Geoffrey Gorisse
email: geoffrey.gorisse@ensam.eu

Olivier Christmann
email: olivier.christmann@ensam.eu

Samory Houzangbe
email: samory.houzangbe@ensam.eu

Simon Richir
email: simon.richir@ensam.eu

From Robot to Virtual Doppelganger: Impact of Avatar Visual Fidelity and Self-esteem on Perceived Attractiveness

Keywords: Human-centered computing → Virtual reality; virtual reality, embodiment, avatar, doppelganger, self-esteem, attractiveness

This paper presents the first study of a series of experiments aiming to investigate the impact of avatar visual fidelity on user experience with emphasis on the sense of embodiment in immersive virtual environments (IVE). This first experiment requires participants to evaluate three characters with several levels of visual fidelity: a robot, a suit and a virtual doppelganger. Statistical analyses were performed to assess the impact of truthfulness (degree of similarity between users and avatars) and self-esteem on perceived avatars' attractiveness. Our results demonstrate the positive impact of truthfulness on the evaluation of attractiveness and suggest a correlation between self-esteem and avatar selection.

INTRODUCTION AND RELATED WORK

User experience in immersive virtual environment (IVE) has been the subject of numerous investigations aiming to determine hardware and software properties of a virtual reality system allowing to immerse users [START_REF] James | How immersive is enough? A meta-analysis of the effect of immersive technology on user presence[END_REF]. In this context, we present herein the results Figure 1: Illustration of three raw bust models (50K polygons) and their optimized versions (2.5K polygons) integrated in the virtual reality application from the first study of a series of experiments addressing the impact of avatar visual fidelity [START_REF] Lugrin | Avatar anthropomorphism and illusion of body ownership in VR[END_REF] on the sense of embodiment [START_REF] Gorisse | First-and Third-Person Perspectives in Immersive Virtual Environments: Presence and Performance Analysis of Embodied Users[END_REF][START_REF] Kilteni | The sense of embodiment in virtual reality[END_REF] and its behavioral implications induced by the Proteus effect [START_REF] Kilteni | Drumming in immersive virtual reality: the body shapes the way we play[END_REF][START_REF] Yee | The Proteus effect: The effect of transformed self-representation on behavior[END_REF]. Previous work classifies visual fidelity according to the following three criteria:

• Anthropomorphism (non-humanoid <-> humanoid): Morphological characteristics of the virtual character. • Realism (few detailed <-> photorealistic): level of detail of the mesh and textures of the 3D model. • Truthfulness (does not look like the user <-> looks like the user): degree of similarity between the user and the virtual character [START_REF] Benford | Embodiments, avatars, clones and agents for multi-user, multisensory virtual worlds[END_REF].

In this theoretical framework, the purpose of our study is to immerse the user in front of three virtual characters with several levels of truthfulness while keeping a constant level of anthropomorphism (humanoid body schema [3]) and realism. The degree of similarity with the user is therefore used as a variable in order to observe and evaluate the subjective impact of truthfulness on perceived avatars' attractiveness [START_REF] Fleming | Appealing female avatars from 3D body scans: Perceptual effects of stylization[END_REF][START_REF] Zell | To Stylize or Not to Stylize?: The Effect of Shape and Material Stylization on the Perception of Computer-generated Faces[END_REF]. At the end of our series of experiments, the first one being introduced here, we will be able to analyze the potential benefits of observing and controlling our 3D reconstructed virtual self-representation (Figure 1) [START_REF] Chague | Digital cloning for an increased feeling of presence in collaborative virtual reality environments[END_REF][START_REF] Jo | The Impact of Avatar-Owner Visual Similarity on Body Ownership in Immersive Virtual Reality[END_REF]. Previous work demonstrates that facing a virtual doppelganger (virtual version of the self) in immersive environments can impact users' behavior [START_REF] Jeremy | Virtual Doppelgangers: Psychological Effects of Avatars Who Ignore Their Owners[END_REF], but few studies have investigated the impact of realtime control (visuomotor synchrony) of one's own representation, especially in terms of embodiment.

In this context, realism and truthfulness levels induced by the 3D reconstruction of the users entails taking into account the Uncanny Valley phenomenon [START_REF] Mori | The uncanny valley [from the field[END_REF]. Indeed, the similarity and the high level of realism can potentially induce revulsion responses toward the 3D models if the participants observe inconsistencies on their virtual self-representation [START_REF] Karl F Macdorman | Too real for comfort? Uncanny responses to computer generated faces[END_REF][START_REF] Seyama | The uncanny valley: Effect of realism on the impression of artificial human faces[END_REF].

Recent work highlights the effect of self-esteem on reactions and emotions aroused when facing 3D reconstructed doppelgangers [START_REF] Park | Emotional reactions to the 3D virtual body and future willingness: the effects of self-esteem and social physique anxiety[END_REF]. Such additional psychological factors may affect user experience. Thus, particular effort was made in the present study to take into account subjects' self-esteem and its possible impact on the evaluation of avatars' attractiveness.

MATERIAL AND METHODS

In this experiment, users are immersed in front of three avatars with several levels of visual fidelity in a virtual environment. At the end of the session, the participants evaluate the attractiveness of each avatar and choose which one they would like to use for a subsequent experiment. These results are then compared with their self-esteem scores.

The visual fidelity of the avatars integrated in the application is categorized into three levels of truthfulness as follows (Figure 2):

• Robot (Figure 2a): the anthropomorphism level of the robot allows users to project their body schema to control it. However, its morphology does not allow them to imagine that they can be physically located "inside" the character as some parts of the robot (neck, abdomen, etc.) are designed not to match human size.

• Suit (Figure 2b): the suit is morphologically congruent with human size, potentially allowing users to imagine a projection of their body inside of it. • Doppelganger (Figure 2c): the doppelganger is also scaled to human size, but unlike the suit it integrates the 3D reconstruction of the participant's head.

It should be noted that the size of the avatars is calibrated to match the size of the users when launching the application.

VR application

The application used for the experiment was developed using the real-time 3D engine Unity. The proposed environment draws its inspiration from the science fiction universe (Figure 2). This universe anchors the avatars, especially the robot, in a coherent whole providing some plausibility to the depicted scene. The avatars are located in transparent stasis boxes within the immersive virtual environment.

Apparatus

The participants' busts were scanned with a Structure Sensor. The HTC Vive virtual reality headset is used to display the virtual environment with a resolution of 2160 x 1200 pixels (1080 x 1200 pixels per eye), a field of view of 110°and a refresh rate of 90 Hz. The computer running the application is composed of an Intel Core I7-6700HQ @ 2.60 GHz processor and a Nvidia GeForce GTX 1070 graphics card.

Participants

34 male participants, aged from 21 to 42 (M = 23.79, SD = 3.80), were recruited for our experiment. Each subject has a correct or corrected vision thanks to vision glasses allowing them to use the VR headset. All the participants have used an immersive virtual reality system at least once and are experienced with video games involving the control of avatars (role playing games, first and third person shooter, platformer, etc.).

Robot's attractiveness

Procedure and Measures

Before the experiment, the subjects were invited to participate in a 3D scan session and to complete the Rosenberg self-esteem scale (cumulated score ranging from 10 to 40) [START_REF] Rosenberg | The measurement of self-esteem[END_REF][START_REF] Vallieres | TRADUCTION ET VALI-DATION CANADIENNE-FRANÇAISE DE L'ÉCHELLE DE L'ESTIME DE SOI DE ROSENBERG[END_REF]. The participants' 3D models were then optimized to be integrated in the application dedicated to the experiment (Figure 1). Each subject was invited, a few days later, to participate in the experiment.

Once equipped with the virtual reality headset, the participants are immersed in the application for a period of time that is left to their discretion (between 3 and 10 minutes) to observe the three avatars freely. At the end of the experiment, participants complete a questionnaire to assess the attractiveness of each avatar using a five-point semantic scale based on the work of Zell et al. [START_REF] Zell | To Stylize or Not to Stylize?: The Effect of Shape and Material Stylization on the Perception of Computer-generated Faces[END_REF]. They also have to choose the avatar they would prefer to use for the next experiment, which will involve direct control of the character via a real-time motion capture system.

Hypotheses

H1: The truthfulness of the avatars' model has a positive impact on their attractiveness level. H2: Participants with high self-esteem will mostly choose their virtual doppelganger, while participants with lower self-esteem will prefer a more abstract representation.

RESULTS

The Shapiro-Wilk Test was carried out to check the normality of the distributions of the answers to the post experiment questionnaire. As the variables did not follow a normal distribution (p < 0.05 for all tested variables), we chose non-parametric tests to compare avatars' attractiveness and self-esteem scores; results are considered significant when p < 0.05. Bonferroni's correction was used to adjust alpha value for post-hoc pairwise comparisons.

Self-esteem scores, measured prior to the experiment, range from 19 to 40 ( x = 31.09, σ = 4.808). The higher the score, the better the self-esteem. The table 1 presents a summary of descriptive statistics concerning the evaluation of avatars' attractiveness levels (Figure 3) and their selection frequency.

The results of the Friedman Test indicated that there was a statistically significant difference in attractiveness scores between the three truthfulness conditions (robot, suit and doppelganger), χ 2 (2, N = 34) = 11.372, p = 0.003. The doppelganger condition recorded the same median score as the suit condition (Md = 4) and a higher one than the robot group (Md = 3.5). These results demonstrate that truthfulness can impact the evaluation of avatars' attractiveness, providing some evidence concerning the validity of our first hypothesis.

Post-hoc Wilcoxon Signed Ranks Tests revealed a significant difference in the avatars' attractiveness scores between the robot condition (Md = 3.5) and the doppelganger one (Md = 4), Z = 2.453, p = 0.014. Furthermore, a strong trend is observed between the groups who chose the robot and the suit Z = 2.197, p = 0.028. However, this result cannot be considered statistically significant due to the Bonferroni's correction applied to the alpha level for post-hoc tests.

A Kruskal-Wallis Test revealed a significant difference of the self-esteem scores between the groups of participants who chose a different avatar (Robot: N = 3, Suit: N = 12, Doppelganger: N = 19), χ 2 (2, N = 34) = 6.734, p = 0.034. The doppelganger group recorded the same median score as the suit group (Md = 32) and a higher one than the robot group (Md = 25). Therefore, the second hypothesis (H2) seems valid.

Post-hoc Mann-Whitney U Tests revealed a significant difference in the self-esteem levels between the participants who chose the robot (Md = 25) and those who chose the doppelganger (Md = 32), U = 1.5, Z = 2.59, p = 0.01. Furthermore, a trend is observed between

Selected avatar

Doppelganger Suit Robot

Self

DISCUSSION

Previous work addressing issues related to 3D reconstruction has demonstrated the impact of avatar stylization [START_REF] Zell | To Stylize or Not to Stylize?: The Effect of Shape and Material Stylization on the Perception of Computer-generated Faces[END_REF], or even behavioral implications induced by the observation of virtual doppelganger [START_REF] Jeremy | Virtual Doppelgangers: Psychological Effects of Avatars Who Ignore Their Owners[END_REF]. In this context, our research contributes to understanding the impact of avatar visual fidelity and self-esteem on perceived attractiveness. It is interesting to note that some participants noticed the progressive evolution of the truthfulness level of the avatars: "I noticed that the three characters were becoming more and more similar to my physical appearance. Size for the first one, shape for the second and the exact 3D image of my head for the last. "

The results of our experiment reveal the positive impact of truthfulness on the evaluation of avatars' attractiveness. This demonstrates the validity of our first hypothesis. Indeed, the impact of visual fidelity is significant when there is an important truthfulness gap between the 3D models. Thus, the avatars resulting from the 3D reconstruction of the participants have recorded higher attractiveness scores compared to more abstract representations such as the robot one (Figure : 3). Furthermore, 56% of the participants report preferring their doppelganger for the next phase of the experiment involving real-time control of the avatar via a motion capture system: "I would really feel like being in the game. Usually I take a lot of time to build a character that looks like me, so if I have one that looks exactly like me, I'll choose this one. " "It's pleasant to have your own avatar, to feel like a "hero"". "I would choose my own representation because it is a unique avatar. The robot and the suit don't really have an identity, they are anonymous, everyone can play these characters. " However, some participants formulated interesting remarks in favor of the avatars with a lower level of truthfulness, underlining the necessity to further investigate the impact of self-representation in virtual environments:

"The robotic character seems interesting to me, because I'd like to see the different interactions one can have with a body which is not his/her own. "

"I play to distract myself, to "cut myself off from the world", I don't necessarily want the character to look like me. "

According to previous studies [START_REF] Park | Emotional reactions to the 3D virtual body and future willingness: the effects of self-esteem and social physique anxiety[END_REF], self-esteem seems to affect users' reactions when facing their doppelganger. Our statistical analysis confirms these findings and suggests a relation between the avatar selected by the participants and their respective level of self-esteem. Participants with higher self-esteem prefer choosing their own representation, while those with lower self-esteem prefer an alternative one. This trend seems to be true for the three avatars, especially when comparing participants who selected the robot and those who chose their own representation (Figure 4). However, while a majority of the participants emphasize the quality and the realism of 3D reconstructions in open-ended questions, some of them (N = 6) seem to be disturbed by the presence of minor issues due to current hardware limitations. This side effect suggests the occurrence of the Uncanny Valley phenomenon [START_REF] Mori | The uncanny valley [from the field[END_REF][START_REF] Seyama | The uncanny valley: Effect of realism on the impression of artificial human faces[END_REF]. Indeed, the higher the level of realism of 3D models, the less the subjects seem to accept the observed flaws. It is therefore necessary to take into account the limitations of 3D reconstruction technologies before considering their use for the production of virtual reality applications.

CONCLUSION AND FUTURE WORK

The presented experiment investigates the impact of truthfulness of avatars (degree of similarity between users and avatars) and selfesteem on perceived attractiveness and character selection. Thanks to a virtual reality application developed in our lab, the participants were immersed in front of three characters with several levels of visual fidelity: a robot (Figure 2a), a suit (Figure 2b) and a virtual doppelganger (Figure 2c).

Our results demonstrate that attractiveness evaluations are significantly higher for the virtual doppelgangers (direct integration of the participants' head enabled by 3D scanning technologies (Figure 2c)) and highlight the impact of self-esteem on character selection, especially between the extreme conditions (robot versus virtual doppelganger). Participants with the lower self-esteem scores are more prone to choose abstract representations, while participants with higher scores prefer to choose their own representation to enter the virtual world. These results demonstrate the interest of proposing personalized avatars, especially based on users' appearance. However, depending on the context of each virtual reality experience and according to the willingness of some of our participants, it could be useful to propose more abstract characters to increase disconnection from reality.

In our next experiment, we will continue to investigate the impact of avatar fidelity, especially in terms of embodiment and behavior. Users will be able to control the different avatars introduced herein via a motion capture system. They will be involved in a series of tasks and situations that may potentially affect their avatars' integrity. It will then be possible to check the occurrence of the Proteus effect [START_REF] Lugrin | Avatar Anthropomorphism and Acrophobia[END_REF][START_REF] Yee | The Proteus effect: The effect of transformed self-representation on behavior[END_REF] induced by users' representation in immersive virtual environments.

Figure 2 :

 2 Figure 2: Screenshots of the three avatars presented to the participants in the virtual environment

Figure 3 :

 3 Figure 3: Distribution of the avatars' attractiveness scores

Figure 4 :

 4 Figure 4: Boxplot of the participants' self-esteem scores regarding their selected avatar

Table 1 :

 1 Statistical descriptive summary of the avatars' attractiveness scores and of their selection frequency chose the robot and the suit U = 5, Z = 1.892, p = 0.59. Further experiments involving a larger panel could probably confirm this trend.

ACKNOWLEDGMENTS

We thank all the members of our lab for their help in conducting our experiments. Many thanks also to all the people who provided us with insightful comments and advice.


Andrey V Shibaev

Anton V Makarov

Alexander I Kuklin

Ilias Iliopoulos

Olga E Philippova

Role of Charge of Micellar Worms in Modulating Structure and Rheological Properties of Their Mixtures with Nonionic Polymer

Keywords: NMR spectroscopy, SANS, and rheology data (

The paper describes phase behavior, microstructure, and rheological properties of the mixtures of surfactant micelles of varying negative charge with nonionic hydrophilic polymer poly(vinyl alcohol) (PVA) weakly interacting with the micelles. To reduce the charge of micelles, a cationic surfactant n-octyltrimethylammonium bromide was gradually added to the anionic surfactant potassium oleate. No appreciable interactions between the micelles and polymer were revealed by NMR spectroscopy. At the same time, the system shows a broad range of compatibility, which may be due to surfactant counterions preventing the demixing. The higher the concentration of added polymer, the higher the charge density of micelles necessary to prevent macrophase separation. However, SANS data demonstrate that upon the addition of polymer the intermicellar distances decrease, which suggests that the micelles are expelled from some area filled by PVA macromolecules, indicating a local demixing. A decrease of micellar charge density induces the growth of micelles from short nonoverlapping cylinders to long entangled wormlike chains both in the presence and in the absence of polymer, which is accompanied by an increase of viscosity by up to 5 orders of magnitude. Despite very weak interactions with the micelles, PVA makes their growth in length much more pronounced and forms the entanglements with micellar chains, thereby enhancing significantly the viscoelastic properties. The effect of polymer on micellar length was attributed to polymer-surfactant microsegregation increasing the local surfactant concentration and consequently the length of micelles. These data demonstrate the effectiveness of the addition of weakly interacting polymer for the modulation of rheology of wormlike surfactant micelles, thus opening a new way for manipulating the rheological properties of viscoelastic surfactants.

■ INTRODUCTION

Wormlike micelles (WLMs) of ionic surfactants can form transient networks imparting viscoelastic properties to aqueous solutions. [START_REF] Zana | Giant Micelles: Properties and Applications[END_REF][START_REF] Feng | Smart Wormlike Micelles: Design, Characteristics and Applications[END_REF][START_REF] Dreiss | Wormlike Micelles: Advances in Systems, Characterisation and Applications[END_REF][START_REF] Magid | The Surfactant-Polyelectrolyte Analogy[END_REF][START_REF] Yang | Viscoelastic Wormlike Micelles and their Applications[END_REF][START_REF] Dreiss | Wormlike Micelles: where Do we Stand? Recent Developments, Linear Rheology and Scattering Techniques[END_REF][START_REF] Chu | Smart Wormlike Micelles[END_REF][START_REF] Zhao | Investigation of Novel Triple-Responsive Wormlike Micelles[END_REF][START_REF] Morishima | Structure and Rheology of Wormlike Micelles Formed by Fluorocarbon-Hydrocarbon-Type Hybrid Gemini Surfactant in Aqueous Solution[END_REF] These properties are widely exploited for thickening and rheology-control applications in many area including cosmetics, turbulent drag reduction, oil recovery, and so on. [START_REF] Zana | Giant Micelles: Properties and Applications[END_REF][START_REF] Feng | Smart Wormlike Micelles: Design, Characteristics and Applications[END_REF][START_REF] Dreiss | Wormlike Micelles: Advances in Systems, Characterisation and Applications[END_REF][START_REF] Yang | Viscoelastic Wormlike Micelles and their Applications[END_REF] A large variety of applications stimulates an appropriate modification of the viscoelastic properties of WLM solutions.

One of the ways to modify the rheology of WLMs consists in their combination with polymers. [START_REF] Hoffmann | Self-Aggregation of Mixtures of Oppositely Charged Polyelectrolytes and Surfactants Studied by Rheology, Dynamic Light Scattering and Small-Angle Neutron Scattering[END_REF][START_REF] Couillet | Synergistic Effects in Aqueous Solutions of Mixed Wormlike Micelles and Hydrophobically Modified Polymers[END_REF][START_REF] Shashkina | Rheology of Viscoelastic Solutions of Cationic Surfactant. Effect of Added Associating Polymer[END_REF][START_REF] Chen | Self-assembly Networks of Wormlike Micelles and Hydrophobically Modified Polyacrylamide with High Performance in Fracturing Fluid Application[END_REF][START_REF] Yoshida | Viscoelastic Synergy in Aqueous Mixtures of Wormlike Micelles and Model Amphiphilic Triblock Copolymers[END_REF][START_REF] Lodge | SANS Evidence for the Cross Linking of Wormlike Micelles by a Model Hydrophobically Modified Polymer[END_REF][START_REF] Ramos | Structure of a New Type of Transient Network: Entangled Wormlike Micelles Bridged by Telechelic Polymers[END_REF][START_REF] Molchanov | Dominant Role of Wormlike Micelles in Temperature-Responsive Viscoelastic Properties of their Mixtures with Polymeric Chains[END_REF][START_REF] Peiffer | Hydrophobically Associating Polymers and their Interactions with Rod-like Micelles[END_REF][START_REF] Oikonomou | Formation of Hybrid Wormlike Micelles upon Mixing Cetyl Trimethylammonium Bromide with Poly(methyl methacrylate-cosodium styrene sulfonate) Copolymers in Aqueous Solution[END_REF][START_REF] Brackman | Influence of Polymers on the Micellization of Cetyltrimethylammonium Salts[END_REF][START_REF] Li | Polymer-Induced Microstructural Transitions in Surfactant Solutions[END_REF][START_REF] Lin | Polymer-Induced Structural Transitions in Oleate Solutions: Microscopy, Rheology, and Nuclear Magnetic Resonance Studies[END_REF][START_REF] Shibaev | Viscoelastic Synergy and Microstructure Formation in Aqueous Mixtures of Nonionic Hydrophilic Polymer and Charged Wormlike Surfactant Micelles[END_REF] In many cases, addition of polymeric chains enhances the viscoelasticity of WLM solutions. [START_REF] Hoffmann | Self-Aggregation of Mixtures of Oppositely Charged Polyelectrolytes and Surfactants Studied by Rheology, Dynamic Light Scattering and Small-Angle Neutron Scattering[END_REF][START_REF] Couillet | Synergistic Effects in Aqueous Solutions of Mixed Wormlike Micelles and Hydrophobically Modified Polymers[END_REF][START_REF] Shashkina | Rheology of Viscoelastic Solutions of Cationic Surfactant. Effect of Added Associating Polymer[END_REF][START_REF] Chen | Self-assembly Networks of Wormlike Micelles and Hydrophobically Modified Polyacrylamide with High Performance in Fracturing Fluid Application[END_REF][START_REF] Yoshida | Viscoelastic Synergy in Aqueous Mixtures of Wormlike Micelles and Model Amphiphilic Triblock Copolymers[END_REF][START_REF] Lodge | SANS Evidence for the Cross Linking of Wormlike Micelles by a Model Hydrophobically Modified Polymer[END_REF][START_REF] Ramos | Structure of a New Type of Transient Network: Entangled Wormlike Micelles Bridged by Telechelic Polymers[END_REF][START_REF] Molchanov | Dominant Role of Wormlike Micelles in Temperature-Responsive Viscoelastic Properties of their Mixtures with Polymeric Chains[END_REF][START_REF] Peiffer | Hydrophobically Associating Polymers and their Interactions with Rod-like Micelles[END_REF][START_REF] Shibaev | Viscoelastic Synergy and Microstructure Formation in Aqueous Mixtures of Nonionic Hydrophilic Polymer and Charged Wormlike Surfactant Micelles[END_REF] In particular, an increase of viscosity by few orders of magnitude was observed at bridging the WLMs by macromolecules interacting simultaneously with different micelles. [START_REF] Hoffmann | Self-Aggregation of Mixtures of Oppositely Charged Polyelectrolytes and Surfactants Studied by Rheology, Dynamic Light Scattering and Small-Angle Neutron Scattering[END_REF][START_REF] Couillet | Synergistic Effects in Aqueous Solutions of Mixed Wormlike Micelles and Hydrophobically Modified Polymers[END_REF][START_REF] Shashkina | Rheology of Viscoelastic Solutions of Cationic Surfactant. Effect of Added Associating Polymer[END_REF][START_REF] Chen | Self-assembly Networks of Wormlike Micelles and Hydrophobically Modified Polyacrylamide with High Performance in Fracturing Fluid Application[END_REF][START_REF] Yoshida | Viscoelastic Synergy in Aqueous Mixtures of Wormlike Micelles and Model Amphiphilic Triblock Copolymers[END_REF][START_REF] Lodge | SANS Evidence for the Cross Linking of Wormlike Micelles by a Model Hydrophobically Modified Polymer[END_REF][START_REF] Ramos | Structure of a New Type of Transient Network: Entangled Wormlike Micelles Bridged by Telechelic Polymers[END_REF][START_REF] Molchanov | Dominant Role of Wormlike Micelles in Temperature-Responsive Viscoelastic Properties of their Mixtures with Polymeric Chains[END_REF][START_REF] Peiffer | Hydrophobically Associating Polymers and their Interactions with Rod-like Micelles[END_REF] The interactions can be either electrostatic or hydrophobic, or both. The electrostatic attraction occurs when polymer is oppositely charged with respect to the micelles like in the case of cationic, cellulose-based polyelectrolyte, and anionic surfactants sodium dodecylbenzenesulfonate and sodium dodecylethoxysulfate. [START_REF] Hoffmann | Self-Aggregation of Mixtures of Oppositely Charged Polyelectrolytes and Surfactants Studied by Rheology, Dynamic Light Scattering and Small-Angle Neutron Scattering[END_REF] The hydrophobic interactions usually prevail when uncharged water-soluble polymers with few hydrophobic side [START_REF] Couillet | Synergistic Effects in Aqueous Solutions of Mixed Wormlike Micelles and Hydrophobically Modified Polymers[END_REF][START_REF] Shashkina | Rheology of Viscoelastic Solutions of Cationic Surfactant. Effect of Added Associating Polymer[END_REF][START_REF] Chen | Self-assembly Networks of Wormlike Micelles and Hydrophobically Modified Polyacrylamide with High Performance in Fracturing Fluid Application[END_REF] or end [START_REF] Yoshida | Viscoelastic Synergy in Aqueous Mixtures of Wormlike Micelles and Model Amphiphilic Triblock Copolymers[END_REF][START_REF] Lodge | SANS Evidence for the Cross Linking of Wormlike Micelles by a Model Hydrophobically Modified Polymer[END_REF][START_REF] Ramos | Structure of a New Type of Transient Network: Entangled Wormlike Micelles Bridged by Telechelic Polymers[END_REF] groups capable to penetrate in the surfactant core are added to WLMs. Such a situation was described for uncharged hydrophobically modified (HM) polysaccharide guar with cationic surfactant erucyl bis(hydroxyethyl)methylammonium chloride (EHAC), [START_REF] Couillet | Synergistic Effects in Aqueous Solutions of Mixed Wormlike Micelles and Hydrophobically Modified Polymers[END_REF] for HM polyacrylamide with EHAC [START_REF] Shashkina | Rheology of Viscoelastic Solutions of Cationic Surfactant. Effect of Added Associating Polymer[END_REF] and cationic gemini surfactant 1,2-N,N′-bis(dimethyloctadecyl)ethene ammonium bromide, [START_REF] Chen | Self-assembly Networks of Wormlike Micelles and Hydrophobically Modified Polyacrylamide with High Performance in Fracturing Fluid Application[END_REF] and for poly(ethylene oxide) end-capped with alkyl groups interacting with cationic cetyltrimethylammonium tosylate [START_REF] Yoshida | Viscoelastic Synergy in Aqueous Mixtures of Wormlike Micelles and Model Amphiphilic Triblock Copolymers[END_REF][START_REF] Lodge | SANS Evidence for the Cross Linking of Wormlike Micelles by a Model Hydrophobically Modified Polymer[END_REF] and cetylpyridinium chloride/sodium salicylate [START_REF] Ramos | Structure of a New Type of Transient Network: Entangled Wormlike Micelles Bridged by Telechelic Polymers[END_REF] micelles. Hydrophobic attraction also governs the bridging of WLMs by HM polyelectrolytes of similar charge in the presence of salt as was demonstrated for partially hydrolyzed polyacrylamide mixed with anionic WLMs of potassium oleate. [START_REF] Molchanov | Dominant Role of Wormlike Micelles in Temperature-Responsive Viscoelastic Properties of their Mixtures with Polymeric Chains[END_REF] Both electrostatic and hydrophobic binding to the WLMs are expected for weakly charged HM polyelectrolytes carrying opposite charge with respect to the micelles. [START_REF] Peiffer | Hydrophobically Associating Polymers and their Interactions with Rod-like Micelles[END_REF] Independently of the nature of polymer-surfactant interactions, it is important to ensure that these interactions are not too strong to violate the geometric balance of the head and tail groups of surfactant (packing parameter) enough to destabilize the cylindrical geometry. [START_REF] Oikonomou | Formation of Hybrid Wormlike Micelles upon Mixing Cetyl Trimethylammonium Bromide with Poly(methyl methacrylate-cosodium styrene sulfonate) Copolymers in Aqueous Solution[END_REF] Otherwise, it will lead to the disruption of WLMs as a result of cylinder-sphere transition [START_REF] Brackman | Influence of Polymers on the Micellization of Cetyltrimethylammonium Salts[END_REF][START_REF] Li | Polymer-Induced Microstructural Transitions in Surfactant Solutions[END_REF][START_REF] Lin | Polymer-Induced Structural Transitions in Oleate Solutions: Microscopy, Rheology, and Nuclear Magnetic Resonance Studies[END_REF] accompanied by the loss of viscoelastic properties or even to the precipitation of the polymersurfactant complexes. [START_REF] Li | Polymer-Induced Microstructural Transitions in Surfactant Solutions[END_REF] Recently, it was shown [START_REF] Shibaev | Viscoelastic Synergy and Microstructure Formation in Aqueous Mixtures of Nonionic Hydrophilic Polymer and Charged Wormlike Surfactant Micelles[END_REF] that a pronounced enhancement of rheological properties can be achieved by using a polymer weakly interacting with the micelles, if one can get a homogeneous system with sufficiently high concentration of the components providing a significant interlacement between polymer and micellar chains. This system seems to be very promising since it can be based on a variety of common commercially available water-soluble polymers. To enhance compatibility of the weakly interacting components, the micellar chains should be charged and the ionic strength of solution low, which makes demixing unfavorable, since it will induce a pronounced loss of translational entropy of surfactant counterions. [START_REF] Shibaev | Viscoelastic Synergy and Microstructure Formation in Aqueous Mixtures of Nonionic Hydrophilic Polymer and Charged Wormlike Surfactant Micelles[END_REF] At the same time, the poor compatibility between polymer and micellar components leads to their microsegregation (microphase separation) with the formation of polymer-rich and surfactant-rich domains, which was evidenced by cryo-transmission electron microscopy (cryo-TEM). [START_REF] Shibaev | Viscoelastic Synergy and Microstructure Formation in Aqueous Mixtures of Nonionic Hydrophilic Polymer and Charged Wormlike Surfactant Micelles[END_REF] The domain structure percolating the whole system gives enough space to counterions to keep high translational entropy, whereas the local segregation of poorly compatible components provides the gain in interaction energy. Charged WLMs in the absence of added salt, which are necessary for the stability of such system, can be prepared from a pair of oppositely charged surfactants [START_REF] Raghavan | Wormlike Micelles Formed by Synergistic Self-Assembly in Mixtures of Anionic and Cationic Surfactants[END_REF][START_REF] Ziserman | Origins of the Viscosity Peak in Wormlike Micellar Solutions. 1. Mixed Catanionic Surfactants. A Cryo-Transmission Electron Microscopy Study[END_REF][START_REF] Kume | Review on Anionic/Cationic Surfactant Mixtures[END_REF][START_REF] Koshy | Viscoelastic Fluids Originated from Enhanced Solubility of Sodium Laurate in Cetyl Trimethyl Ammonium Bromide Micelles through Cooperative Self-Assembly[END_REF][START_REF] Huang | Rheological Properties and Application of Wormlike Micelles Formed by Sodium Oleate/Benzyltrimethyl Ammonium Bromide[END_REF] (OCS). Up to now, surfactant-polymer systems were studied only for OCS micelles of constant composition, i.e., at fixed degree of charging. [START_REF] Shibaev | Viscoelastic Synergy and Microstructure Formation in Aqueous Mixtures of Nonionic Hydrophilic Polymer and Charged Wormlike Surfactant Micelles[END_REF] At the same time, one can suggest that the charge of micelles should play a key role in the behavior of weakly interacting surfactant-polymer system, in particular, in the compatibility of the components and in the viscoelastic properties.

Thus, the aim of this paper is to investigate the effect of the degree of charging of surfactant micelles on the rheology and the microstructure of their mixtures with nonionic polymer weakly interacting with the micelles. For this purpose, we used charged micelles of anionic surfactant potassium oleate and cationic surfactant n-octyltrimethylammonium bromide (C 8 TAB) and nonionic water-soluble polymer PVA. The charge of the OCS micelles was varied by changing the molar ratio β of cationic and anionic surfactants. To make the effect of micellar charge clearer, no low molecular weight salt was added to the solutions. We demonstrate that lowering of the charge density of potassium oleate micelles at the addition of oppositely charged surfactant leads to the growth of micelles in length and the transition of the system from dilute to semidilute regime. The presence of polymer makes this growth much more pronounced and induces the interlacing between polymer and WLMs, which results in the significantly enhanced rheological properties. These findings provide new insights and foster a better understanding of the behavior of the mixed systems based on a combination of "living" micellar assemblies and polymeric chains, which can open the way for new practical applications of these industrially important systems.

■ EXPERIMENTAL SECTION

Materials. Potassium oleate (potassium cis-9-octadecanoate, C 9 H 18 = C 8 H 15 COOK) was purchased from TCI (purity >98%), C 8 TAB was obtained from ABCR (purity >98%), and PVA with a molar mass 27 000 g/mol (degree of polymerization N ≈ 600) and residual content of acetate units 1.1-1.9% (Mowiol 4-98) was obtained from Aldrich. All chemicals were used without further purification. Distilled deionized water (Millipore Milli-Q) was used for preparation of the samples for phase behavior and rheological studies; D 2 O obtained from AstraChem (Russia, 99.9% isotopic purity) was used for SANS and NMR measurements.

The critical micelle concentrations of potassium oleate and C 8 TAB are ∼0.9 mM 29 and 0.14 M, [START_REF] Raghavan | Wormlike Micelles Formed by Synergistic Self-Assembly in Mixtures of Anionic and Cationic Surfactants[END_REF] , respectively. In all experiments, the concentration of C 8 TAB never surpassed 0.1 M, so this surfactant did not form micelles itself. The overlap concentration C* of PVA macromolecules is 0.7 monomol/L as determined by viscometric measurements. [START_REF] Shibaev | Viscoelastic Synergy and Microstructure Formation in Aqueous Mixtures of Nonionic Hydrophilic Polymer and Charged Wormlike Surfactant Micelles[END_REF] Sample Preparation. To obtain stock solutions, surfactants were dissolved in water overnight at room temperature. PVA stock solution was made by dissolving it in water for 1 h in an oil bath at 90 °C. Then, the samples were prepared by mixing stock water solutions of surfactants and PVA in appropriate ratios and stirring them with a magnetic stirrer for 1-2 days. After preparation, the samples were left at room temperature for 1-3 weeks before examination.

Phase Behavior. For phase behavior studies, the samples were visually inspected 3 weeks after preparation. To determine the composition of each phase, the samples were prepared in D 2 O and left to phase segregate, and after that the phases were carefully separated from each other by a syringe and examined by 1 H NMR. For these experiments, the upper highly viscous phase was diluted 1:1 with D 2 O, whereas the lower phase was studied as is.

1 H Nuclear Magnetic Resonance. NMR measurements were performed with an Agilent 400 MR spectrometer operating at a frequency of 400 MHz and equipped with an automated triple broadband detector. The samples prepared in D 2 O were put into standard 5 mm quartz tubes (Norell); the spectra were recorded at 20 °C and accumulated from eight scans. The data were processed using ACD Laboratories 6.0 software, including baseline and reference correction and calculation of peak integrals. Concentration ratios of different compounds in the samples were calculated from the ratio of areas under corresponding peaks.

Small-Angle Neutron Scattering. SANS measurements were done at the IBR-2 pulsed reactor, Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research (Dubna, Russia). A YuMO spectrometer was used, which has two ring detectors of scattered intensity covering the scattering vectors q dynamical range 0.005-0.7 Å -1 due to a two-detector system. [START_REF] Andreeva | Effect of the Mobility of Charged Units on the Microphase Separation in Amphiphilic Polyelectrolyte Hydrogels[END_REF][START_REF] Kuklin | New Opportunities Provided by Modernized Small-Angle Neutron Scattering Two-Detector System Instrument (YUMO)[END_REF] The intensity was measured in absolute units (cm -1 ) by using a vanadium standard. Since most of the samples were highly viscous, they were put in the specially constructed dismountable cells with parallel quartz plates (beam path 2 mm). The temperature during measurements was controlled by a water-circulating thermostat at 20.0 ± 0.5 °C.

All compounds (surfactants and polymer) were hydrogenated; therefore, the samples were prepared in D 2 O to obtain high contrast. The scattering length densities of surfactant alkyl tails, polymer, and D 2 O are equal to -0.30 × 10 -6 , 0.65 × 10 -6 , and 6.36 × 10 -6 Å -2 , respectively. However, the scattered intensity of polymer solutions is 1-2 orders of magnitude lower than that of surfactants, since micelles are much "thicker" objects. Therefore, it was assumed that the scattered intensity is mostly contributed by surfactant micelles.

Primary treatment of the SANS data included corrections for the sample transmission, sample thickness, and electronic noise by the SAS program. [START_REF] Soloviev | SAS Program for Two-Detector System: Seamless Curve from Both Detectors[END_REF] Incoherent (background) scattering was subtracted from the data by using a blank solvent (D 2 O).

Fitting of the scattering curves was performed by the program SasView (http://www.sasview.org/). A part of the scattering curve at wave vectors q higher than the structure peak position q* (0.06-0.07 Å -1 ) was fitted by a form factor of an infinite cylinder (without structure factor). Two fitting parameters were used: radius of the cylinder and background level. Fitting of the scattering curves in the full q-range was performed by combining a finite cylinder form factor with a Hayter-Penfold potential which accounts for electrostatic repulsion of charged objects. [START_REF] Hayter | An Analytic Structure Factor for Macroion Solutions[END_REF] The radius of the cylinder and background were fixed, and their values were taken from the high qrange fitting by an infinite cylinder. In the full q-range fit, two fitting parameters were used: length of the cylinder and its charge. In the dilute regime, a similar fitting procedure has been recently applied for elliptical charged micelles of cetyltrimethylammonium chloride with sodium salicylate, [START_REF] Lutz-Bueno | Intermicellar Interactions and the Viscoelasticity of Surfactant Solutions: Complementary Use of SANS and SAXS[END_REF] and in our case it allows direct calculation of the length of cylindrical micelles. In the semidilute regime, the mesh size of the entangled micellar network ξ is obtained from the SANS fit instead of the micellar length, since the micelles are much longer than ξ, so that the largest size of an "inhomogeneity" is the mesh size, and the network is a homogeneous object on the length scales larger than ξ. [START_REF] Pedersen | Scattering from wormlike micelles[END_REF] Rheology. Rheological measurements were carried out with a stress-controlled rotational rheometer Physica MCR 301 (Anton Paar, Austria) as described elsewhere. [START_REF] Shibaev | Rheological Behavior of Oil-Swollen Wormlike Surfactant Micelles[END_REF][START_REF] Philippova | Structure and Rheology of Solutions and Gels of Stiff Polyelectrolyte at High Salt Concentration[END_REF] In order to study highly viscous samples (with zero-shear viscosity η 0 > 0.1 Pa s), a stainless steel cone-plate (diameter 50 mm, cone angle 1°) was used. For samples with lower viscosity (η 0 < 0.1 Pa s), double-gap coaxial cylinders (mean diameter 26.4 mm, height 40 mm, gap 0.42 mm) were implied. During measurements, the temperature was set at 20.00 ± 0.05 °C by a water-circulating thermostat and Peltier elements. A special measuring cell cover filled with solvent was used to prevent solvent evaporation from the sample. To equilibrate the sample after putting it into the rheometer, it was kept inside the measuring cell for 10-30 min and subjected to low-amplitude (0.5%) oscillatory deformation with a frequency ω of 1-10 s -1 and amplitude 0.5-3% prior to investigation. Rheological measurements were carried out at least two times to ensure that they coincide and the sample is equilibrated in the cell.

In oscillatory shear experiments, the angular frequency dependences of the storage G′ (ω) and loss G″ (ω) moduli were measured. All measurements were made in the linear viscoelastic regime at the deformation amplitudes of 0.5-3%, at which the storage and loss moduli were independent of deformation, as estimated previously by amplitude sweep tests performed at the frequency of 10 s -1 . The plateau modulus G 0 was determined from the G′(ω) dependence at the frequency ω min where G″ gets a minimum value. [START_REF] Liu | Evaluation of Different Methods for the Determination of the Plateau Modulus and the Entanglement Molecular Weight[END_REF] The terminal relaxation time τ was estimated as τ = 1/ω 0 from the frequency ω 0 corresponding to the interception of G′(ω) and G″(ω). In steady shear experiments, the flow curves (variation of viscosity with shear rate) were obtained. From these curves, the values of the zero-shear viscosity η 0 were determined by fitting the rheological data with the Carreau-Yasuda model.

■ RESULTS AND DISCUSSION

Phase Behavior. First, we studied the effect of charge density of surfactant micelles on the phase behavior of potassium oleate/C 8 TAB/PVA mixtures. In these experiments, the concentration of anionic surfactant (potassium oleate) was kept constant at 0.078 M (2.5 wt %), whereas the concentration of cationic surfactant (C 8 TAB) was changed from 0.0078 to 0.1 M (0.2 to 2.5 wt %), which corresponds to the variation of the molar ratio [C 8 TAB]/[potassium oleate] β in the range 0.1-1.3.

The partial phase diagram of potassium oleate/C 8 TAB/PVA mixtures in water is presented in Figure 1. It shows that in the absence of PVA mixed surfactants form one-phase homogeneous solutions in the whole studied range of [C 8 TAB]/ [potassium oleate] molar ratios β. In the presence of PVA, solutions are homogeneous at low molar ratios β but phase separate when C 8 TAB content is increased. According to 1 H NMR spectroscopy (Figures 1S and2S) and elemental analysis data for the demixed systems, the viscous upper phase represents the surfactant solution with some amount of polymer, whereas the lower phase of small viscosity contains only polymer, which indicates the segregation 39 of the components. This is consistent with the results of [START_REF] Zana | Giant Micelles: Properties and Applications[END_REF] H NMR studies of model systems (potassium oleate/PVA and C 8 TAB/ PVA) presented in Figure 3S. It is seen that the chemical shifts in the spectra of polymer-surfactants mixtures do not differ from those in the spectra of PVA (Figure 1Sb), potassium oleate (Figure 2Sb) and C 8 TAB (Figure 2Sc) taken separately. Therefore, one can conclude that the molecular environment of surfactant protons does not change upon the addition of polymer, which implies that they do not attract each other.

Similar segregative phase separation was observed, for instance, in the mixtures of two slightly incompatible polymers. [START_REF] Lindman | Phase Behavior of Polymer-Surfactant Systems in Relation to Polymer-Polymer and Surfactant-Surfactant Mixtures[END_REF] In such systems, two counteracting factors govern the phase behavior: on the one hand, weak repulsive force between the components promotes phase separation and, on the other hand, entropic reasons countervail it. In the present system, the entropic reason counteracting demixing consists in the loss of entropy of surfactant counterions, when they accumulate mainly in one phase.

At low C 8 TAB content, the micelles are strongly negatively charged, and the phase separation is unfavorable for entropic reasons. When the molar ratio [C 8 TAB]/[potassium oleate] β becomes higher, the net charge of micelles decreases alongside with the amount of their counterions, and above a certain point the entropy losses become less important than the repulsion between the micellar and polymer chains, and the phase separation occurs. Note that the WLMs are "living" objects, and the decrease of their charge density is inevitably accompanied by their growth in length. [START_REF] Magid | The Surfactant-Polyelectrolyte Analogy[END_REF][START_REF] Cates | Reptation of Living Polymers: Dynamics of Entangled Polymers in the Presence of Reversible Chain-Scission Reactions[END_REF] Indeed, with decreasing charge density the electrostatic repulsion in the corona of micelles becomes smaller, which makes tighter packing of surfactant molecules in the middle cylindrical part of the micelle more favorable in comparison with the semispherical ends, thus reducing the fraction of the end-caps in the system A smaller fraction of end-caps at the same amount of surfactant suggests longer micelles. Increased length of micelles can also contribute to the demixing, since longer chains are poorer in entropy, but this entropic contribution is much smaller than the entropy of counterions.

From Figure 1 it is seen that the region of phase compatibility narrows with the increase of polymer concentration; i.e., the higher the amount of added PVA, the more charged micelles can be demixed into a separate phase. This is due to the enhancement of the repulsion between the components. At the largest studied polymer concentration (1.34 monomol/L), the solutions are homogeneous only for highly charged (and short) micelles at very low molar ratios β ≤ 0.2. Further experiments were performed only with homogeneous samples.

Structure. To investigate the structural changes, which occur in the potassium oleate/C 8 TAB/PVA system at varying micellar charge, SANS was used. In the experiments, the concentration of PVA was kept at 0.89 monomol/L (4 wt %), which is slightly higher than its overlap concentration in water (C* = 0.7 monomol/L). [START_REF] Shibaev | Viscoelastic Synergy and Microstructure Formation in Aqueous Mixtures of Nonionic Hydrophilic Polymer and Charged Wormlike Surfactant Micelles[END_REF] The concentration of potassium oleate was equal to 0.078 M, whereas the value of the molar ratio [C 8 TAB]/[potassium oleate] β was varied from 0.1 to 0.45, which corresponds to homogeneous solutions (Figure 1) with strongly negatively charged micelles. Since surfactant micelles in D 2 O scatter neutrons much stronger than PVA (Figure 4S), the SANS curves in mixed surfactant/polymer systems represent mainly the scattering from the micellar component.

Effect of Micellar Charge. Figure 2a shows the evolution of the scattering pattern with decreasing degree of charge of micelles (i.e., increasing amount of added C 8 TAB) at fixed concentrations of both potassium oleate and PVA. It is seen that in the high q-range (at q > 0.07 Å -1 ) the curves superimpose perfectly, indicating that the local structure of surfactant aggregates is the same independently of the micellar charge. In this range, the curves can be fitted by a form factor of a cylinder with the radius of 18.1 ± 0.4 Å (Figure 2a), which is close to the length of oleate tail (19 Å) [START_REF] Shibaev | How a Viscoelastic Solution of Wormlike Micelles Transforms into a Microemulsion upon Absorption of Hydrocarbon: New Insight[END_REF] and is much larger than the length of C 8 TAB alkyl group (8 Å), suggesting that at the studied molar ratios β = 0.1-0.45 the radius of an OCS micelle is governed by the size of the longer anionic surfactant tail and does not depend on the content of C 8 TAB. Similar behavior was previously observed for sodium oleate/C 8 TAB micelles in the absence of polymer. [START_REF] Raghavan | Wormlike Micelles Formed by Synergistic Self-Assembly in Mixtures of Anionic and Cationic Surfactants[END_REF] Fitting of the high q-range of the scattering curves in order to obtain the micellar radii was applied for several charged surfactant-micellar systems. [START_REF] Raghavan | Wormlike Micelles Formed by Synergistic Self-Assembly in Mixtures of Anionic and Cationic Surfactants[END_REF][START_REF] Flood | Wormlike Micelles Mediated by Polyelectrolyte[END_REF] Thus, according to SANS data, at β values under study, the micelles of locally cylindrical shape are always present in potassium oleate/C 8 TAB/PVA solution, and their radius is not altered by the amount of added C 8 TAB.

At the same time, at low q-values (q < 0.05 Å -1 ) reflecting larger scale structural features the scattering curve is strongly affected by the charge of micelles: with decreasing charge density (i.e., with increasing molar ratio β) the scattered intensity I is greatly enhanced by nearly an order of magnitude (see also the scattering curves in linear representation on Figure 5S). An increase in SANS intensity at low q was previously observed at the screening of the micellar charges with low molecular weight salt [START_REF] Flood | Wormlike Micelles Mediated by Polyelectrolyte[END_REF] or oppositely charged surfactant. [START_REF] Raghavan | Wormlike Micelles Formed by Synergistic Self-Assembly in Mixtures of Anionic and Cationic Surfactants[END_REF] It was attributed to the elongation of cylindrical micelles. Indeed, addition of oppositely charged surfactant produces two main effects: (i) the decrease of the net charge of micelles and (ii) the release of counterions increasing the ionic strength of the solution. [START_REF] Raghavan | Wormlike Micelles Formed by Synergistic Self-Assembly in Mixtures of Anionic and Cationic Surfactants[END_REF] Both these effects reduce the electrostatic repulsion in the corona of the micelles, thus favoring tighter packing of surfactant molecules in a cylinder at the expense of spherical end-caps. The lower the fraction of end-caps, the longer the micelles. In our work, we show that growth of cylindrical micelles in length with decreasing their charge density occurs also in the presence of PVA. Besides, one should note that decreasing charge of micelles will make the intermicellar repulsive interactions weaker, thereby reducing the contribution of the structure factor. As the structure factor decreases the scattering intensity at low q, the lowering of its contribution will enhance the intensity. So, the increase of scattering intensity at low q can be attributed to two reasons: elongation of micelles and reducing of the intermicellar repulsion. One can expect that the first reason will be important mainly in dilute solutions because in semidilute regime the scattering will characterize the mesh size of the transient network.

Figure 2a demonstrates that at low q the intensity I of experimental curves is smaller than the predicted cylinder form factor, which can be assigned to strong electrostatic repulsion between the similarly charged cylindrical micelles, [START_REF] Shibaev | Viscoelastic Synergy and Microstructure Formation in Aqueous Mixtures of Nonionic Hydrophilic Polymer and Charged Wormlike Surfactant Micelles[END_REF][START_REF] Klymenko | Multiresponsive Hydrogels Formed by Interpenetrated Self-Assembled Polymer Networks[END_REF] that is, to the contribution of the structure factor. The scattering curves of surfactant micelles (in the absence of polymer) can be wellfitted in the whole q-range by a model combining a finite cylinder form factor with a Hayter-Penfold potential [START_REF] Hayter | An Analytic Structure Factor for Macroion Solutions[END_REF] which accounts for electrostatic repulsion of charged objects (Figure 6S). The fitting gives an estimate of the length of micelles (Table 1S): with increasing β from 0.2 to 0.275 (dilute regime) the length of micelles grows from 28 to 40 nm. Note that in this part of the curve we do not observe the scaling dependence I ∼ q -1 typical for cylindrical objects [START_REF] Shibaev | How a Viscoelastic Solution of Wormlike Micelles Transforms into a Microemulsion upon Absorption of Hydrocarbon: New Insight[END_REF] at qR ≪ 1 because their form factor is hidden by the contribution of the structure factor. [START_REF] Raghavan | Wormlike Micelles Formed by Synergistic Self-Assembly in Mixtures of Anionic and Cationic Surfactants[END_REF] At intermediate q-values (q = 0.05-0.07 Å -1 ) a correlation peak is observed. It is better seen in I•q versus q representation (Figure 2b) which eliminates the contribution of the form factor in this part of the curve. [START_REF] Sommer | Wormlike Micelles as "Equilibrium Polyelectrolytes": Light and Neutron Scattering Experiments[END_REF] The structure peak characterizes the mutual arrangement of similarly charged micelles resulting from electrostatic repulsion between them, which should be rather strong since no salt was added to shield the repulsion. The variation of the position of the peak q* with molar ratio [C 8 TAB]/[potassium oleate] β for the potassium oleate/C 8 TAB/PVA system is illustrated in Figure 3 (red circles). It is seen that the curve consists of two distinct regions. In the first one (0.1 < β < 0.25), the lowering of the micellar charge induces a pronounced decrease of q*, indicating that the intermicellar distances 2π/q* become much longer, which can be due to the growth of micelles in length. [START_REF] Gamez-Corrales | Shear-Thickening Dilute Surfactant Solutions: Equilibrium Structure as Studied by Small-Angle Neutron Scattering[END_REF] Indeed, from simple geometrical considerations it can be concluded that in the dilute regime the average distance between longer cylindrical objects should be larger than between the shorter ones made of the same amount of material (the concentration of C 8 TAB added in this range is several times lower than that of potassium oleate). At the molar ratio β ≈ 0.25, a sharp inflection is seen at the curve (Figure 3). A similar dependence with an inflection point was observed in the literature for cylindrical micelles of cetyltrimethylammonium tosylate at increasing concentration of surfactant, and the inflection was attributed to the crossover from dilute to semidilute regime. [START_REF] Gamez-Corrales | Shear-Thickening Dilute Surfactant Solutions: Equilibrium Structure as Studied by Small-Angle Neutron Scattering[END_REF] Although in our system the composition of the surfactant mixture β (instead of the concentration of surfactant) was varied, one can suggest that at β ≈ 0.25 the transition to semidilute regime occurs. Thus, the first region on the curve (0.1 < β < 0.25) corresponds to the dilute regime, whereas the second one (β > 0.25) to semidilute regime (Figure 3). In semidilute regime, the micelles overlap and their growth soon results in the formation of an entangled network (as will be evidenced later by the rheological data). In the semidilute entangled regime, 2π/q* roughly corresponds to the mesh size ξ of the network. [START_REF] Gamez-Corrales | Shear-Thickening Dilute Surfactant Solutions: Equilibrium Structure as Studied by Small-Angle Neutron Scattering[END_REF] As seen from Figure 3, in the second region (β > 0.25), q* slightly increases with C 8 TAB concentration, indicating the reduction of ξ, i.e., the formation of denser network. Plotting q* vs total (potassium oleate and C 8 TAB) surfactant concentration (Figure 3, inset) gives a straight line. The slope of this line is close to the theoretical dependence [START_REF] Gamez-Corrales | Shear-Thickening Dilute Surfactant Solutions: Equilibrium Structure as Studied by Small-Angle Neutron Scattering[END_REF] for strongly interacting cylindrical objects in semidilute regime: q* ∼ C 0.5 . Therefore, the observed slight growth of q* in the second region can be simply explained by the increase of the total amount of surfactant molecules building the micelles.

Thus, the analysis of the SANS data suggests that decreasing micellar charge induces the growth of cylindrical micelles in length in the presence of polymer, which leads finally to the transition from dilute to semidilute regime at β ≈ 0.25 and to the formation of a polymer-micellar network.

Effect of Polymer. In order to reveal the role of polymer in the microstructure formation, let us compare the scattering curves of potassium oleate/C 8 TAB solutions in the presence and in the absence of PVA at a constant molar ratio [C 8 TAB]/ [potassium oleate] β. As depicted in Figure 4, at intermediate qvalues (0.06 Å -1 < q < 0.2 Å -1 ), the curves coincide with each other showing that the local structure of surfactant aggregates is not affected by PVA. A clear effect of polymer is seen at high and at low q-ranges (Figure 4). At high q-range (q > 0.2 Å -1 ), polymer increases the background intensity of the scattering curve (cf. Figure 4S). In the low q-range, the effect of polymer is more complicated. Without PVA, the scattered intensity levels off at small q. This may be explained by the formation of an entangled micellar network (which will be evidenced later by the rheological data). The network can be regarded as a "homogeneous" object at length scales larger than its mesh size (i.e., there are no larger inhomogeneities than one mesh), which results in the constant intensity at low q-range. [START_REF] Pedersen | Scattering from wormlike micelles[END_REF] At the same time, in the presence of PVA, the intensity is higher, and moreover it grows with decreasing q, which indicates the formation of structures larger than ∼1/q min = 150 nm. This is consistent with our recent cryo-TEM data [START_REF] Shibaev | Viscoelastic Synergy and Microstructure Formation in Aqueous Mixtures of Nonionic Hydrophilic Polymer and Charged Wormlike Surfactant Micelles[END_REF] on potassium oleate/C 8 TAB/PVA mixtures demonstrating the formation of large (several hundreds of nanometers) domains enriched either by WLMs or by polymer, which arise from poor compatibility between polymer and surfactant micelles. These domains seem to be responsible for the enhancement of intensity at low q. Therefore, if we return to the scattering curves at different molar ratios β (Figure 2 and Figure 5S), we can state that in the presence of PVA the rise of low-q intensity at decreasing charge density of micelles proceeds due to three reasons (formation of microdomains, increase of micellar length, and reduction of repulsive interactions), whereas in pure surfactant only last two reasons (the growth of micelles [START_REF] Raghavan | Wormlike Micelles Formed by Synergistic Self-Assembly in Mixtures of Anionic and Cationic Surfactants[END_REF] and the decrease of repulsion) will contribute to this effect. Indeed, as was discussed above, the scattering curve of the surfactant micelles (without PVA) is well-fitted in the whole q-range by a model combining a finite cylinder form factor with the Hayter-Penfold potential [START_REF] Hayter | An Analytic Structure Factor for Macroion Solutions[END_REF] which accounts for electrostatic repulsion of charged objects (Figure 4 and Figure 6S). Similar fitting of polymer-surfactant system deviates from the experimental scattering curve (Figure 4) at low q-values, indicating additional factor affecting the scattering, which most probably concerns the polymer-surfactant microsegregation with the formation of microdomain structure.

Figure 3 demonstrates the influence of polymer on the dependence of the structure peak position q* on the molar ratio [C 8 TAB]/[potassium oleate] β. It is seen that the curves with and without PVA show similar behavior, suggesting that the general structural evolution of micelles with the decrease of their charge proceeds in the same way in both cases. The most significant effect produced by polymer consists in the shift of the whole curve to higher q*-values, indicating that at all micellar charges under study (i.e., at all [C 8 TAB]/[potassium oleate] molar ratios β) the average distance between the micelles decreases when PVA is added. This implies the local concentrating of micelles induced by their segregation from polymeric chains poorly compatible with the micelles. Indeed, as the surfactant micelles cannot occupy some area filled by PVA macromolecules, they need to come closer to each other upon addition of polymer; i.e., their local concentration increases. This should lead to the additional elongation of micellar chains, since the length of wormlike micelles grows with their concentration. [START_REF] Magid | The Surfactant-Polyelectrolyte Analogy[END_REF][START_REF] Cates | Reptation of Living Polymers: Dynamics of Entangled Polymers in the Presence of Reversible Chain-Scission Reactions[END_REF] Also, Figure 3 shows that in the presence of PVA the minimum on the curve q*(β) is slightly shifted to lower β, indicating that the overlap concentration C* of the micelles in polymer-surfactant system is observed for more charged micelles, which may be due to their additional elongation caused by polymer.

Thus, SANS data suggest that in the presence of polymer the local concentration of micelles and their length are higher in comparison with PVA-free micellar solutions and that the inhomogeneities at the scale larger than ca. 150 nm are formed. This is consistent with the behavior described by us recently [START_REF] Shibaev | Viscoelastic Synergy and Microstructure Formation in Aqueous Mixtures of Nonionic Hydrophilic Polymer and Charged Wormlike Surfactant Micelles[END_REF] for potassium oleate/C8TAB/PVA solutions at fixed β = 0.4 and can be assigned to the local segregation of polymer and surfactant components in the solution.

Rheology. In order to relate the structural changes in potassium oleate/C 8 TAB/PVA solutions with their macroscopic behavior, rheological studies were performed. Figures 5 and6 show the flow curves and the dynamic rheological data at different [C 8 TAB]/[potassium oleate] molar ratios β and fixed concentration of PVA (0.89 monomol/L), whereas Figure 7 depicts the variation of zero-shear viscosity η 0 , relaxation time τ, and plateau modulus G 0 with increasing β at different amounts of polymer. In all the experiments the concentration of potassium oleate was equal to 0.078 M.

Effect of Micellar Charge. Let us first consider the evolution of rheological data with decreasing micellar charge (i.e., at increasing β) at constant PVA concentration of 0.89 monomol/ L. The corresponding viscosity results are presented on Figures 5 and7a (red curve). From Figure 7a, it is seen that at β = 0.1 the viscosity is low (0.006 Pa s) and only slightly higher than the viscosity of 0.89 monomol/L PVA solution without surfactants (0.005 Pa s), which is in accordance with the presence of rather short cylindrical micelles. When the molar ratio β is raised from 0.1 to 0.23, the viscosity becomes only slightly higher suggesting the elongation of cylindrical micelles in dilute regime. At molar ratio β ≈ 0.23, the rheological behavior changes drastically. The zero-shear viscosity starts to rise sharply (Figure 7a), indicating the transition from dilute to semidilute regime, and finally grows by nearly 4 orders of magnitude, reaching the value of 900 Pa s at β = 0.46. As seen from flow curves (Figure 5), viscous solutions exhibit shearthinning behavior.

Dynamic rheological data (Figure 6) demonstrate that with decreasing micellar charge at the addition of C 8 TAB the solutions progressively gain viscoelastic properties. The intercept point between G′(ω) and G″(ω) dependences shifts to lower frequency indicating the increase of the relaxation time τ. Note that the present systems do not show simple Maxwell behavior with a single relaxation time; [START_REF] Shibaev | Viscoelastic Synergy and Microstructure Formation in Aqueous Mixtures of Nonionic Hydrophilic Polymer and Charged Wormlike Surfactant Micelles[END_REF] therefore, the relaxation time determined from the intersection of G′(ω) and G″(ω) curves can be regarded as a terminal one. At molar ratios β > 0.38, one can observe a well-defined high-frequency plateau on G′(ω) dependence indicating to the formation of an entangled wormlike micellar network. [START_REF] Magid | The Surfactant-Polyelectrolyte Analogy[END_REF][START_REF] Dreiss | Wormlike Micelles: where Do we Stand? Recent Developments, Linear Rheology and Scattering Techniques[END_REF][START_REF] Rehage | Viscoelastic Surfactant Solutions: Model Systems for Rheological Research[END_REF] The dynamic rheological data for lower polymer concentration 0.22 monomol/L are quite similar (Figure 7S). Overall, the observed evolution of rheological properties can be explained by the elongation of micelles upon decreasing their charge leading to the transition of the solution to semidilute regime.

Figures 7a and7b show that η 0 and τ grow up to maximum and slightly decrease after it. The maximum on the viscosity curves versus salt concentration is usually attributed to the formation of branching points on WLMs. [START_REF] Lequeux | Reptation of Connected Wormlike Micelles[END_REF][START_REF] Khatory | Entangled versus Multiconnected Network of Wormlike Micelles[END_REF][START_REF] Rogers | Rheology of Branched Wormlike Micelles[END_REF][START_REF] Kwiatkowski | Impact of Salt Co-and Counterions on Rheological Properties and Structure of Wormlike Micellar Solutions[END_REF] Unlike branches in polymers, micellar branches are labile. They can slide along a micelle contour, thus accelerating the stress relaxation and therefore decreasing relaxation time τ and the zero-shear viscosity η 0 . Although this mechanism of the viscosity reduction is widely accepted, a thorough study of sodium oleate/C 8 TAB micelles (in the absence of polymer) by cryo-TEM [START_REF] Ziserman | Origins of the Viscosity Peak in Wormlike Micellar Solutions. 1. Mixed Catanionic Surfactants. A Cryo-Transmission Electron Microscopy Study[END_REF] has evidenced that the maximum of viscosity as a function of the composition of the surfactant mixture is not related to the branching, but it is due to the formation of longest linear WLMs followed by a shortening of worms at higher amount of added C 8 TAB. The same seems to be true for the system with PVA. As for plateau modulus values G 0 (Figure 7c), they continue to get higher when zero-shear viscosity η 0 and terminal relaxation time τ already stay constant or even slightly decrease. As was shown for polymer-free sodium oleate/C 8 TAB system, [START_REF] Raghavan | Wormlike Micelles Formed by Synergistic Self-Assembly in Mixtures of Anionic and Cationic Surfactants[END_REF] in the vicinity of the viscosity maximum the value of G 0 is independent of the composition of OCS micelles; therefore, one can suggest that the rise of G 0 with β can be due to the increase of the total concentration of surfactants upon addition of C 8 TAB.

Effect of Polymer. Let us reveal the role of polymer in the evolution of rheological properties with decreasing charge density of micelles by comparing the data at different content of PVA and in the absence of PVA (Figure 7). First, one can note that in the presence of polymer the transition to semidilute regime corresponding to the onset of sharp rise of viscosity (Figure 7a) proceeds at lower β (0.23 instead of 0.27 for polymer-free system), which fully agrees with SANS data (Figure 3). As was discussed above, this is due to longer micelles observed in polymer-surfactant system. Second, in the presence of polymer the formation of the network of entanglements reflected in the appearance of the plateau modulus (Figure 6 and Figure 8S) also occurs at smaller molar ratio β (0.38 instead of 0.41 for polymer-free surfactants), that is, for more charged micelles. Therefore, polymer decreases the β values corresponding to the transition from the unentangled to entangled semidilute regime. Third, one can state that at any β value before the maximum polymer increases significantly the viscosity of the system (Figure 7a). For example, at β = 0.4 the zero-shear viscosity of polymer-surfactant system containing 0.89 monomol/L PVA is 617 Pa s, whereas for surfactant solution it equals only 5 Pa s and for PVA solution 0.005 Pa s. Therefore, the viscosity of the mixed polymer-surfactant system is by more than 2 orders of magnitude higher than the viscosity of its components taken separately. Such a pronounced synergistic effect can be attributed not only to higher length of micelles in the presence of PVA. As was shown recently, [START_REF] Shibaev | Viscoelastic Synergy and Microstructure Formation in Aqueous Mixtures of Nonionic Hydrophilic Polymer and Charged Wormlike Surfactant Micelles[END_REF] the entanglements between polymer and micellar chains can also contribute to enhanced viscosity. Note that the concentration of PVA in the system is near the overlap concentration C* (0.7 monomol/L) and well below the entanglement concentration C e , which is usually 5-10 times higher than C*. [START_REF] Colby | Structure and Linear Viscoelasticity of Flexible Polymer Solutions: Comparison of Polyelectrolyte and Neutral Polymer Solutions[END_REF] Therefore, the polymer-polymer entanglements can be neglected. Thus, an enhancement of viscosity in semidilute regime in the presence of polymer seems to be due to the elongation of micelles induced by PVA and to the formation of the entanglements between micellar and polymeric chains. For the same reason the polymer increases the terminal relaxation time and the plateau modulus (Figure 7) as well as the β values corresponding to the transition from the unentangled to entangled semidilute regime. At the same time, the maximum values of viscosity and terminal relaxation time do not depend on the presence of PVA (Figure 7). Therefore, PVA helps to reach the maximum viscosity and relaxation time at smaller β, i.e., at higher degree of charging. Thus, the addition of nonionic polymer instead of an ionic compound (for instance, cationic surfactant) may help to obtain a solution of highly charged micelles with high rheological properties, whereas in the absence of polymer the micelles need to be less charged in order to have the same viscosity and elasticity.

■ CONCLUSIONS

In this paper, we studied the behavior of the solutions of ionic surfactant micelles of variable charge and nonionic polymer PVA. To decrease the degree of charging of micelles, we gradually added a cationic surfactant C 8 TAB to oppositely charged potassium oleate micelles. We used a combination of rheological measurements exploring the macroscopic properties (viscosity, elasticity, etc.) of the system and SANS revealing the structural rearrangements occurring at the microscopic level. We show that decreasing charge of micelles promotes their elongation and consequently the enhancement of the rheological properties (zero-shear viscosity, terminal relaxation time, and plateau modulus) both in the absence and in the presence of polymer. At a given degree of charging of micelles, the polymer induces the formation of longer micellar chains and of polymer-micellar entanglements and therefore increases significantly the rheological characteristics. We explain the role of polymer in the elongation of micelles by its local segregation from surfactant, which reduces the volume of solution accessible for the micelles, thus increasing their local concentration and promoting their growth in length. This suggestion is confirmed by SANS data, which demonstrate (i) a shift of the structure peak position toward high q-values upon addition of polymer indicating the decrease of intermicellar distance and (ii) an enhancement of low-q scattering pointing to the formation of longer micelles and large-scale inhomogeneities.

The findings reported here demonstrate the effectiveness of the addition of weakly interacting polymer for the modulation of rheology of wormlike surfactant micelles, thus opening a new way for manipulating the rheological properties of viscoelastic surfactants.

Figure 1 .

 1 Figure 1. Phase diagram of potassium oleate/C 8 TAB/PVA/water system at 20 °C: open symbols, one phase; semifilled symbols, two phases. Concentration of potassium oleate: 0.078 M.

Figure 2 .

 2 Figure 2. Scattering curves in I versus q (a) and I•q versus q (b) representations for 0.078 M aqueous solutions of potassium oleate containing 0.89 monomol/L PVA and different amounts of C 8 TAB corresponding to molar ratios [C 8 TAB]/[potassium oleate] β: 0.10 (violet reverse triangles), 0.15 (red stars), 0.20 (blue diamonds), 0.25 (green triangles), 0.30 (red circles), 0.45 (black squares) at 20 °C. Solid line is a fit of the scattering curves by a form factor of a cylinder with radius R = 18.1 ± 0.4 Å.

Figure 3 .

 3 Figure 3. Dependences of the position of the correlation peak q* on the molar ratio [C 8 TAB]/[potassium oleate] β and on the total surfactant concentration (inset) for 0.078 M aqueous solutions of potassium oleate with different concentrations of C 8 TAB in the absence (blue triangles) and in the presence of 0.89 monomol/L PVA (red circles) at 20 °C. The straight lines are power law fits yielding the exponents of 0.42 and 0.71 in the absence and in the presence of polymer, respectively.

Figure 4 .

 4 Figure 4. Scattering curves for aqueous solutions containing 0.078 M potassium oleate and 0.023 M C 8 TAB (molar ratio [C 8 TAB]/ [potassium oleate] β = 0.3) in the absence (open symbols) and in the presence of 0.89 monomol/L PVA (filled symbols) at 20 °C. Solid lines are fits of the scattering curves by a model of finite cylinder with electrostatic repulsion with the Hayter-Penfold potential.

Figure 5 .

 5 Figure 5. Flow curves of 0.078 M potassium oleate aqueous solutions containing 0.89 monomol/L PVA and different amounts of C 8 TAB corresponding to molar ratios [C 8 TAB]/[potassium oleate] β: 0.1 (reverse cyan triangles), 0.24 (gray stars), 0.32 (green triangles), 0.34 (red diamonds), 0.38 (blue circles), and 0.46 (black squares) at 20 °C.

Figure 6 .

 6 Figure 6. Frequency dependences of storage G′ (filled symbols) and loss G″ (open symbols) moduli for 0.078 M potassium oleate aqueous solutions containing 0.89 monomol/L PVA and different amounts of C 8 TAB corresponding to molar ratios [C 8 TAB]/[potassium oleate] β: 0.32 (green triangles), 0.34 (red diamonds), 0.38 (blue circles), 0.42 (orange reverse triangles), and 0.46 (black squares) at 20 °C.

Figure 7 .

 7 Figure 7. Dependences of zero-shear viscosity η 0 (a), terminal relaxation time τ (b), and plateau storage modulus G 0 (c) on the molar ratio [C 8 TAB]/[potassium oleate] β for 0.078 M aqueous solutions of potassium oleate containing C 8 TAB and different concentrations of PVA: 0 (blue triangles), 0.22 monomol/L (green diamonds), and 0.89 monomol/L (red circles). Dashed black line (a) indicates the zeroshear viscosity of 0.89 monomol/L PVA solution.

This work was supported by the Russian Science Foundation (project no. 15-13-00114). The authors express their gratitude Ms. T. A. Ganina for her help in NMR measurements and to Mrs. A. L. Aleshina for the preparation of some samples for NMR experiments.