Polymer Communication The signi®cance of the zero-concentration diffusivity value obtained from integral desorption data M.S. Hedenqvist a, * , F. Doghieri b a Department of Polymer Technology, Royal Institute of Technology, SE-100 44 Stockholm, Sweden b Department of Chemical Engineering, Mining and Environmental Technologies, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy Received 23 July 2001; received in revised form 20 August 2001; accepted 28 August 2001 Abstract n-Hexane zero-concentration diffusivity in high density polyethylene obtained `indirectly' from integral desorption measurements using the free volume concept was compared with the zero-concentration diffusivity obtained directly at low-n-hexane activities using a quartz- spring system. The difference between the results obtained by the indirect and direct methods was within the experimental error. The concentration dependence of the diffusivity predicted by the Cohen±Turnbull±Fujita free volume theory was in accordance with experi- mental data. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: Diffusion; Sorption; Desorption 1. Introduction Integral sorption and desorption experiments are fre- quently used to determine diffusion and permeability properties of solutes in polymers [1,2]. The experiment is easy to perform, and this explains its popularity. A typical sorption experiment involved exposing the specimen to a gas/vapour or liquid and at the same time recording its weight increase as a function of time. A typical desorption experiment is performed by exposing the solute-saturated specimen to an environment different from that in which it was saturated and subsequently recording the weight decrease as a function of time. By ®tting the weight increase/decrease-time curves to Fick's equation, it is possible to obtain the diffusion coef®cient. In cases where the solute solubility is high, the diffusivity generally increases with increasing solute concentration plasticisa- tion effects) [3]. In these cases, the weight increase/ decrease-time data can be ®tted to Fick's equation, only if an expression for the solute-concentration-dependent diffusivity is included. The diffusivity is often expressed according to an empirical exponential relationship [3]: DC D co e ac 1 where D co is the zero-concentration diffusivity and a is the plasticisation power. A particularly powerful exponential expression for describing the solute concentration depen- dence of D and which also has a theoretical basis is the Cohen±Turnbull±Fujita free-volume equation [4±8]: D T  Aexp 2 B d v a 1 f 1 1 v a 2 f 2  ! 2 where A is a constant, v a 1 and v a 2 are, respectively, the volume fractions of solute and polymer in the amorphous part of the polymer, f 1 is the fractional free volume of the pure solute and f 2 is the fractional free volume of the amorphous frac- tion of the pure polymer. B d is a constant that depends only on the size of the penetrant molecule [6] and D T is the thermodynamic diffusivity which is related to the diffusivity extracted from the sorption/desorption curves through a thermodynamic correction: D  D m 1 2 v a 1  D T 2 ln a 1 2 ln v a 1  ! 3 where D m is the mutual diffusivity [5,9] and a 1 is the pene- trant activity in the polymer. Using the Flory±Huggins theory, Fels and Huang [10] showed that the activity of the solute absorbed in the non-crystalline part of the poly- mer is given by: 2 ln a 1 2 ln v a 1 1 2 v a 1 1 2 2x 12 v a 1  4 where x 12 is the Flory±Huggins interaction parameter. Polymer 43 2002) 223±226 0032-3861/02/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S0032-386101)00595-X www.elsevier.com/locate/polymer * Corresponding author. Tel.: 146-8-790-7645; fax: 146-8-20-8856. E-mail address: mikaelhe@polymer.kth.se M.S. Hedenqvist).