1(3):270–278
Berens AR, Hopfenberg HB (1982) Diffusion of organic vapors at low concentrations in glassy pvc, polystyrene, and PMMA. J Membr Sci 10(2–3):283–303
Coutandin J et al (1985) Diffusion of dye molecules in polymers above and below the glass-transition temperature studied by the holographic grating technique. Macromolecules 18(3):587–589
van Krevelen DW, te Nijenhuis K (2009) Chapter 18 - Properties determining mass transfer in polymeric systems, in Properties of polymers: Their correlation with chemical structure, their numerical estimation and prediction from additive group contributions. Elsevier, Amsterdam, pp 655–702
Southern E, Thomas AG (1967) Diffusion of liquids in crosslinked rubbers. Trans Faraday Soc 63:1913–1921
Vesely D (2001) Molecular sorption mechanism of solvent diffusion in polymers. Polymer 42(9):4417–4422
Harogoppad SB, Aminabhavi TM (1991) Diffusion and sorption of organic liquids through polymer membranes. II. Neoprene, SBR, EPDM, NBR, and natural rubber versus n-Alkanes. J Appl Polym Sci 42:2329–2336
Mills PJ, Kramer EJ (1986) The effect of molecular-size on non-fickian sorption in glassy-polymers. J Mater Sci 21(12):4151–4156
Gall TP, Lasky RC, Kramer EJ (1990) Case-II diffusion - effect of solvent molecule size. Polymer 31(8):1491–1499
Kwan KS, Subramaniam CNP, Ward TC (2003) Effect of penetrant size and shape on its transport through a thermoset adhesive: I. n-alkanes. Polymer 44(10):3061–3069
Kwan KS, Subramaniam CNP, Ward TC (2003) Effect of penetrant size, shape, and chemical nature on its transport through a thermoset adhesive. II Esters Polymer 44(10):3071–3083
Bernardo G, Vesely D (2008) Solubility of alkanes in a polystyrene matrix. J Appl Polym Sci 110:2393–2398
Bernardo G, Vesely D (2010) Anomalous swelling of a polystyrene matrix in organic solvents. J Appl Polym Sci 115(4):2402–2408
Crank J (1979) The mathematics of diffusion, 2nd edn. Oxford Science, Oxford
Bernardo G, Choudhury RP, Beckham HW (2012) Diffusivity of small molecules in polymers: Carboxylic acids in polystyrene. Polymer 53:976–983
Brandrup J, Immergut EH, Grulke EA (2003) Polymer Handbook. 4th ed. John Wiley & Sons
van Krevelen DW, te Nijenhuis K (2009) Chapter 4 - Volumetric properties, in Properties of polymers: their correlation with chemical structure, their numerical estimation and prediction from additive group contributions. Elsevier, Amsterdam, pp 71–108
von Meerwall E et al (1998) Diffusion of liquid n-alkanes: free-volume and density effects. J Chem Phys 108(10):4299–4304
Daubert TE et al (1988) Physical and thermodynamical properties of pure chemicals. Taylor & Francis
Hansen CM (2007) Hansen solubility parameters - a user’s handbook. CRC, Boca Raton
Acknowledgements
Gabriel Bernardo acknowledges financial support from the IPC’s (Institute for Polymers and Composites) strategic project: “PEst-C/CTM/LA0025/2011” (Projecto Estratégico -LA 25 - 2011–2012 - Strategic Project - LA 25 - 2011–2012).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bernardo, G. Diffusivity of alkanes in polystyrene. J Polym Res 19, 9836 (2012). https://doi.org/10.1007/s10965-012-9836-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10965-012-9836-2