PHYSICAL REVIEW E 84, 011604 (2011) Effect of polymer on the elasticity of surfactant membranes: A light scattering study Ram´ on I˜ niguez-Palomares, Heriberto Acu˜ na-Campa, and Amir Maldonado Departamento de F´ ısica, Universidad de Sonora, 83000 Hermosillo, Sonora, Mexico (Received 21 August 2010; published 8 July 2011) We have performed a dynamic light-scattering (DLS) investigation of the effect of a water-soluble polymer, polyethylene glycol (PEG), on the bending elastic modulus κ of surfactant membranes. The polymer, in concentrations ranging from 0 to 8 g/L (0 to 0.4 mM), was incorporated into the solvent of sponge phases of the sodium dodecyl sulfate (SDS)-hexanol-brine system. PEG adsorbs into the SDS membranes. The correlation functions of the polymer-doped sponge phases displayed a stretched-exponential decay, appropriately described by the Zilman-Granek (Z-G) theory for fluctuating membranes. The dynamics of the surfactant bilayers was slowed down by the addition of the polymer: Increasing PEG concentrations increase the DLS relaxation times. From the Z-G model we extracted the membrane-bending elastic modulus, as a function of polymer concentration, C PEG = κ increases with C PEG , a behavior opposite to that expected from available models for the interaction between fluid membranes and adsorbing polymers. Our results suggest that the polymer penetrates to some extent the surfactant bilayers. DOI: 10.1103/PhysRevE.84.011604 PACS number(s): 68.15.+e, 82.70.Uv, 87.64.Cc I. INTRODUCTION Surfactants in solution give rise to different equilibrium phases [1], depending on the values of the physicochem- ical variables (concentration, temperature, concentration of additives, etc.). There are two basic local structures: mi- celles (spherical or cylindrical) and bilayers (membranes). In both cases the hydrophobic tail of the surfactant molecule avoids water contact by hiding in the interior of the structure. Bilayers in aqueous solutions are formed by two surfactant monolayers facing each other through their hydrophobic moieties. At a larger scale, surfactant bilayers can adopt several configurations. Two of the most common are the so-called lamellar [2] and sponge phases [3]. In the first case, the membranes arrange in a parallel stack of fluctuating bilayers separated by solvent; the system is characterized by the interbilayer distance d and the bilayer thickness δ, related through the surfactant volume fraction φ by the classical dilution law φ = δ/d. On the other hand, the sponge phase (Fig. 1) is a disordered array of bilayers continually connected in the three dimen- sions; this phase can be pictured as a structure containing pores or passages separating two equivalent volumes of solvent. A characteristic distance d is measured in appropriate static scattering experiments; it can be interpreted as a mean interbilayer distance or as the mean diameter of the pores in the structure. In the sponge phase, d is also related to the bilayer thickness by the dilution law: φ = αδ/d, where α depends on the topology of the phase and has a value near to 1.5. It is interesting to study and understand the properties of lamellar or sponge phases doped with polymers of dif- ferent chemical characteristics: water-soluble, nonadsorbing polymers, adsorbing polymers, or amphiphilic polymers. The interaction between surfactant structures and polymers is of interest because of the applications of the mixed systems. Surfactants are relevant in detergency, wetting, foaming, or emulsification, while polymers are usually added to control the viscosity of the solutions. The phase behavior as well as the physical properties of these systems strongly depend on the polymer-membrane interactions. In the literature there are several reports, both experimental [4–20] and theoretical [21–25], on the effect of polymers on lamellar or sponge phases. For instance, in a previous work, it has been shown that the addition of polyethylene glycol (PEG) to the lamellar or sponge phase of the sodium dodecyl sulfate (SDS)-hexanol- brine system produces the appearance of a vesicular phase in coexistence with excess solvent [20]. The actual mechanism of this transformation is not completely understood so far, but one can argue that the polymer modifies the Gaussian elastic constant of the surfactant bilayers and thus triggers a topological phase transformation. In order to obtain a better insight into the mechanism of the reported lamellar (sponge)- vesicular transformation, it is interesting to study the elastic properties of the membranes of this system, as a function of polymer concentration. In this context, we have carried out a systematic light- scattering study of the effect of increasing concentrations of PEG on the bending elastic modulus of SDS-hexanol-brine sponge phases. The experimental results are reported in this paper. The aim is to understand the effect of the polymer on the elastic properties of the surfactant membranes. The paper is organized as follows. In the next section we provide a brief theoretical as well as experimental background to our work. In Sec. III we give the details of our experiments. In Sec. IV we present and discuss our results. Finally, in Sec. V we draw conclusions of our investigation. In the supplementary material, we present related experimental results obtained for our system [40]. II. BACKGROUND A. Bilayer elastic constants The elastic properties of surfactant membranes can be described by the bending elastic modulus κ and the Gaussian 011604-1 1539-3755/2011/84(1)/011604(6) ©2011 American Physical Society