Compression of poly(vinyl alcohol) gels by ultracentrifugal forces Shoji Nosaka a, * , Shinichi Okada b , Yoshiyuki Takayama a , Kenji Urayama a , Hiroshi Watanabe b , Toshikazu Takigawa a a Department of Material Chemistry, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan b Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan Received 9 May 2005; received in revised form 26 September 2005; accepted 10 October 2005 Available online 2 November 2005 Abstract Compression due to ultracentrifugal forces was investigated for poly(vinyl alcohol) (PVA) gels. The concentration gradient profiles for the gels were obtained by experiment and were then compared with a theoretical prediction. By the application of the centrifugal forces, the concentration gradient near the bottom increases sharply whereas the gradient inside the gel remains almost constant in the region far from the bottom. Further application of the centrifugal forces enhances the peak near the bottom. These are well explained by the theory proposed in the previous paper [Urayama et al. J Chem Phys 2005;122:024906.]. The frictional coefficient f for the PVA gels, which originates from the friction between the polymer network and solvent molecules, is estimated to be 3.5!10 14 Nsm K4 . q 2005 Elsevier Ltd. All rights reserved. Keywords: Poly(vinyl alcohol) gel; Ultracentifuge; Frictional coefficient 1. Introduction Control of the permeation of low molecular weight substances through a membrane is a key to the separation technique. Permeability as well as selectivity is strongly affected by the structure of membranes. To utilize a polymer gel as a membrane, studies on the frictional properties of the gel membranes becomes very important. However, there exist only a few studies on the frictional properties of the polymer gels. Tokita and Tanaka have examined the frictional proper- ties of poly(N-isopropylacrylamide) gels showing the volume- phase transition [1]. They focused on the behavior near the transition point and found an anomaly on the frictional coefficient at the transition. The mode coupling theory was used to analyze the anomaly of the frictional coefficient [2]. We have also shown the frictional properties of poly(vinyl alcohol) (PVA) gels in one-dimensional as well as two- dimensional flow [3,4]. From the one-dimensional flow experiment the frictional coefficient was estimated for the PVA gel. A limited number of the studies on the friction is mainly due to the difficulty of experiment; of course, no commercial apparatus is available for the measurements. We have shown in the previous paper that a ultracentrifuge is available to estimate the frictional coefficient of the ‘chemical’ gels, i.e. poly(acrylamide) gels whose cross-links are formed by covalent bonds [5]. The present study treats the PVA gals cross-linked by microcrystallites which are classified into the ‘physical’ gels. The compression behavior of the physical gels under ultracentrifugal forces have not been investigated before. In this paper, the frictional coefficient of PVA gels is estimated by an untracentifuge, and the data are analyzed in terms of the theory proposed in the previous paper [5]. 2. Theoretical background In the previous paper [5], a governing equation which determines the shrinking kinetics of polymer gels in an ultracentrifuge has been proposed. Let a sample cell of the ultracentrifuge be rectangular in shape and mounted on a rotor of the apparatus. When the rotor operates, a compressive force acts in the radial direction on a gel in the cell. We define r as the distance from the center of rotation, and r 2 as the position at the immobile bottom of the cell (i.e. the bottom of the gel). The position of the top of the gel, which corresponds to a moving boundary between the gel and pure solvent phases, is designated as r 1 . Here r 1 !r 2 .When the friction between the gel and side walls is negligible, the equation of motion for a volume element in the gel is reduced to a one-dimensional problem [5]. Polymer 46 (2005) 12607–12611 www.elsevier.com/locate/polymer 0032-3861/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymer.2005.10.055 * Corresponding author. Tel.: C81 75 383 2455; fax: C81 75 383 2458. E-mail address: nosaka@rheogate.polym.kyoto-u.ac.jp (S. Nosaka).