Ph.D Jamel Khenfer
email: jamel.khenfer@zu.ac.ae

Ph.D Oliver Steven Shepherd
email: steven.shepherd@okstate.edu

Ph.D Trendel

Dr Naveen Donthu

Dr Anders Gustafsson

Steven Shepherd

Olivier Trendel
email: olivier.trendel@grenoble-em.com

Customer Empowerment in the Face of Perceived Incompetence: Effect on Preference for Anthropomorphized Brands

Keywords: brand anthropomorphism, brand preference, power, customer empowerment, perceived competence, self-efficacy brand anthropomorphism, brand preference, power, customer empowerment, perceived competence

Brands often tell consumers that they have power, either directly through slogans such as Burger King's famous "Have it your way" or by allowing them to exert control over the purchasing process (e.g., product and service customization). Yet, not everyone may feel competent enough to handle a sudden increase in empowerment. Would then variations in perceived competence affect how power influences social interactions in the marketplace? In this research, we address this question in relation to brand anthropomorphism given managers' widespread practice of imbuing brands with human features. In five studies, we found evidence that customer empowerment heightened a sense of social dominance and drove preference for anthropomorphized brands when feelings of competence were high. In contrast, when feelings of competence were threatened, customer empowerment drove people away from anthropomorphized brands because resentment overcame feelings of social dominance.

Introduction

Managers often anthropomorphize brands; that is, they imbue brands with physical characteristics and behaviors that resemble those of people. This may include visual cues such as logos and displays of inanimate objects in human postures (e.g., the M&M's mascots, the Pixar lamp), verbal tactics such as names (e.g., Mr. Clean), and rhetoric designed to attribute human-like capacities to inanimate objects (e.g., "Like a good neighbor, State Farm is there") [START_REF] Macinnis | Humanizing brands: When brands seem to be like me, part of me, and in a relationship with me[END_REF]. In general, imbuing brands with human features generates more favorable consumer attitudes [START_REF] Aggarwal | When brands seem human, do humans act like brands? Automatic behavioral priming effects of brand anthropomorphism[END_REF].

Previous research suggests that empowered consumers respond favorably to brands bearing human-like features because such brands can entice consumers to feel socially dominant, even if it involves inanimate objects [START_REF] Kim | Do materialists prefer the "brand-as-servant"? The interactive effect of anthropomorphized brand roles and materialism on consumer responses[END_REF][START_REF] Kim | Gaming with Mr. Slot or gaming the slot machine? Power, anthropomorphism, and risk perception[END_REF][START_REF] Hayes | Introduction to mediation, moderation, and conditional process analysis: A regression-based approach[END_REF][START_REF] Maeng | Facing Dominance: Anthropomorphism and the Effect of Product Face Ratio on Consumer Preference[END_REF]. In this research, we suggest that this is not always true.

Consider the following example. Banks increasingly empower their customers by having them conduct operations on their own to reduce physical service encounters (e.g., managing their financial portfolio online). Yet, some customers may feel incompetent, perhaps, because of difficulties in managing their money (e.g., the 30% of Americans with a credit score lower than 650, Bloomberg, 2017), or because they are disconnected from the digital world despite its key role in customer empowerment strategies (e.g., the 40% of Americans above 65 who do not use the Internet, Pew, 2014). Would such individuals respond favorably to anthropomorphic virtual assistants such as Bank of America's Erica? Or would they be reluctant to share their lack of competence?

In the present research, we suggest that empowered consumers respond favorably to anthropomorphic brands only when their feelings of competence-i.e., their perceived ability to skillfully interact with and alter the environment [START_REF] Fast | When the boss feels inadequate: Power, incompetence, and aggression[END_REF])-are high. We argue that the feeling of dominance experienced over a (non-human) entity projecting intelligence and personality may conflict with the negativity associated with heightened feelings of incompetence in the presence of others. Evidence shows that when power holders feel unable to meet the demands of the leadership situation they are in, their relationship with subordinates becomes strained because they experience insecurity and diminished self-worth [START_REF] Fast | Managing to stay in the dark: Managerial self-efficacy, ego defensiveness, and the aversion to employee voice[END_REF][START_REF] Fast | When the boss feels inadequate: Power, incompetence, and aggression[END_REF]. Therefore, we propose that when a given situation heightens feelings of incompetence, empowered consumers respond unfavorably to anthropomorphized brands because they experience resentment. We argue that the negativity their forceful presence entails overshadow the experience of social dominance that was promised through empowerment. We report on five studies that provide support for the moderating role of perceived competence both as a trait and a state.

Theoretical background

2.1. Brand anthropomorphism in light of power People readily and easily attribute and perceive human features in non-human entities, a phenomenon known as anthropomorphism [START_REF] Epley | On seeing human: a three-factor theory of anthropomorphism[END_REF]. Therefore, managers often imbue brands with humanlike characteristics, motivations, and behaviors (either visually, textually, and/or rhetorically) to enable consumers to perceive the brand as an intentional agent that is capable of interacting with them [START_REF] Fournier | Brands as relationship partners: Warmth, competence, and in-between[END_REF].This high degree of sociality leads consumers to establish relationships that resemble those they establish with actual people [START_REF] Fournier | Consumers and their brands: Developing relationship theory in consumer research[END_REF][START_REF] Macinnis | Humanizing brands: When brands seem to be like me, part of me, and in a relationship with me[END_REF].

As such, using anthropomorphized brands may facilitate purchase decisions based on consumers' desire to bond with a social entity [START_REF] Fournier | Consumers and their brands: Developing relationship theory in consumer research[END_REF][START_REF] Puzakova | Should Anthropomorphized Brands Engage Customers? The Impact of Social Crowding on Brand Preferences[END_REF]. If establishing social relationships with inanimate objects can help reduce feelings of loneliness, it can also help people feel in control over their environment (what MacInnis and Folkes

[2017] labelled an "effectance motivation"). From this perspective, brands are used not to satisfy social needs through their perceived warmness, but to satisfy a need for control through their perceived ability to help consumers accomplish tasks and obtain desired outcomes [START_REF] Fournier | Brands as relationship partners: Warmth, competence, and in-between[END_REF][START_REF] Khenfer | Interventionist external agents make specific advice less demotivating[END_REF]. Thus, brand anthropomorphism may drive purchase based on the potential usefulness of the brand, thereby making consumerbrand relationships potentially hierarchical and endowing consumers with a position of power over the brand.

Power refers to people's beliefs regarding their capacity to control or influence the state of others according to their own will; a capacity conferred by the individual's ability to allocate or withhold valuable resources and administer punishments [START_REF] Rucker | Power and consumer behavior: How power shapes who and what consumers value[END_REF]). People's subjective sense of power can be the result of their experience in occupying powerful positions, and thus, be expressed as a stable trait [START_REF] Anderson | Power, optimism, and risk-taking[END_REF]. Research has also extensively shown that people can feel powerful independently of their hierarchical position in their personal or professional life. Subjective sense of power can be activated when people are placed in a position where they are enabled to make decisions that affect others [START_REF] Galinsky | From power to action[END_REF]. Since an elevated sense of power relates to positive outcomes such as increased optimism [START_REF] Anderson | Power, optimism, and risk-taking[END_REF] and perceived control (Fast et al., 2009), power can be conceived as a desirable state that, once activated, people seek to maintain.

In their review of the effect of power on consumer behavior, Rucker and colleagues (2012) report that an elevated sense of power fosters the expression of dominant acts whereas powerlessness fosters a disposition to consider others while engaging in decision-making.

Unless brands have succeeded in becoming relationship partners, perhaps going as far as becoming friends and family [START_REF] Fournier | Brands as relationship partners: Warmth, competence, and in-between[END_REF], the inherent implication of buying products is to make use of them, which establishes a vertical relationship. As such, the brand preferences of people who perceived themselves low in power may be driven more by their unwillingness to make use of a fellow powerless social agent than by seeking companionship.

In contrast, feelings of powerfulness encourage self-assertive and dominant behaviors [START_REF] Rucker | Power and consumer behavior: How power shapes who and what consumers value[END_REF], which very essence lies in the presence of others (Weber, 1947(Weber, /1978)). This suggests that power fosters a disposition to seek out social targets, and thus anthropomorphized brands.

A budding marketing literature has begun to examine the relationship between power and brand anthropomorphism. For instance, [START_REF] Kim | Gaming with Mr. Slot or gaming the slot machine? Power, anthropomorphism, and risk perception[END_REF] showed that consumers with high power were more willing to take risks when dealing with an anthropomorphized object (e.g., slot machine, illness) because they perceived a greater degree of control over it.

In the same vein, researchers showed that constructs associated with power such as materialism [START_REF] Kim | Do materialists prefer the "brand-as-servant"? The interactive effect of anthropomorphized brand roles and materialism on consumer responses[END_REF] and financial status [START_REF] Kim | Minions for the Rich? Financial Status Changes How Consumers See Products with Anthropomorphic Features[END_REF] increased willingness to pay and product evaluations for products displaying anthropomorphic features related to submissiveness. Conversely, when abstract concepts such as time [START_REF] May | When time has a will of its own, the powerless don't have the will to wait: Anthropomorphism of time can decrease patience[END_REF] or the digestive system [START_REF] Newton | This is your stomach speaking: Anthropomorphized health messages reduce portion size preferences among the powerless[END_REF] were imbued with humanlike features, people who perceived themselves low (versus high) in power felt under the influence of the anthropomorphized entity and showed obedience toward it.

Thus, converging evidence shows that an elevated sense of power leads to a preference for anthropomorphized brands because power fosters feelings of social dominance and increases consumers' willingness to use such brands. Nevertheless, research makes no assumption regarding consumers' sense of competence. Perhaps this is because people tend to be optimistic about their ability to perform well when feelings of competence are not threatened [START_REF] Bandura | Self-efficacy[END_REF]. Hence, when chronic and situational feelings of competence are high, we expected results to be in line with previous research:

H1: When chronic and situational feelings of competence are high (vs. low), an elevated sense of power increases the appeal of anthropomorphized brands.

H2:

The increased appeal of anthropomorphized brands following an elevated sense of power in the context of high (vs. low) chronic and situational feelings of competence, is driven by increased feelings of social dominance.

Yet, not everyone feels constantly competent, nor can people escape situations that challenge feelings of competence. Then, would the relationship between power and brand anthropomorphism hold when perceived competence is low or under threat?

The moderating role of perceived competence

Empowering consumers involves providing them with sufficient knowledge and autonomy to allow them to exert control over a certain decision [START_REF] Ozer | Mechanisms governing empowerment effects: a self-efficacy analysis[END_REF].

Evidence shows that consumers enjoy settings where they are enabled to demonstrate competence and creativity to the extent that such experiences do not leave them overwhelmed by a flow of instructions or too many product attributes [START_REF] Thompson | Feature fatigue: When product capabilities become too much of a good thing[END_REF][START_REF] Dahl | Thinking inside the box: Why consumers enjoy constrained creative experiences[END_REF]. The viability of customer empowerment therefore relies on consumers perceiving their skills and abilities as adequate enough to act successfully, regardless of their actual competence.

Importantly, the relationship between empowerment and perceived competence is not necessarily causal. It is true that perceived competence can be conceived as a byproduct of power, insofar as power can produce an inflated perception of one's ability to reach desired outcomes on their own (Fast et al., 2009;[START_REF] Tost | Power, competitiveness, and advice taking: Why the powerful don't listen[END_REF]. Nevertheless, people can feel competent or incompetent regardless of the power state they are in [START_REF] Cho | Power, defensive denigration, and the assuaging effect of gratitude expression[END_REF][START_REF] Fast | When the boss feels inadequate: Power, incompetence, and aggression[END_REF][START_REF] Rucker | Power and consumer behavior: How power shapes who and what consumers value[END_REF]. Suppose, for instance, Jack is told that he is in charge of building and monitoring his financial portfolio. Jack might feel inadequate in handling that sudden empowerment because of his inexperience in financial matters, the complexity of the information he is presented with, or because Jack is non-tech savvy and the task requires digital devices. Jack may possess the actual competence to perform the task but view himself as not competent enough to handle the requirements the task implies.

Past research suggests power holders whose competence has been threatened experience insecurity and diminished self-worth which they then compensate for by displaying denigration and aggressive tendencies toward their subordinates [START_REF] Cho | Power, defensive denigration, and the assuaging effect of gratitude expression[END_REF][START_REF] Fast | When the boss feels inadequate: Power, incompetence, and aggression[END_REF]). Lacking competence is especially threatening to power holders in the context of social interactions with subordinates, where the power holder may feel at risk of being discredited. In a management context, Fast and colleagues (2014) showed that managers whose sense of competence was low were less willing to solicit input from employees and more negatively evaluated employees who spoke up.

In the context of brand anthropomorphism, brand relationships are not unidirectional but include consumers' perception of what they think brands think of them [START_REF] Macinnis | Humanizing brands: When brands seem to be like me, part of me, and in a relationship with me[END_REF][START_REF] Kim | Minions for the Rich? Financial Status Changes How Consumers See Products with Anthropomorphic Features[END_REF]. We expected that threats to feelings of competencethat is, situations heightening feelings of incompetence (e.g., negative feedback following a task)-would lead empowered consumers to feel negatively toward anthropomorphized brands. Specifically, we expected that they would avoid such brands, or when forced to engage with an anthropomorphized brand, feel resentment and dislike the product they represent. Resentment refers to the feeling of bitterness elicited by a situation perceived as unfair [START_REF] Marticotte | Schadenfreude, attitude and the purchase intentions of a counterfeit luxury brand[END_REF]. As empowered consumers whose perceived competence has been threatened forcefully engage with an anthropomorphized brand, the negativity they experience because of it (e.g., insecurity) may overshadow and negate the positive experience of social dominance. Such consumers may feel resentful because they believe they were deprived from the enjoyable experience of social dominance that empowerment entails. Put differently, feelings of situational incompetence in presence of an anthropomorphized brand might dampen feelings of social dominance and heighten resentment toward a brand perceived as an obstacle preventing them from enjoying empowerment.

H3: When situational feelings of competence are low (vs. high), an elevated sense of power decreases the appeal of anthropomorphized brands.

H4:

The decreased appeal of anthropomorphized brands following an elevated sense of power in the context of low (vs. high) situational feelings of competence, is driven by increased feelings of resentment.

In contrast to situational incompetence, chronic sense of incompetence is fairly rare (e.g., severe case of depression; [START_REF] Bandura | Self-efficacy[END_REF]. We thus expected that when chronic sense of competence is below a certain threshold, an elevated sense of power would no longer lead individuals to seek out anthropomorphized brands to experience dominance, but would not lead to negativity toward them. Although self-doubts naturally set in following domainspecific perceptions of incompetence (e.g., failure to pass a test), most people endorse optimistic self-appraisals of capabilities, which allow them to go through life despite its impediments and difficulties [START_REF] Bandura | Self-efficacy[END_REF].

Overview of studies

Our hypotheses were tested across five studies. Studies 1 and 2 tested H1 by measuring participants' chronic perceived competence. We expected that the negative effect of power on preference for anthropomorphized brands would be triggered by threats to perceived competence. Accordingly, Studies 3, 4A, and 4B manipulated perceived competence and tested H3. Study 4A shed light on mechanisms and tested H2 and H4.

Throughout our studies, we tested our hypotheses using real brands (Studies 1 and 2) and fictitious brands (Studies 3, 4A, and 4B). We considered sense of power as a chronic difference (Study 1) and a psychological state which we experimentally induced using memory tasks (Study 2) and marketing-relevant scenarios (Studies 3, 4A, and 4B). Pretests and manipulation checks designed to ascertain the effectiveness and orthogonality of our manipulations are provided in the Web Appendix.

Study 1

The purpose of Study 1 was to provide initial support for our hypothesis H1 that an elevated sense of power drives preference for anthropomorphized brands when chronic perceived competence is high but not low. This study consisted of two measured factors (sense of power and perceived competence).

Procedure

Participants were 103 American residents (37.9% female, Mage=33.8, SDage=11.3) who completed a study online (provider: Prolific). They were invited to participate in two unrelated studies. The "first study" was portrayed as focusing on consumer-brand relationships and contained our dependent variable. The "second study" was portrayed as a questionnaire investigating people's perception of themselves. Here, participants completed the sense of power scale [START_REF] Anderson | Power, optimism, and risk-taking[END_REF] and the general self-efficacy scale (GSE) alongside filler questions (e.g., material value scale). The GSE scale measures "one's belief in one's overall competence to effect requisite performances across a wide variety of achievement situations" (Chen, Stanley, & Eden, 2001, p. 63). Existing research highlights a slight difference between perceived competence and self-efficacy based on the notion that the former includes considerations of personal importance of the task [START_REF] Rodgers | Distinguishing perceived competence and self-efficacy: An example from exercise[END_REF].

However, the fact that the GSE scale measures competence as stable trait makes that divergence inconsequential.

Independent variables

Perceived competence. Participants completed the 8-item GSE scale on a 7-point scale (1=disagree strongly, 7=agree strongly; α=.95, M=5.15, SD=1.10). Scores were averaged.

Example items include "When facing difficult tasks, I am certain that I will accomplish them," and "I am confident that I can perform effectively on many different tasks" (See Web Appendix).

Sense of power.

Participants completed the 8-item power scale on a 7-point scale (1=disagree strongly, 7=agree strongly; α=.92, M=4.64, SD=1.08). Scores were averaged. All items started with "In my relationships with others." Example items include "I can get people to listen to what I say" and "My wishes do not carry much weight (reversed)" (See Web Appendix).

Dependent variable

Participants were asked to choose which brands they preferred in each of five pairs of anthropomorphized versus neutral brands. Participants were told to choose as if they had to buy the product right now (snacks, breakfast cereal, canned vegetables, pancake mix, and house cleaners; see Appendix). A pretest (N=168) found that for each of the five pairs of brands, there were as few differences as possible in terms of brand recognition, brand liking, frequency of buying, and sign of status (see Web Appendix). Further testing revealed that the anthropomorphized brands were successfully perceived as such (see Web Appendix). Five additional pairs of brands that did not differ with respect to anthropomorphism were included as fillers. The ten pairs of brands were presented in random order, as was the display order of the anthropomorphized versus neutral brand.

Results

We first tested for multicollinearity because of the expected correlation between power and GSE (r=.61, p < .001). The variance inflation factors were equal to 1.91, which is far below the critical threshold level of 10 [START_REF] Hair | Multivariate Data Analysis[END_REF], thus suggesting no multicollinearity concerns. Next, we conducted a repeated measures logistic regression analysis. Regressing preference for anthropomorphized brands on mean-centered power, mean-centered GSE, and their interaction revealed a marginally significant power × GSE interaction (b=.11, SE=.06, Z=3.19, p=.074, Exp(B)=1.12) (along with no main effect of power, b=.14, SE=.11,Z=1.72,p=.190,Exp(B)=1.16,or GSE,SE=.10,Z=.30,p=.585,Exp(B)=.945). To decompose further this interaction, we ran a floodlight analysis based on the Johnson-Neyman (JN)

technique to identify regions of GSE in which the effect of power on preference for anthropomorphized brands was significant [START_REF] Spiller | Spotlights, floodlights, and the magic number zero: Simple effects tests in moderated regression[END_REF]. Supporting H1, we found that the effect of power on preference for anthropomorphized brands was significant (p ≤ .05) among participants whose GSE was higher than 6.05 (bJN=.25, SE=.13, Exp(B)=1.28; 30% of participants) and was non-significant below that threshold.

To conclude, we find evidence that chronic perceived competence is an important driver of the influence of power on preference for anthropomorphized brands. Specifically, Study 1 demonstrates that the probability of choosing an anthropomorphized (versus neutral) brand increases as consumers' sense of power grows concomitantly with their sense of competence.

Study 2

Study 1 measured sense of power as an enduring, stable difference and thus could not conclusively speak to the effect of engaging individuals in ad hoc power relations. Study 2 addressed this limitation and tested H1 by manipulating sense of power (high vs. low vs.

neutral) and measuring chronic perceived competence.

Procedure

Participants were 260 American residents (41.5% female, Mage=32.3 years, SDage=11.9) who completed a study online (provider: Prolific). Participants were invited to participate in two unrelated studies. The "first" study was portrayed as a recall task designed to investigate people's daily routine and served as our manipulation of sense of power. The "second" study was portrayed as focusing on consumer-brand relationships and served as our dependent variable. Finally, participants completed the GSE scale used in Study 1 to measure perceived competence.

Independent variables

Perceived competence. Participants completed the 8-item GSE scale used in Study 1 (α=.95, M=5.18, SD=1.15).

Sense of power.

Participants were assigned to one of three conditions. In the highpower condition, participants thought of two occasions in their daily life or weekly routine when they feel powerful. We specified that "by power, we mean a situation in which you control the ability of another person or persons to get something they want, or are in a position to evaluate those individuals." In the low-power condition, participants thought of ten such occasions. We modeled these two conditions after ease-of-retrieval manipulations [START_REF] Schwarz | Ease of retrieval as information: another look at the availability heuristic[END_REF] and designed them to minimize differences in the content of the manipulation while altering people's sense of power. Our hypothesis was that people would feel less powerful after they tried to think of ten occasions when they are in a powerful position than after trying to think of two. Moreover, we included a neutral condition to test that powerfulness, and not powerlessness, was the driving force of our effect. Participants in the neutral condition were asked to think of two routine activities that they typically do on an average day. Pretesting revealed that participants in the high-power condition reported higher feelings of power than both those in the low-power condition (p=.016) and the neutral condition (p=.056). We found no difference between these last two (p=.628). The absence of a significant difference between the neutral and low-power conditions is not surprising given that lacking power tends to be a more common psychological state than feeling powerful in life [START_REF] Schaerer | Low power individuals in social power research: A quantitative review, theoretical framework, and empirical test[END_REF].

Dependent variable

Participants completed the dependent variable used in Study 1.

Results

We conducted a repeated measures logistic regression analysis. Regressing preference for anthropomorphized brands on the three power conditions (dummy coded with the highpower condition serving as baseline), mean-centered GSE, and the two interaction terms (high-power vs. low-power × GSE, and high-power vs. neutral × GSE) revealed a significant high-power vs. low-power × GSE 1) but not below that threshold. Therefore, participants with a high chronic perceived competence (above 6.34) expressed a preference for anthropomorphized brands when they were placed in a high (vs. low)-power situation.

Moreover, Figure 1 suggests that the responses of participants in the neutral condition were in between those of participants in the two power conditions, yet closer to the responses of participants in the low-power condition. While we found that the effect of high-power vs.

neutral mind-set was marginally significant when GSE reached 6.34 (b=-.31, SE=.19, Z=2.75, p=.097, Exp(B)=.732), further analyses failed to reveal significant differences between lowpower and neutral mind-sets at any value of GSE. This is consistent with the results of the pretest of sense of power whereby participants in the neutral condition provided responses closer to those in the low-power condition than those in the high-power condition. Thus, the results of Study 2 suggest, as expected, that our effect was driven by feelings of powerfulness and not powerlessness. Furthermore, Study 2 suggests that an elevated sense of power can foster people's willingness to show dominance even if the boost in power is contextually disconnected from the purchasing decision.

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Study 3

Study 3 tested H1 and H3 by manipulating perceived competence. Moreover, this study aimed to test the robustness of our results to the inclusion of the perceived amiability of the preferred brand as a control variable. In Studies 1 and 2, we used brands ostensibly projecting amiability through smiles and overall positive expressions (see Appendix). One could therefore argue that we found our effect because the relationship between power and preference for anthropomorphized brands was distorted by the appeal of friendly brands.

Study 3 ruled out this alternative explanation and used a 2 (sense of power: high vs. low) × 2 (perceived competence: high vs. low) between-subjects design.

Procedure

Participants were 212 British residents (70.5% female, Mage=39.3 years, SDage=10.8)

who completed a study online (provider: Prolific). We used the consumption-relevant context of car rentals under the pretense of investigating people's reaction to renting a car in unfamiliar situations. Participants were asked to imagine that they wanted to spend a few days away in France. They further imagined that, as they were flying to their destination, they were thinking of renting a car to visit the surroundings. Participants were then informed that the renting procedure at the airport was done through a self-service machine. Our manipulations and measurements were portrayed as steps of the car renting procedure. The first step was a driving test designed to assess people's ability to drive in France (as foreigners) and served as our manipulation of perceived competence. The second step consisted of the renting procedure and served as our manipulation of sense of power. The third step consisted of a choice between two travel apps as a token of our appreciation and served as our dependent variable.

Independent variables

Perceived competence. Participants were asked to complete a driving test composed of ten multiple-choice questions based on real driving situations. Each webpage presented a photograph followed by a question about the lawful way to behave (see Web Appendix).

Upon completion of the test, participants were reminded that the ten questions were based on a real driving test designed by the French driving and transport authority. They were then randomly assigned their scores via the software. Five categories of scores were possible:

"Poor", "Fair", "Average", "Good", and "Excellent" and participants saw that their scores either fell in the range of "Poor" (low-perceived-competence condition) or "Excellent" (highperceived-competence condition). All participants subsequently received explanations about the meaning of their score regarding their ability to drive safely in France (see Web Appendix). Testing confirmed the credibility of the feedback following the test (see Web Appendix). A manipulation check revealed that our manipulation influenced perceived competence in the expected direction (p<.001) without influencing feelings of powerfulness (ns).

Sense of power. Participants in the high-power condition (random assignment) were introduced to a fictitious car rental company (Procar) with the following slogan "Your (temporary) car, your rules." They further read that "At Procar, you're in charge. You decide all there is to decide about the car. You decide about the model. You decide about the color.

You decide where and when you want the car delivered to you. We comply with all your wishes." Participants were then asked a series of questions about their preferences to match this statement. In the low-power condition, participants read the slogan "Your (temporary) car, our rules" and that "At Procar, we assign you a car. The model displayed in the following screen will be attributed to you. By accepting the car, you agree to comply with our policy."

All low-power participants were then given a series of statements about the designated car in terms of model, color, and delivery. Daily rates would be the same for all models across conditions (see Web Appendix). A manipulation check revealed that our manipulation influenced feelings of powerfulness in the expected direction (p<.001) without influencing perceived competence (ns).

Dependent variable

Next, participants were told that, as a token of our appreciation, they could choose one of two travel apps. The apps were identical except for their logo. One logo was anthropomorphized while the other was not (see Appendix

Control variable

Finally, to measure perceived amiability, participants were asked to what extent they perceived the app they chose as a friend, a playmate, a companion, and a comrade on a 7point scale (1=Not at all, 7=A lot; α=.91). Neither experimental factors, nor their interaction, had a significant effect on the perceived amiability of the chosen app (ps>.36). The following results account for the covariate but remained very similar without it (see Web Appendix).

Results

We conducted a logistic regression analysis to test the effects of power (low power=-.5, high power=.5), perceived competence (low competence=-.5, high competence=.5), their interaction, and the perceived amiability of the chosen app (i.e., the covariate) on preference for the anthropomorphized brand. The power × perceived competence interaction was significant, b=1. who completed a study online (provider: Prolific). While Studies 1 to 3 relied on a rule of thumb whereby we allocated at least 50 participants per cell, the sample size of Study 4A was based on an a priori power analysis to detect an effect size of f=0.16 (estimated from previous studies) with a power of 0.80 and α=0.05 [START_REF] Cohen | Statistical Power Analysis for the Behavioral Sciences[END_REF] and given non-random assignment within the competence conditions. We used the consumption-relevant context of financial services. Participants were instructed to imagine that they received a rather significant amount of money relative to their household income (e.g., work bonus, unexpected cash gift) and that they wanted to invest the money. They then imagined that while looking for investment information online, they found P&M Capital (a fictitious investment firm). Participants read that many banks and financial institutions try to get a sense of their customers' level of familiarity with financial matters as a preliminary step toward investment. In that vein, they were asked to complete a 16-question financial literacy test. This served as our manipulation of perceived competence. Next, participants imagined they continued exploring P&M Capital's website and stumbled on their service offering. This second phase served as both our manipulation of sense of power and our manipulation of brand anthropomorphism. Finally, participants completed the dependent variable and mechanism variables followed by manipulation-check questions.

Independent variables

Perceived competence. Participants were asked to complete a financial literacy test adapted from Fernandes, Lynch, and Netemeyer (2014) which assesses people's ability to understand and engage in both short-term financial management and long-term financial planning (see Web Appendix). Following each question, participants could see the correct answer and were provided their score upon completion. They were further told that the same test had been completed by a large representative sample of consumers and a graph displayed the score distribution (see Web Appendix). Participants who scored lower than 60 percent ( 9or less correct answers), were told that they had scored lower than most people (lowperceived-competence condition, n=168). Participants who scored higher than 60 percent (10 or more correct answers, high-perceived-competence condition, n=276) were told they had scored higher than most people. The 60-percent threshold was based on a pretest (N=100). All participants subsequently read an explanatory statement about the meaning of their score (see Web Appendix). A manipulation check revealed that our manipulation influenced perceived competence in the expected direction (p<.001) without influencing feelings of powerfulness (ns).

Sense of power. Participants were randomly assigned to one of two power conditions.

In the high-power condition, participants were introduced to the fictitious investment firm with the following slogan "Take charge of your money" and description "Experience more power, more control. P&M Capital introduces you to an online platform designed to let you build your own customized investment portfolio, to monitor your performances in real time, and to make adjustments as you see fit. You can access the online platform 24/7, anywhere in the world." In the low-power condition, participants read the following slogan "The investment firm in charge of your money" and description "Experience more sincerity, more authenticity. Call on our team of professionals to get started with your investment portfolio, to monitor your performances, and to make adjustments as they see fit. You can call our team 24/7 or find them in our local branches." Hence, low-power participants were told that they needed to go through the investment firm to manage their money, whereas high-power participants were empowered to do it themselves. In both conditions, the description of the service offering was extended across four webpages (see Web Appendix). A manipulation check revealed that our manipulation influenced feelings of powerfulness in the expected direction (p<.001) without influencing perceived competence (ns).

Brand anthropomorphism.

As participants learned about P&M Capital's service offering, they were randomly exposed to one of two logos (see Appendix). The logo was present on the four webpages describing the service offering. While the service offering description was identical across conditions, the anthropomorphized-brand condition included speech bubbles to emphasize the anthropomorphic features of the logo (see Web appendix).

Dependent and mediating variables

Next, participants rated P&M Capital's service offering on three items using a 7-point semantic differential scale (1=Bad, Unappealing, Negative; 7=Good, Favorable, Positive, α=.95). Participants then rated how dominant they felt (i.e., "dominant/strong," r=.82, p<.001)

and how resentful they felt (i.e., "resentful/bitter," r=.93, p<.001) while looking over P&M Capital's service offerings on a 7-point scale (1=Not at all, 7=Very).

Control variable

We measured perceived amiability of the brand (i.e., "I see P&M Capital as friendly/ sympathetic/ welcoming" 1=Not at all, 7=Completely, α=.90) as a covariate as in Study 3. A 2×2×2 ANOVA on perceived amiability revealed nonsignificant effects. The following results account for the covariate but remained similar without it (see Web Appendix).

Results

Service offering ratings. An ANCOVA predicting participants' ratings of the service offering yielded the predicted three-way interaction, F( 1 Put differently, when perceived competence was high, high-power participants exposed to an anthropomorphized brand rated the service offering more positively than highpower participants exposed to a neutral brand (MAnthro=5.65 vs. MNeutral=5.06, SD=1.48, F(1, 435)=3.67, p=.056, η²p=.008). This difference was reversed when perceived competence was low. High-power participants exposed to an anthropomorphized brand rated the service offering more negatively than high-power participants exposed to a neutral brand (MAnthro=5.04 vs. MNeutral=5.47, SD=1.02, F(1, 435)=3.23, p=.073, η²p=.007). Effects remained when controlling for education and participants' score at the financial literacy test.

INSERT_FIGURE_3_ABOUT_HERE

Mechanism. We then ran a moderated mediation model following Hayes (2018, model 12). We predicted that feelings of dominance (resentment) drove the effect of power on the appeal (rejection) of anthropomorphized brands, but not neutral brands, when feelings of competence were bolstered (threatened). In separate regressions predicting the two mechanism variables from power, perceived competence, brand anthropomorphism, and all their interactions, we found that the three-way interaction was marginally significant on feelings of dominance SE=.45,|t(435)|=1.68,p=.093,d=.16) and significant on feelings of resentment (b=-1.32, SE=.50, |t(432)|=2.63, p=.009, d=.25).

Spotlight analyses [START_REF] Spiller | Spotlights, floodlights, and the magic number zero: Simple effects tests in moderated regression[END_REF] Moreover, using a bootstrapping procedure with 5,000 samples, we found that given an anthropomorphized brand and under high-perceived competence, power predicted ratings through feeling of dominance (CI95: .040 to .271), thus supporting H2. We also found that given an anthropomorphized brand and under low-perceived competence, power predicted ratings through feelings of resentment (CI95: -.289 to -.016), thus supporting H4. No other indirect effect emerged (see Web Appendix). Thus, feelings of dominance (resentment) mediated the effect of power on the appeal (rejection) of anthropomorphized brands, but not neutral brands, when feelings of competence were bolstered (threatened).

Study 4B

Because Study 4A forced participants to engage with a brand (anthropomorphized or neutral), it did not include a measure of brand preference. Hence, to provide more direct evidence for our assumption that lower (higher) service offering ratings suggested brand rejection (endorsement), we ran a follow-up study in which we measured brand preferences.

Moreover, this follow-up study aimed to account for confounding factors stemming from the context of financial services used in Study 4A. One could argue that the perceived difficulty of taking financial decisions and the desire to seek advice could have confounded with our independent variables and led participants to assess more favorably the anthropomorphized option because of its perceived inherent ability to help. Study 4B ruled out these alternative explanations and used a 2 (sense of power: high vs. low) × 2 (perceived competence: high vs.

low) between-subjects design.

8.1.Procedure

Participants were 252 American residents (51.6% female, Mage=36.5 years, SDage=9.2)

who completed a study online (provider: Prolific). Sample size was determined using the rules previously provided. Study 4B replicated the manipulations of perceived competence and sense of power used in Study 4A before measuring brand preference between two financial instruments whose resemblance was betrayed by their brand names and logos (anthropomorphized or neutral).

Independent variables

Perceived competence. Participants completed the manipulation used in Study 4A with two notable differences. First, we modified the threshold we used to allocate participants to conditions because of the large discrepancy in cell size we observed in Study 4A. Participants who provided 10 or less correct answers out of 14 were allocated to the low-perceivedcompetence condition (n=114) whereas those who provided 11 or more correct answers out of 14 were allocated to the high-perceived-competence condition (n=138). Second, the feedback participants received following the test varied depending on conditions. High (vs. low)perceived-competence participants read that the average score obtained by a large sample of consumers to the same test was 60% (vs. 75%). In doing so, we aimed to highlight their performance or lack thereof. Manipulation checks provided results consistent with Study 4A

(see Web Appendix).

Sense of power. Participants completed the manipulation used in Study 4A.

Manipulation checks revealed that the manipulation had the expected effect (see Web Appendix).

Dependent variable

Participants were asked to imagine that after further exploring the P&M Capital website, they were looking over a selection of investment products, which led them to develop an interest for Exchanged Traded Funds (ETFs). After reading information on ETFs, participants imagined that they decided to invest their sudden infusion of cash through one of the two ETFs based on US offerings provided by P&M Capital. The two EFTs were virtually identical (e.g., return; see Web Appendix) except for their name and logo (see Appendix).

Preference for one or the other served as our dependent variable. We employed three items, captured on 11-point scales: "Which ETF would you prefer to buy between Cape Expertise and The Expert?" "Which ETF would you choose between Cape Expertise and The Expert?"

and "For which ETF would you pay the management fees between Cape Expertise and The Expert? (+5=Definitely prefer Cape Expertise, +5=Definitely prefer The Expert; α=.92). The scales were subsequently converted to be anchored by (-5) and (+5) with higher scores representing preference for the anthropomorphized option. Presentation order (left or right)

was randomized across participants.

8.4.Control variables

Finally, we measured the perceived difficulty of making a financial decision on a 7point scale (1=Extremely difficult, 7=Extremely easy). Neither experimental factors, nor their interaction, had a significant effect on perceived difficulty (ps>.13). We also measured

General discussion

Five studies supported our hypotheses. In Studies 1 and 2, we measured perceived competence as a stable trait under the assumption that individuals tend to form positive selfappraisals of capabilities, and found that an elevated sense of power drives preference for anthropomorphized brands when chronic sense of competence is high but not low. In Studies 3, 4A, and 4B, we found that when participants' perceived competence was threatened (vs.

bolstered), consumer empowerment lowered (vs. increased) the appeal of anthropomorphized brands. Study 4A further examined mechanism and revealed that empowering consumers while their feelings of competence were threatened no longer heightens feelings of dominance but led to feelings of resentment. Overall, these results provide evidence for the existence of divergent effects of power on preference for anthropomorphized brands depending on consumer perceived competence.

1 Four weeks after data collection, we contacted the participants and asked them to fill the GSE scale from Studies 1 and 2 (M=5.30, SD=1.14); 203 of them participated (dropout rate was identical between conditions).

Regressing preference for the anthropomorphized option on power, mean-centered GSE, their interaction, and the three covariates revealed a marginally significant power × GSE interaction (b=.44,SE=.25,t(193)=1.77,p=.077;without covariates: p=.043). Further analyses based on the JN technique revealed that the effect of high (vs. low)-power was significant (p ≤ .05) among participants whose GSE was higher than 5. 96 (bJN=.64 SE=.32,t(193)=1.97; 34% of participants) and was non-significant below that threshold. This is consistent with the results of Studies 1 and 2.

Theoretical contributions

This research adds to the budding literature on power and brand anthropomorphism.

First, our work highlights that the relationship between power and brand anthropomorphism holds only when consumers feel competent. Consistent with others [START_REF] Bandura | Self-efficacy[END_REF][START_REF] Fast | Managing to stay in the dark: Managerial self-efficacy, ego defensiveness, and the aversion to employee voice[END_REF], Studies 1 and 2 found that feelings of competence were relatively high in the absence of threat (i.e., significantly higher than mid-scale, ps <.001). While this can explain the results of prior works (e.g., [START_REF] Kim | Gaming with Mr. Slot or gaming the slot machine? Power, anthropomorphism, and risk perception[END_REF], we showed that the appeal of anthropomorphized brands based on the experience of power disappeared when perceived competence was not high. What's more, our findings suggest that empowering customers when they must deal with competency threats can lead to an avoidance tendency or negative evaluations of product bearing anthropomorphic features.

Second, this research highlights the role of brand engagement in empowerment contexts crippled with threats to perceived competence. Incompetence in high-power situations can heighten insecurity and trigger mechanisms of ego defensiveness [START_REF] Cho | Power, defensive denigration, and the assuaging effect of gratitude expression[END_REF][START_REF] Fast | When the boss feels inadequate: Power, incompetence, and aggression[END_REF][START_REF] Fast | Managing to stay in the dark: Managerial self-efficacy, ego defensiveness, and the aversion to employee voice[END_REF]. However, past research has not shown when incompetent power holders denigrate or merely avoid subordinates. Put all together, our studies suggest that when low-competence empowered consumers have a choice, they choose to avoid the unpleasantness of exposing their incompetence by preferring neutral brands.

However, when forced to engage with an anthropomorphized brand, this unpleasantness seems to translate into resentment, which in turn negatively affects product evaluation.

Third, this research brings insight on the motivational factors that drive brand anthropomorphism. Despite predictions that consumers would prefer anthropomorphized brands under competency threat as a way of helping them regain control over their environment (MacInnis & Folkes, 2017), we found the opposite depending on one's level of power. This does not mean that we discard desire for competence as a potential driver of brand anthropomorphism. Brands may be seen as enabling the self by providing consumers with a sense of competence [START_REF] Park | Attachment-aversion (AA) model of customer-brand relationships[END_REF], especially if the brand projects competence and reliability [START_REF] Khenfer | Interventionist external agents make specific advice less demotivating[END_REF]. The current research highlights the interplay between power and perceived competence on brand relationships.

Managerial implications

Our findings suggest that managers should be mindful when empowering customers.

We found that providing consumers with the power to make decisions that affects others or the company did not necessarily bear the expected effects. While we focused on brand anthropomorphism, we found that perceived competence played a crucial role on the behavioral consequences of power. Therefore, programs designed to empower customers should occur concurrently with initiatives to boost their sense of competence, for instance, through positive feedback and encouragements.

Moreover, although managers often attribute anthropomorphic features to their brands, this practice is not always relevant and may even backfire. Consumers are often told that they have power regardless of whether or not they actually have any kind of control over the purchasing process or the various aspects of their lives. For instance, Burger King famously declares "Have it your way." Relying as such on cues of empowerment in contexts of brand anthropomorphism-Burger King' mascot: "the King"-appears effective, or at the very least, not detrimental, as long as consumer perceived competence is not threatened. If perceived competence is threatened, activating a high-power mind-set may drive consumers away. As such, non-tech savvy consumers may be put off by the perspective of "having it their way" through a self-service kiosk under the eyes of the well-known mascot.

Limitations and future research

Although our findings were replicated across several studies, some questions remain.

While Study 2 shows that our effect is driven by feelings of powerfulness, the results of Study 3 lead us to wonder whether feelings of powerlessness can also influence consumer preference for anthropomorphized brands. The effect of our power manipulation in the lowperceived-competence condition seems to rely on feelings of powerlessness (see fig. 3). We found that when sense of power was lowered, low (vs. high)-perceived-competent participants preferred the anthropomorphized brand more SE=.41,p=.024 Exp (B)=.40; MLow competence=61.1%, vs. MHigh competence=38.5%). We found no significant difference between the preferences of low-power/low-competence participants and those of high-power/high competence participants. Nevertheless, this result does not discard our claim that power decreases the appeal of anthropomorphized brands when feelings of perceived competence are threatened. It suggests that, in such circumstances, taking power away from consumers leads them to seek social support even among inanimate objects. This is consistent with research suggesting that being lower in the hierarchy makes individuals more dependent on others for valuable resources [START_REF] Rucker | Power and consumer behavior: How power shapes who and what consumers value[END_REF]).

Moreover, one could argue that the anthropomorphized brands used throughout our studies were docile, unthreatening. A brand displaying a strong and authoritarian character as its logo (e.g., Captain Morgan) might repel individuals who feel powerful. Despite high levels of perceived competence, they might see a challenger to their power and prefer to avoid it as a way of maintaining their desire to dominate. On top of brand personality, the personal importance of the task for which feelings of competence have been altered may also play a critical moderating role in how our effects unfold. To the extent that people put their sense of competence into perspective when they take on personally important tasks [START_REF] Rodgers | Distinguishing perceived competence and self-efficacy: An example from exercise[END_REF], it is possible that the unappealing effect of anthropomorphized brands weakens (strengthens) if the purchasing context has little (strong) relevance for them. These remaining questions constitute as many directions for further research.

Finally, one could note that some of our results were only marginally significant with small effect sizes. While sample size plays a crucial role in the statistical power of a test and may have been a factor in the present case [START_REF] Cohen | Statistical Power Analysis for the Behavioral Sciences[END_REF], it may be that our estimates are correct but the size of our effect is small in the real world. The reality is that estimates of effect sizes in past literature tend to be inflated and that most true effect sizes tend to be small [START_REF] Meyvis | Increasing the power of your study by increasing the effect size[END_REF]. Nevertheless, it does not mean that our effects are irrelevant. In a marketing environment where competition grows ever more aggressive, every bit helps.

10.

Fig. 1 . 34 Fig. 2 .Fig. 3 .

 13423 Fig. 1. Effect of sense of power on preference for anthropomorphized brands for all values of

Fig. 4 .

 4 Fig. 4. Effect of sense of power on preference for the anthropomorphized option depending on levels of perceived competence (Study 4B).

  ). Presentation order (left vs. right) was randomized. A pretest (N=55) found no differences between logos in terms of familiarity (|t(41)|=.46, p=.645) and liking (|t(47)|=.91, p=.366). Furthermore, participants indicated to what extent they felt each logo looked like a person, had its own personality and seemed almost as if it had intentions on a 7-point scale (1=Not at all, 7=A lot; αanthro=.74, αneutral=.65).

The anthropomorphized logo was perceived as more human-like (M=4.60, SD=1.27) than the neutral logo (M=2.

53, SD=1.18, |t(46)|=10.11, p<.001)

.

  , 435)=5.58, p=.019, η²p=.013 (along

with a main effect of perceived amiability, F(1, 435)=165.27, p<.001, η²p=.275, but no main effect of power, F(1, 435)=.04, p=.847, η²p=.000, perceived competence, F(1, 435)=.14, p=.714, η²p=.000, or brand anthropomorphism, F(1, 435)=.23, p=.630, η²p=.001). Simple effects revealed that the interaction unfolded as expected (fig.

3

). First, supporting H1, when the brand was anthropomorphized and perceived competence was high, high (vs. low)-power participants rated the service offering more positively (MHigh power=5.65, SD=.91 vs. MLow power=5.14, SD=1.30, F(1, 435)=5.58, p=.019, η²p=.013). Second, supporting H3, when the brand was anthropomorphized and perceived competence was low, high (vs. low)-power participants rated the service offering less positively (MHigh power=5.04,

SD=1.61 vs. MLow power=5.65, SD=.99, F(1, 435)=3.76, p=.053, η²p=.009)

.

  Given a neutral brand, we found no difference between power conditions under high-perceived competence(b=.10, SE=.22, |t(432)|=.46, p=.647, d=.04) or under low-perceived competence SE=.28, |t(432)|=1.34, p=.182, d=.13).Next, in a single regression predicting participants' ratings of the service offering with perceived amiability, the two mediators, the experimental variables, and all the interactions, feelings of dominance(b=.25, SE=.04, |t(430)|=6.69, p<.001, d=.64) and feelings of resentment SE=.04, |t(430)|=3.91, p<.001, d=.40) were significant predictors.

	SE=.21, |t(435)|=1.50, p=.136, d=.14) and a negative effect of power under low-perceived
	competence (b=-.76, SE=.27, |t(435)|=2.79, p=.006, d=.27). Further spotlight analyses
	revealed that high (vs. low)-power participants reported greater feelings of resentment given
	an anthropomorphized brand and under low-perceived competence (b=.87, SE=.28,
	|t(432)|=3.13, p=.002, d=.30) but not under high-perceived competence (b=.03, SE=.22,

revealed that high (vs. low)-power participants reported greater feelings of dominance given an anthropomorphized brand and under highperceived competence (b=.60, SE=.21, |t(435)|=2.88, p=.004, d=.28) but not under lowperceived competence

(b=.35, SE=.27, |t(435)|=1.32, p=.19, d=.13)

. Given a neutral brand, we found no difference between power conditions under high-perceived competence

(b=.31, |t(432)|=.13, p=.90, d=.01)

.

  participants' desire to seek advice: "To what extent do you think you require the help of a professional advisor when it comes to investment products?" and "To what extent do you think you need someone to give you advice when it comes to investment products?" on 7point scales (1=Not at all, 7=A lot; r=.82, p<.001). Although perceived competence had a significant effect on desire to seek advice (p<.001), the effects of power and the competence ×

	further support to our theorizing. Effects remained when controlling for education and
	participants' score at the financial literacy test. 1
	power interaction were not significant (ps>.46). We measured perceived amiability of the INSERT_FIGURE_4_ABOUT_HERE
	chosen ETF using the items in Study 4A; a 2×2 ANOVA revealed nonsignificant effects. The
	following results account for the three covariates but remained similar without them (see Web 9.
	Appendix).
	8.5.Results
	An ANCOVA predicting preference for the anthropomorphized option yielded the
	predicted two-way interaction, F(1, 245)=12.11, p=.001, η²p=.047 (along with no main effects
	of perceived amiability, F(1, 245)=.33, p<.568, η²p=.001, perceived difficulty, F(1, 245)=.00,
	p=.987, η²p=.000, desire for advice, F(1, 245)=1.22, p=.267, η²p=.005, perceived competence,
	F(1, 245)=.00, p=.949, η²p=.000, or power, F(1, 245)=.22, p=.716404, η²p=.001). Simple
	effects revealed that the interaction unfolded as expected (fig. 4). First, supporting H1, when
	feelings of perceived competence were high, high (vs. low)-power participants preferred the
	anthropomorphized option to the neutral option (MHigh power=.99, SD=1.87 vs. MLow power=-.02,
	SD=1.56, F(1, 245)=8.64, p=.004, η²p=.034). Second, supporting H3, when feelings of
	perceived competence were low, high (vs. low)-power participants preferred the neutral
	option to the anthropomorphized option (MHigh power=.23, SD=2.06 vs. MLow power=.99,
	SD=2.27, F(1, 245)=4.17, p=.042, η²p=.017). A moderated mediation analysis revealed that
	none of the covariates mediated our effects (i.e., confidence intervals included zero, Hayes
	2018, model 8). The fact that our effects persisted when accounting for the covariates brings


Prof. Dr Michiel Postema
email: michiel.postema@ift.uib.no

Spiros Kotopoulis

Anthony Delalande

Helge Odd

Gilja

Odd Helge Gilja

Sonoporation: why microbubbles create pores

Ultrasound contrast agents are commonly added to the blood stream in ultrasonic imaging: contrast-enhanced ultrasound (CEUS). They consist of microscopically small bubbles (microbubbles) encapsulated by elastic shells. The most common shell materials are phospholipids. During an ultrasound cycle microbubbles oscillate, i.e., they expand and subsequently contract. Depending on their elastic properties, on the local conditions, and on the acoustic settings, they move in the direction of the sound field, coalesce with other microbubbles, fragment, jet, cluster, release their contents, and dissolve in the surrounding liquid. [START_REF] Postema | Contrast-enhanced and targeted ultrasound[END_REF] The diverse behaviour of encapsulated microbubbles in different acoustic regimes has triggered the idea to use them as ultrasound-controlled vehicles to facilitate the delivery of therapeutic agents to a site of interest. Such a noninvasive, localised, side-effect-free method would revolutionise drug delivery as we know it.

Cellular uptake of drugs and deoxyribonucleic acid (DNA) is increased when the region of interest is under sonication, and even more so when an ultrasound contrast agent is present. [START_REF] Postema | Ultrasound-directed drug delivery[END_REF] This increased uptake has been attributed to the formation of transient porosities in the cell membrane that have diameters up to 0.1 µm, i.e., big enough for the transport of drugs into the cell. The pores reseal themselves within one minute. The ultrasound-assisted transient permeabilisation of a cell membrane is called sonoporation. Understanding the physics underlying sonoporation is of uttermost importance for the development of ultrasound-activated therapeutic agents.

There are five non-exclusive hypotheses for explaining the sonoporation phenomenon from a physics point of view. [START_REF] Postema | CEUS and sonoporation[END_REF] These have been summarised in Figure 1. It is noted that fragmenting microbubbles cannot create pores in cells, since fragmentation costs energy.

(a) Push During its expansion phase, a microbubble might touch a cell membrane surface. The pushing motion would then cause the cell membrane to be locally disrupted. The pushing mechanism would occur within half an ultrasound cycle. However, under typical sonication conditions, microbubble excursion amplitudes are low. Also, typically, microbubbles are much more flexible than cells. Our current understanding of microbubble physics does not support the push mechanism if the microbubble is not attached. However, if the microbubble is already attached to the cell membrane whilst expanding, pushing under influence of radiation forces might cause the membrane to rupture. The latter mechanism might occur over multiple cycles.

(b) Pull

During the contraction phase of an oscillating microbubble, the plasma filling the void left by the contracting bubble might pull the cell membrane towards the microbubble. This pulling motion would then cause the cell membrane to be locally disrupted. The pulling mechanism would occur within half an ultrasound cycle. However, under typical sonication conditions, microbubble contractions do not result in an inertial collapse. Moreover, the replacive mass of a contracting microbubble is much lower than the fluid supposedly causing the pull. Therefore, this mechanism is less plausible than the push mechanism in non-attached conditions. However, if the microbubble is attached to the cell membrane, a similar mechanism might occur as described under (a), where pulling under the influence of radiation forces might cause the membrane to rupture.

(c) Jetting

Jetting is the asymmetric collapse of a bubble, creating a funnel-shaped protrusion through the bubble that is directed towards a boundary. This spectacular phenomenon has actually been optically observed on a microscopic scale through cells. [START_REF] Prentice | Membrane disruption by optically controlled microbubble cavitation[END_REF] The jetting phenomenon occurs within half an ultrasound cycle. However, jetting exclusively occurs when using high acoustic amplitudes, at the upper end of clinical settings. Also, there has not been any proof yet of cell survival after jetting. Based on empiric studies that relate jet length to pore size, we excluded the role of jetting as a dominant mechanism involved in sonoporation. [START_REF] Postema | Jetting does not cause sonoporation[END_REF]

(d) Streaming

If a microbubble is fixed to a membrane, the fluid streaming around the oscillating bubbles creates enough shear to rupture the membrane. [START_REF] Marmottant | Controlled vesicle deformation and lysis by single oscillating bubbles[END_REF] Here, long pulse lengths are required to set the fluid in motion. However, low acoustic amplitudes should suffice to create the rupturing shear of a typical cell membrane. Existing research has proven the feasibility of the streaming mechanism in bound conditions, so this mechanism should work for targeted contrast agents that attach to cells. Further research will show whether streaming around weakly-attached microbubbles creates enough shear for cell membranes to rupture.

(e) Translation

Owing to radiation forces, lipid-encapsulated microbubbles may translate through cell membranes or channels in the cell membrane. The microbubble may loose part of its shell whilst passing through the cell membrane. As a result, the gas will dissolve after entry. Figure 2 shows a graphic representation of the translation mechanism. In case of therapeutic loading, the load would be delivered directly into the target cell. This mechanism requires long pulse lengths and low acoustic amplitudes. Very recently, fluorescence-coated ultrasound contrast agent microbubbles were observed to move into HeLa cells at a low mechanical index (MI) of 0.15, using high-speed video footage under confocal microscopy. [START_REF] Delalande | Sonoporation at a low mechanical index[END_REF] The microbubbles dissolved after entering the cells. The cells survived the sonoporation treatment, confirming the transient character of sonoporation.

All five of these mechanisms require the presence of a microbubble in the vicinity of the cell. Yet, increased drug uptake has also been reported without the use of any ultrasound contrast agent, but merely an ultrasound field itself. Despite speculations about the role of inertial cavitation in the latter, clinical ultrasound scanners do not generate fields strong enough to create such spontaneous microbubbles in blood.

Recently, it was found that (bilayer) cell membranes themselves act as cavitation nuclei. [START_REF] Krasovitski | Intramembrane cavitation as a unifying mechanism for ultrasound-induced bioeffects[END_REF] Even at modest acoustic pressures, cell membranes might rupture due to the building up of gas cavities inside the bilayer. This important finding would explain the sonoporation in the absence of ultrasound contrast agent microbubbles. Moreover, it explains why bubbles are attracted to cells that are not in the travel path of the ultrasound wave. However, given the low MI at which cells attract microbubbles, more study is required regarding the safe use of ultrasound contrast agents in longpulse-length imaging.

In conclusion, in current clinical settings, four non-exclusive mechanisms are plausible for the physical explanation for sonoporation with the aid of ultrasound contrast agent microbubbles.

Figure 1 :

 1 Figure 1: Schematic representation of the five physical mechanisms supposedly involved in sonoporation.

Figure 2 :

 2 Figure 2: Schematic representation of a lipid-encapsulated microbubble translating into a cell owing to radiation forces (frames a-g) and subsequently dissolving (frames h-i).


Kristoffer Johansen

Michiel Postema. Introduction to antibubbles. Spiros Kotopoulis

Michiel Postema
email: michiel.postema@ift.uib.no

Introduction to antibubbles

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

smaller bubbles interacting. Both of the two respective phenomena mentioned above change the dynamics of the complete system with respect to the initial behaviour when separated. Indeed, similar to what is observed in economics when bubbles develop and interact over time.

From these examples it can be appreciated that bubble dynamics in physics has clear analogies to bubble dynamics in economics. Linear and non-linear oscillations [START_REF] Prosperetti | Bubble phenomena in sound fields: part two[END_REF], primary radiation forces [START_REF] Dayton | A preliminary evaluation of the effects of primary and secondary radiation forces on acoustic contrast agents[END_REF], secondary radiation forces, fragmentation [START_REF] Postema | Ultrasound-induced encapsulated microbubble phenomena[END_REF], coalescence [START_REF] Postema | Ultrasound-induced microbubble coalescence[END_REF], microfoam formation [START_REF] Kotopoulis | Microfoam formation in a capillary[END_REF], shock wave emission [START_REF] Johnston | Periodic shock-emission from acoustically driven cavitation clouds: a source of the subharmonic signal[END_REF], and microjetting [START_REF] Prentice | Membrane disruption by optically controlled microbubble cavitation[END_REF][START_REF] Postema | High-speed photography during ultrasound illustrates potential therapeutic applications of microbubbles[END_REF] are all important phenomena in bubble-physics, serendipitously direct equivalents can be found in economics when trying to understand the life and death of a bubble.

Although it is interesting to understand the iconographic role of bubbles in Western culture, that is not the prime objective of this thesis. This thesis is based on three published articles:Acoustically Active Antibubbles [START_REF] Kotopoulis | Acoustically Active Antibubbles[END_REF], Ultrasonic Driven Antibubbles Encapsulated by Newtonian Fluids for Active Leakage Detection [START_REF] Johansen | Ultrasonic driven antibubbles encapsulated by newtonian fluids for active leakage detection[END_REF], and Acoustic Filtering of Particles in a Flow Regime [START_REF] Johansen | Acoustic filtering of paricles in a flow regime[END_REF]. Overall the objective of this thesis is to derive the fundamental equations of antibubble dynamics. Starting from the simplest system that can be imagined, an antibubble with no shell in an ideal fluid, to solving the most complex system, the spatio-temporal dynamics of antibubbles with a shell in Newtonian viscous surrounding fluid. The results are analysed with respect to applying antibubbles for clinical diagnostic imaging, targeted drug and gene delivery, and active leakage detection from subsea production facilities. Furthermore, motivated by our understanding of how sound fields interact with microscopic particles, a separate study is conducted, where we utilise this strong interaction to create an acoustic filter for streaming fluids contaminated by microscopic particles.

Ultrasound contrast agents consist of microscopically small gas bubbles, encapsulated by elastic shells. These agents are commonly used in clinical diagnostic imaging to enhance the acoustic contrast between blood and other tissues to improve the quality of ultrasonic images [START_REF] Dietrich | EFSUMB-European Course Book[END_REF]. Furthermore, ultrasound contrast agents are employed in therapy as a vehicle for targeted drug and gene delivery. This process is defined as sono dynamic therapy, the transient formation of micronsized pores in cell membranes induced by ultrasound in combination with microbubbles [START_REF] Postema | Ultrasound-directed drug delivery[END_REF]. This technique shows promise in cancer treatment as it allows increased localised drug delivery [START_REF] Kotopoulis | Sonoporation-enhanced chemotherapy significantly reduces primary tumour burden in an orthotopic pancreatic cancer xenograft[END_REF][START_REF] Kotopoulis | Treatment of human pancreatic cancer using combined ultrasound, microbubbles, and gemcitabine: a clinical case study[END_REF]. Nevertheless, during sono dynamic therapy treatment, patients are still affected by systemic side effects as the chemotherapeutics are still systemically delivered. An ideal solution to this problem would be to encapsulate a therapeutic load into a delivery tool and to release it at the desired location.

Many attempts have been made to incorporate chemotherapeutics into microbubbles [START_REF] Postema | Contrast-enhanced and targeted ultrasound[END_REF]. The most common technique is to embed or bond a therapeutic load into the microbubbles' shell [START_REF] May | Dynamics and fragmentation of thickshelled microbubbles[END_REF][START_REF] Shortencarier | A method for radiation-force localized drug delivery using gasfilled lipospheres[END_REF]. However, adding a thick viscoelastic layer to a microbubble greatly impedes its oscillation amplitude, making it challenging to disrupt and release its therapeutic load at low acoustic amplitudes. A solution would be to incorporate the therapeutic load into the gas core of the microbubble. Such antibubbles should allow for easy manipulation and disruption in sound fields [START_REF] Postema | Generation of a droplet inside a microbubble with the aid of an ultrasound contrast agent: first result[END_REF]. Figure 1 presents a schematic drawing of an antibubble.

Stable, micron-sized antibubbles have already been produced. These have a load volume of approximately half the entire bubble volume, significantly higher than with any other loading method [START_REF] Poortinga | Long-lived antibubbles: stable antibubbles through pickering stabilization[END_REF][START_REF] Silpe | Generation of antibubbles from core shell double emulsion templates produced by micro fluidics[END_REF]. Figure 2 shows a microscopy image of an antibubble.

Using harmonic imaging methods in combination with ultrasound contrast agents, it is possible to effectively evaluate whether patients have leakage of blood from veins and arteries as a complication after surgery [START_REF] Bendick | Efficacy of ultrasound scan contrast agents in the noninvasive follow-up of aortic stent grafts[END_REF][START_REF] Frinking | Ultrasound contrast imaging: current and new potential methods[END_REF]. Antibubbles, who carry the same properties as ultrasound contrast agents, should in principle be applicable in a completely different field. Thus, translating the knowledge from clinical diagnostic ultrasound, it is hypothesised that acoustically driven antibubbles can be used for active leakage detection from subsea production facilities [START_REF] Johansen | Ultrasonic driven antibubbles encapsulated by newtonian fluids for active leakage detection[END_REF]. Recently, it has been proposed to locate offshore hydrocarbon production facilities subsea instead of at the surface [START_REF] Moreno-Trejo | Mapping Factors Influencing the Selection of Subsea Petroleum Production Systems[END_REF]. Locating production facilities subsea is not only to decrease cost, but also to initiate production of hydrocarbons at greater depths. Furthermore, several of the new production fields in the Northern Hemisphere are placed in Arctic climates. Therefore, low temperatures are becoming a major challenge. Hence, using subsea production plants to extract hydrocarbon in such region solves several problems.

However, when establishing subsea production plants, it is essential to secure appropriate maintenance surveillance. An up-and-coming method is ultrasound-based active leakage detection [START_REF] Miller | Ultrasonic detection of resonant cavitation bubbles in a flow tube by their second-harmonic emissions[END_REF]. This is achieved by studying the composition of sound scattered back to the ultrasound source. Knowing that gas bubbles scatter sound more effectively than solid objects or liquids, it is possible to differentiate them [START_REF] Frinking | Ultrasound contrast imaging: current and new potential methods[END_REF][START_REF] Miller | Ultrasonic detection of resonant cavitation bubbles in a flow tube by their second-harmonic emissions[END_REF]. In oil exploration, the flow coming up from the reservoir is a mixture of water, oil and gas. Therefore it can be assumed that leaks from subsea production facilities inhibit the three components necessary for the production of antibubbles [START_REF] Dorbolo | Fluid instabilities in the birth and death of antibubbles[END_REF]: gas, a hydrophobic liquid, and water containing plenty of surface-active agents. Mixing under the right conditions might create a gas cavity with a droplet core of a hydrophobic liquid, and a thin shell of surface-active agents. It is therefore of interest to understand, from a theoretical point of view, how antibubbles with an encapsulation behave in a sound field. Increased understanding could lead to improved active leakage detection, clinical diagnostic imaging and targeted drug and gene delivery.

Lord Rayleigh was the first to publish on the radial pulsation of a gas cavity when subjected to an external pressure change [START_REF] Rayleigh | On the pressure developed in a liquid during the collapse of a spherical cavity[END_REF], Plesset also contributed to the development of what today is known as the Rayleigh-Plesset equation [START_REF] Plesset | The dynamics of cavitation bubbles[END_REF]. The pioneering work done by these researchers were motivated towards understanding the dynamics of the cavitation phenomenon observed on ship propellers [START_REF] Rayleigh | On the pressure developed in a liquid during the collapse of a spherical cavity[END_REF].

All current models for bubble dynamics, both uncapsulated and encapsulated have their origin in the Rayleigh-Plesset equation for a free gas bubble. Antibubbles are fundamentally different from gas bubbles because of an incrompressible droplet core in the centre of the bubble. Nevertheless, the first mathematical model for an acoustically active antibubble is derived during the work on this thesis. This Rayleigh-Plesset-like equation enables us to study differences in oscillator behaviour compared to gas bubbles, both with and without an encapsulating shell [START_REF] Kotopoulis | Acoustically Active Antibubbles[END_REF].

Antibubble

Although many papers have been written on the dynamic behaviour of free and encapsulated microbubbles, especially on ultrasound contrast agents [START_REF] Doinikov | Review of shell models for contrast agent microbubbles[END_REF], only two paper has been published on acoustically active antibubbles [START_REF] Kotopoulis | Acoustically Active Antibubbles[END_REF][START_REF] Johansen | Ultrasonic driven antibubbles encapsulated by newtonian fluids for active leakage detection[END_REF]. Here the term microbubbles is defined as gas bubbles with a diameters less than 10 µm.

Figure 1 :

 1 Figure 1: Schematic drawing of liquid (light blue) containing and antibubble cosisting of a droplet core (brown), surrounded by a gas layer (white) and with a thin shell (dark blue).

Figure 2 :

 2 Figure 2: Optical microscopy image of antibubble with single core.


Michiel Postema

Spiros Kotopoulis

Anthony Delalande

Odd Helge Gilja

Ultrasound-guided delivery and sonoporation

Ultrasound contrast agents are commonly added to the blood stream in ultrasonic imaging: contrast-enhanced ultrasound (CEUS). They consist of microscopically small bubbles (microbubbles) encapsulated by elastic shells. The most common shell materials are phospholipids. During an ultrasound cycle microbubbles oscillate, i.e., they expand and subsequently contract. Depending on their elastic properties, on the local conditions, and on the acoustic settings, they move in the direction of the sound field, coalesce with other microbubbles, fragment, jet, cluster, release their contents, and dissolve in the surrounding liquid. [START_REF] Postema | Contrast-enhanced and targeted ultrasound[END_REF] The diverse behaviour of encapsulated microbubbles in different acoustic regimes has triggered the idea to use them as ultrasound-controlled vehicles to facilitate the delivery of therapeutic agents to a site of interest. Such a noninvasive, localised, side-effect-free method would revolutionise drug delivery as we know it. Cellular uptake of drugs and deoxyribonucleic acid (DNA) is increased when the region of interest is under sonication, and even more so when an ultrasound contrast agent is present. [START_REF] Postema | Ultrasound-directed drug delivery[END_REF] This increased uptake has been attributed to the formation of transient porosities in the cell membrane that have diameters up to 0.1 µm, i.e., big enough for the transport of drugs into the cell. The pores reseal themselves within one minute. The ultrasound-assisted transient permeabilisation of a cell membrane is called sonoporation. Understanding the physics underlying sonoporation is of uttermost importance for the development of ultrasound-activated therapeutic agents.

There are five non-exclusive hypotheses for explaining the sonoporation phenomenon from a physics point of view. [START_REF] Postema | CEUS and sonoporation[END_REF] These have been summarised in Figure 1. It is noted that fragmenting microbubbles cannot create pores in cells, since fragmentation costs energy. (a) Push: During its expansion phase, a microbubble might touch a cell membrane surface. The pushing motion would then cause the cell membrane to be locally disrupted. The pushing mechanism would occur within half an ultrasound cycle. However, under typical sonication conditions, microbubble excursion amplitudes are low. Also, typically, microbubbles are much more flexible than cells. Our current understanding of microbubble physics does not support the push mechanism if the microbubble is not attached. However, if the microbubble is already attached to the cell membrane whilst expanding, pushing under influence of radiation forces might cause the membrane to rupture. The latter mechanism might occur over multiple cycles. (b) Pull: During the contraction phase of an oscillating microbubble, the plasma filling the void left by the contracting bubble might pull the cell membrane towards the microbubble. This pulling motion would then cause the cell membrane to be locally disrupted. The pulling mechanism would occur within half an ultrasound cycle. However, under typical sonication conditions, microbubble contractions do not result in an inertial collapse. Moreover, the replacive mass of a contracting microbubble is much lower than the fluid supposedly causing the pull. Therefore, this mechanism is less plausible than the push mechanism in non-attached conditions. However, if the microbubble is attached to the cell membrane, a similar mechanism might occur as described under (a), where pulling under the influence of radiation forces might cause the membrane to rupture. (c) Jetting: Jetting is the asymmetric collapse of a bubble, creating a funnel-shaped protrusion through the bubble that is directed towards a boundary. This spectacular phenomenon has actually been optically observed on a microscopic scale through cells. [START_REF] Prentice | Membrane disruption by optically controlled microbubble cavitation[END_REF] The jetting phenomenon occurs within half an ultrasound cycle. However, jetting exclusively occurs when using high acoustic amplitudes, at the upper end of clinical settings. Also, there has not been any proof yet of cell survival after jetting. Based on empiric studies that relate jet length to pore size, we excluded the role of jetting as a dominant mechanism involved in sonoporation. [START_REF] Postema | Jetting does not cause sonoporation[END_REF] (d) Streaming: If a microbubble is fixed to a membrane, the fluid streaming around the oscillating bubbles creates enough shear to rupture the membrane. [START_REF] Marmottant | Controlled vesicle deformation and lysis by single oscillating bubbles[END_REF] Here, long pulse lengths are required to set the fluid in motion. However, low acoustic amplitudes should suffice to create the rupturing shear of a typical cell membrane. Existing research has proven the feasibility of the streaming mechanism in bound conditions, so this mechanism should work for targeted contrast agents that attach to cells. Further research will show whether streaming around weakly-attached microbubbles creates enough shear for cell membranes to rupture. (e) Translation: Owing to radiation forces, lipid-encapsulated microbubbles may translate through cell membranes or channels in the cell membrane. The microbubble may loose part of its shell whilst passing through the cell membrane. As a result, the gas will dissolve after entry. In case of therapeutic loading, the load would be delivered directly into the target cell. This mechanism requires long pulse lengths and low acoustic amplitudes. Very recently, fluorescence-coated ultrasound contrast agent microbubbles were observed to move into HeLa cells at a low mechanical index (MI) of 0.15, using highspeed video footage under confocal microscopy, [START_REF] Delalande | Sonoporation at a low mechanical index[END_REF] an example of which is given in Figure 2. The microbubbles dissolved after entering the cells. The cells survived the sonoporation treatment, confirming the transient character of sonoporation. All five of these mechanisms require the presence of a microbubble in the vicinity of the cell. Yet, increased drug uptake has also been reported without the use of any ultrasound contrast agent, but merely an ultrasound field itself. Despite speculations about the role of inertial cavitation in the latter, clinical ultrasound scanners do not generate fields strong enough to create such spontaneous microbubbles in blood.

Recently, it was found that (bilayer) cell membranes themselves act as cavitation nuclei. [START_REF] Krasovitski | Intramembrane cavitation as a unifying mechanism for ultrasound-induced bioeffects[END_REF] Even at modest acoustic pressures, cell membranes might rupture due to the building up of gas cavities inside the bilayer. This important finding would explain the sonoporation in the absence of ultrasound contrast agent microbubbles. Moreover, it explains why bubbles are attracted to cells that are not in the travel path of the ultrasound wave. However, given the low MI at which cells attract microbubbles, more study is required regarding the safe use of ultrasound contrast agents in longpulse-length imaging.

In conclusion, in current clinical settings, four non-exclusive mechanisms are plausible for the physical explanation for sonoporation with the aid of ultrasound contrast agent microbubbles.

Figure 1 :

 1 Figure 1: Schematic representation of the five physical mechanisms supposedly involved in sonoporation.