Dynamics of a Polymer Solution in a Rigid Matrix. 2 Carmen Kloster, †,‡ Clara Bica, ‡ Cyrille Rochas, † Dimitrios Samios, ‡ and Erik Geissler* ,† Laboratoire de Spectrome ´ trie Physique, CNRS UMR 5588, B.P. 87, 38402 St Martin d’He ` res Cedex, France, and Laboratorio de Instrumentac ¸ a ˜ o e Dina ˆ mica molecular, Instituto de Quimica, Universidade Federal do Rio Grande do Sul, Porto Alegre, Bento Gonc ¸ alves 9500, Rio Grande do Sul, Brazil Received November 30, 1999; Revised Manuscript Received June 1, 2000 ABSTRACT: Dynamic light scattering measurements of the diffusion coefficient D and the Rayleigh ratio R θ are reported for dextran molecules confined in agarose gel networks of various concentrations. In this condition, the light scattered by the dextran is some 2 orders of magnitude less intense than that from the agarose. Three molecular weights of dextran were investigated: 7 × 10 4 ,5 × 10 5 , and 2 × 10 6 g mol -1 . For the lowest molar mass it is confirmed that, below the dextran overlap concentration c*, the product DRθ is independent of the agarose concentration, showing that the reduction of the rate of diffusion inside the gel is the result of a decrease in the osmotic pressure in the confined geometry. For the higher molar masses, entanglement effects between the dextran and the network become noticeable in the more highly concentrated gels. The dynamic light scattering intensity measurements are also found to yield reasonable estimates of the molar mass Mw and radius of gyration RG of the trapped dextran molecules. The second virial coefficient A2 is positive, indicating that the agarose-water matrix acts as a good solvent for dextran, but the ratio of RG to the hydrodynamic radius is less than 1.5. These results are interpreted in terms of branching of the dextran molecule. Introduction Over the past two decades, a number of investigations have been made into the diffusion of probe particles inside polymer solutions and gels using dynamic light scattering. 1-8 Recently, we extended this technique to include measurements of the intensity of the scattered light, applied to low molar mass dextran solutions (M w ≈ 70 000 g mol -1 ) trapped inside agarose gels. 9 In this system, the two components are miscible over a limited concentration range, above which the gel that is formed displays phase separation on a macroscopic scale. In the range of miscibility the dextran molecules migrate freely throughout the volume of the sample that is not oc- cupied by the agarose, and their behavior is therefore similar to that of a liquid. The light scattered by the gel structure itself was found to be some 2 or 3 orders of magnitude more intense than that scattered by the mobile macromolecules, with the result that the latter was strongly heterodyned. In this situation, photon correlation spectroscopy can be used to discriminate between these two components since, in the concentra- tion range of interest, agarose gels are virtually im- mobile at room temperature; in the pure gel residual motions were found to scatter between 0.01 and 0.05% of the total light, depending on the agarose concentra- tion. In this system, then, the only significant dynamic component is that of the mobile guest polymer. Analysis of the resulting intensity correlation functions accord- ingly yields not only the corresponding diffusion coef- ficient D but also the Rayleigh ratio R θ . The results of ref 9 may be summarized as follows. For concentrations below the overlap concentration c*, the diffusion coefficient D of the dextran in the gel is depressed with respect to the free solution. Conversely, the intensity R θ scattered by the trapped molecules is enhanced over that in the free state. The product of these two quantities, DR θ , however, was found to depend only on the dextran concentration c and to be independent of the gel concentration c g . These results showed that the reduction in diffusion rate is not due to frictional effects but instead comes from a depression of the osmotic pressure due to configurational entropy loss in the confined volume of the gel. It is natural to try to extend these observations to larger guest molecules in order to explore larger length scales in the gel. For this reason, in this article we report measurements on agarose gels containing dextran solu- tions of higher molar mass, namely 5 × 10 5 and 2 × 10 6 g mol -1 , the radii of gyration R G of which are appreciably larger. Experimental Section The sample preparation was described in detail in ref 9. Three lots of dextran, of molar mass Mw ) 7 × 10 4 , 5.0 × 10 5 , and 2.0 × 10 6 g mol -1 , were used as supplied by Sigma. The molar mass of the agarose, kindly provided by R. Armisen (Hispanagar, Spain), was Mw ) 1.2 × 10 5 g mol -1 (sulfate content 0.1%, methyl content 0.6%). Previous measurements 10 of the molar mass of these samples yielded the results displayed in Table 1. The appropriate weights of agarose and dextran were mixed in deionized water and heated to 100 °C and stirred to complete dissolution. The solutions were sealed in 10 mm diameter cylindrical glass tubes, then melted again at 100 °C, and allowed to cool to room temperature. Gelation of the agarose occurred as the temperature fell to 45 °C. Dextran and agarose form uniform gels in water over a limited concentration range, above which macroscopic phase separation occurs. The phase diagram is shown in Figure 1. The experiments described in this article were all conducted in the region of miscibility. Dynamic light scattering measurements were made with a Spectra Physics SP1161 laser working at 488 nm and a Malvern Instruments 7032 multibit correlator. All measure- ments were made in a temperature-controlled bath at 25 °C. † Laboratoire de Spectrome ´trie Physique. ‡ Laboratorio de Instrumentac ¸ a ˜o e Dina ˆ mica molecular. 6372 Macromolecules 2000, 33, 6372-6377 10.1021/ma992005q CCC: $19.00 © 2000 American Chemical Society Published on Web 07/29/2000