Measuring the Mutual Diffusion Coefficient for Dodecyl Acrylate in Low Molecular Weight Poly(dodecyl acrylate) with Laser Line Deflection (Wiener’s Method) and the Fluorescence of Pyrene Daniel Antrim, † Patrick Bunton, ‡ Lydia Lee Lewis, § Brian D. Zoltowski, † and John A. Pojman* ,† Department of Chemistry and Biochemistry, The UniVersity of Southern Mississippi, Hattiesburg, Missisippi 39406, Department of Physics, William Jewell College, 500 College Hill, Liberty, Missouri 64068, and Department of Chemistry, Millsaps College, Jackson, Mississippi 39210 ReceiVed: January 14, 2005; In Final Form: April 16, 2005 Diffusion of small molecules into glassy polymers is quite complicated and almost always non-Fickian. Little work has been done with the diffusion of low molecular weight polymers that are liquids at room temperature (such as poly(dodecyl acrylate)) into their miscible monomers. We have studied three molecular weights under 20 000 to determine if poly(dodecyl acrylate) diffusion into dodecyl acrylate could be treated with Fick’s law and if so to determine the values of the diffusion coefficients. We compare two methods for measuring the diffusion of dodecyl acrylate into poly(dodecyl acrylate): We used laser line deflection (Wiener’s method) and improved upon the method from published reports. We also used the dependence of pyrene’s fluorescence on the viscosity to measure the concentration distribution, and thus to extract the diffusion coefficient. After an initial relaxation period, diffusion in all cases followed Fick’s law with a single concentration-independent diffusion coefficient. Comparison of the diffusion coefficients obtained by both methods yielded the same order of magnitude for the diffusion coefficients (10 -7 cm 2 /s) and showed the same trend in the dependence on the average molecular weight of the polymer (a decrease in the diffusion coefficient with an increase in the molecular weight). 1. Introduction Korteweg first discussed the possibility that sharp, compo- sitional gradients in miscible fluids could act like interfacial tensions. 1 He proposed that such a transient, or effective, interfacial tension could be represented by a term that accounts for nonlocal interactions, and this term was proportional to the square of the compositional gradient. These interfacial tensions at miscible interfaces have been studied by Zeldovich, who considered the problem of an effective interfacial tension between miscible fluids, 2 and by Joseph and Renardy, who provided a superb review of the topic up to 1992. 3 We have been investigating the possible role of effective, or transient, interfacial tension in miscible fluids, particularly how such stresses could cause convection at a sharp transition zone between miscible fluids (analogous to Marangoni convection). Specifically, we have shown through simulations that when a Korteweg stress term is added to the Navier-Stokes equations for miscible fluids that convection can indeed occur. 4-6 To accurately perform these simulations, we need to know the nature of the mass transport, or diffusion, between a polymer (e.g., poly(dodecyl acrylate) or PDDA) and its monomer (e.g., dodecyl acrylate or DDA). There are two general cases of solvent diffusion into polymers: 7 diffusion into a glassy polymer and diffusion into a nonglassy polymer. Solvent diffusion into a glassy polymer is anomalous diffusion (two different diffusion rates for the monomer diffusion into the polymer and the polymer diffusion into the monomer) and cannot be adequately represented by Fick’s law or by a single, concentration-independent diffusion coefficient. 7-12 Solvent diffusion into a nonglassy polymer exhibits mutual diffusion, which can be represented by Fick’s law and which may be represented by a single, concentration- independent diffusion coefficient. 7 The polymer in our studies of fluid motion induced by Korteweg stresses must be able to flow. 4-6 Thus, low molecular weight PDDA is not a glassy polymer, and these PDDA systems may have mutual diffusion. We had two goals for this work: To determine if the mutual diffusion of low molecular weight PDDA and DDA could be represented by a single concentration-independent diffusion coefficient and to determine the value of that coefficient for three different molecular weights. We monitored the diffusion of PDDA and DDA by two methodsslaser line deflection (LLD or Wiener’s method 13 ) and the viscosity dependence of ultraviolet- excited fluorescence of pyrenesand determined the diffusion coefficient by three analysessa Gaussian curve fit (full-curve fit) and the method of Rashidnia et al. 14 for the LLD data and a complementary error-function fit for the fluorescence data. The two monitoring techniques showed the evolution of an initial, sharp concentration gradient, which experienced a relaxation time of 30 to 50 min after which the system continued to relax according to Fick’s law. For the portion of the system that experienced Fickian diffusion, all three analyses provided nearly the same value for the diffusion coefficient for a given molecular weight of the PDDA. The analysis technique of Rashidnia et al. 14 utilized only a portion of the data obtained * Author to whom correspondence should be addressed. E-mail: john@ pojman.com. † The University of Southern Mississippi. ‡ William Jewell College. § Millsaps College. 11842 J. Phys. Chem. B 2005, 109, 11842-11849 10.1021/jp0502609 CCC: $30.25 © 2005 American Chemical Society Published on Web 05/18/2005