Journal of Colloid and Interface Science 239, 168–177 (2001) doi:10.1006/jcis.2001.7546, available online at http://www.idealibrary.com on A PFG-NMR Study of Restricted Diffusion in Heterogeneous Polymer Particles John Georg Seland, ∗, 1 Matteo Ottaviani,† and Bjørn Hafskjold ∗ ∗ Department of Chemistry, Norwegian University of Science and Technology, N-7491 Trondheim, Norway; and †Department of Physical Chemistry, University of Padova, 35131 Padova, Italy E-mail: johnsel@chembio.ntnu.no; matteo@pcﬂ.chembio.ntnu.no; bhaf@chembio.ntnu.no. Received October 4, 2000; accepted March 15, 2001 The diffusion resistance to monomers during heterogeneous poly- merization of polyoleﬁn particles may have a signiﬁcant effect on the observed activity. This diffusivity is, in general, unknown. To gain more information on this diffusion resistance in such systems, PFG- NMR has been used to measure the diffusion of organic solvents in various systems of porous polymer particles. In such systems the complex morphology and geometry demands careful analysis of the PFG-NMR attenuation curve. In this study, effects from restricted diffusion, domains having different diffusivity, and internal mag- netic ﬁeld gradients are expected. Thus, the obtained diffusivities have to be considered carefully, and a way to analyze the data taking these effects into account is presented. C  2001 Academic Press Key Words: PFG-NMR; restricted diffusion; polymer particles; internal magnetic ﬁeld gradients;tortuosity. INTRODUCTION The inﬂuence of restricting geometry on the measured diffu- sivity is of great importance in different kinds of porous media, like porous rocks, biological systems, and polymer systems. In a pulsed ﬁeld gradient nuclear magnetic resonance (PFG-NMR) experiment, the observation time can be varied from a few mil- liseconds up to several seconds. Because of effects from the re- stricting geometry, the measured self-diffusion coefﬁcient, D(t ), depends on the observation time, t d , and is sensitive to physi- cal parameters like permeability and the volume fraction of the diffusing species. D(t ) can be related to certain characteristics of the porous medium such as the surface-to-volume ratio and the tortuosity (1–5). Taking into account only geometrical re- strictions of the medium, D(t ) of a diffusing ﬂuid is found to decrease with observation time and reach a plateau value, which represents the tortuosity, T , of the system (1–3). During a heterogeneous polymerization of polyoleﬁns the original catalyst particles fracture and are encapsulated in solid polymer. Porous polymer particles are made, and they grow as the polymerization proceeds (6, 7). The diffusion resistance to 1 To whom correspondence should be addressed. monomers during polymerization to polyoleﬁn particles may have a signiﬁcant effect on the observed activity. This diffusion resistance depends on the diffusivity of the monomers in the different areas of the particles, and this diffusivity is, in general, unknown (7, 8). The purpose of this article is to show how PFG-NMR can be used to measure diffusion of small molecules in porous polymer particles and to discover which effects one has to take into con- sideration to give reliable values for the diffusion coefﬁcient in different areas of the particles. The PFG-NMR method has been used to measure diffusion coefﬁcients of liquids in different areas of such a system. Mea- surements done in polyethylene (PE) particles produced in a full- scale industrial reactor are compared with measurements done in model systems consisting of monodisperse porous polystyrene particles having various pore size distributions. In heterogeneous systems, internal magnetic ﬁeld gradients may be a signiﬁcant source of error. These internal gradients are induced because of differences in magnetic susceptibility between the different areas in an heterogeneous sample and may consist of a broad distribution of values with both polarities (9–11). A coupling between the applied and internal magnetic ﬁeld gradients will occur (12), and depending on the relative strength between the internal gradients and the applied ones, the measured diffusion coefﬁcient may not correspond to the actual diffusivity in the system. This source of error can often be eliminated by introducing bipolar gradients in the pulse sequence (13–17), but in a recent publication (18), it was shown that when bipolar gradients are used to suppress the effects of internal gradients, the observation time must be kept to a level where the square root of mean square displacement does not exceed the distance in which it is likely that an internal gradient will change its polarity or its strength signiﬁcantly. This has to be taken into account at long observation times in some of the systems studied here, and we discuss how this error can be compensated for. The PE particles have a complex morphology and geometry. When a liquid is added to this system, it will occupy different domains of the particles. The two main domains will be the 168 0021-9797/01 $35.00 Copyright C  2001 by Academic Press All rights of reproduction in any form reserved.