14.2: Contexts- Love and Romance in Middle Adulthood
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Learning Objectives
By the end of this section, you will be able to:
- Explain how attachment applies to development in middle adulthood
- Distinguish among various types of love
- Describe how marriage and divorce are changing in our society
- Discuss factors that influence dating , marital satisfaction , and divorce in middle adulthood
Sarah and Alex’s relationship started out with lots of passion and intimacy when they were in their twenties. Once each other’s safe haven in times of uncertainty and stress, they now—well into their forties—find themselves living separate lives. Sarah has lost trust in her spouse and finds herself snooping through Alex’s text messages and emails. Alex complains that Sarah never shares what’s on her mind anymore, so their arguments usually end in a stony silence. Both Alex and Sarah are unhappy, but neither one of them knows what to do next.
As theories of adult psychosocial and personality development suggest, the development of self in middle adulthood is inextricably tied to a person’s relationships with others. In this section, you will examine the predictors and outcomes of attachment and romantic relationships in middle adulthood.
Attachment and Love in Middle Adulthood
In many ways, attachment theory is consistent with Erikson’s psychosocial framework of the development of self in middle adulthood, perhaps because both are influenced by the psychoanalytic developmental perspective. At its core, attachment theory asserts that secure attachment relationships provide children with a secure base or safe haven from which to encounter new and challenging experiences. This framework was later extended by Hazan and Shaver (1987) to apply to relationships in adulthood. Similarly, Erikson’s psychosocial theory proposes that the comfort and security derived from forming and maintaining intimate relationships in young adulthood provide a developmental foundation for successfully encountering new generative responsibilities in middle adulthood.
A person’s attachment style can be used to characterize close relationships in which a person has a relationship partner at any stage of life, such as to a romantic partner, a developing child, on aging parent. Evidence is somewhat inconclusive on the extent to which individual attachment styles vary across relationships and over time, with the stability of attachment style varying by attachment style, gender, life events, how attachment is measured, and time of measurement (Fraley, 2002; Hazan & Shaver, 1987; Pinquart et al., 2012; Waters, 2022).
Most adults identify their overall relationship styles as consistent with secure attachment (Hazan & Shaver, 1987). Securely attached adults are more likely to receive support from their partners in times of stress (Collins & Feeney, 2004), and they are also more likely to provide support to their significant others (Simpson et al., 1992), a behavior consistent with Erikson’s generative virtue of care. Secure attachment to aging parents also increases adult children’s likelihood of providing help to them while decreasing their perceived burden in providing such care. Conversely, avoidant attachment decreases the likelihood that adult children will provide care to aging parents and increases their perceived caregiver burden (Carpenter, 2001; Cicirelli, 1993; Karantzas, 2010).
Insecure attachment style in middle adulthood predicts poor health outcomes for adults, including inflammatory immune responses (Ehrlich et al., 2019; Gouin et al., 2019; Kidd et al., 2014). Stress is likely the mediating factor between insecure attachment style and immune dysfunction. Whether avoidant or anxious, adults with insecure attachment styles lack confidence that they will reliably receive support from others, and a perceived lack of social support is a primary predictor of stress-related health effects (Baron et al., 2016; Cohen, 2004).
A 2019 study of Mexican adults aged twenty to sixty-five years found that while secure attachment predominated among couple who were younger or were dating, anxious attachment was more common in middle adulthood relationships and first marriages (Pérez-Aranda et al., 2019). Pérez-Aranda and colleagues (2019) suggest that this increase in anxious attachment may be explained by the stress of simultaneously providing care to spouse, children, and aging parents in middle adulthood. These maladaptive attachment responses to the stress of caregiving in middle adulthood may also affect the quality of caregiving provided to children, with research finding that insecurely attached mothers are more likely to exhibit insensitive parenting during times of stress (van Ee et al., 2017) and promote unhealthy eating practices in their children (Messina et al., 2019); (Bost et al., 2014).
Adults with secure attachment styles demonstrate a greater willingness to form committed and psychological intimate relationships, which in turn increases their satisfaction with close relationships (Madey & Rogers, 2009). According to Sternberg’s triangular theory of love (1986), intimacy and commitment form a type of close relationship that he called companionate love , which can exist across many types of family, friends, and other platonic relationships. Companionate love relationships feature the self-disclosure afforded by the closeness of psychological intimacy and the loyalty and reliability established when two people commit to spend time together. The third component of Sternberg’s triangular theory of love is passion . Passion refers to feelings of longing, excitement, and attraction to another person. Sternberg referred to relationships that include all three components as complete or consummate love (2014). The three components of intimacy, commitment, and passion can exist singularly in relationships or in any combination, which can result in seven different kinds of relationships (Figure 14.4).
Sternberg’s classification of love has been measured and validated cross-culturally (Sorokowski et al., 2021); however, the extent to which individuals experience each of the three components in their romantic relationships appears to vary across the lifespan. Feelings of passion and intimacy are increasingly experienced across adolescence, peak in early adulthood and show a slight decrease throughout middle adulthood (but always remaining present at a meaningful level). Across the lifespan, men report somewhat higher levels of passion in their relationships than women (Sumter et al., 2013). Commitment also peaks in young adulthood but does not exhibit much decline into middle adulthood. All three components are predictive of marital satisfaction in middle adulthood, with intimacy showing the strongest association, followed by commitment and passion (Yoo & Joo, 2022).
Marriage
Marriage is an important predictor of health and well-being in adulthood. Longitudinal studies find that married adults accumulate 77 percent more net worth than those who are single (Zagorsky, 2005). Marriage can reduce stress and protect health by acting as a source of economic security and available social support. Subsequently, married adults have lower mortality rates than single adults (Curtin & Tejada-Vera, 2019; Robles & Kiecolt-Glaser, 2003). For example, following the COVID pandemic in 2020–2021, married adults reported fewer negative impacts to their mental health, even when the lockdown resulted in the loss of household income (Jace & Makridis, 2021).
Contemporary Marriage in the United States
The median age for first marriage in the United States has climbed rapidly since the mid-1900s and is currently thirty years for men and twenty-eight years for women (Figure 14.5).
The gender gap in marital age has remained relatively constant, but the rising age is likely associated with other changing variables in adult development. These include an increase in the number of people who continue their education beyond high school (especially women and communities of color), an increase in the number of women in the workforce, and longer lifespans. Gender, education, race, and socioeconomic status also predict likelihood of marriage. College-educated women are more likely to marry than their non-college educated peers, and lower socioeconomic status is negatively correlated with likelihood of marriage. This trend is similar to that seen in Western European countries (Esping-Anderson, 2016; Jalovaara, 2002). By age forty years, about 25 percent of U.S. adults have never been married (compared to 6 percent in 1980) (Figure 14.6).
The last thirty years have also seen important changes to marriage equality . In the 1990s, human rights advocates pushed for states to legalize what were called “civil unions” for same-sex couples. This separate-but-equal status attempted to provide same-sex couples with access to many of the legal rights of marriage, including tax, medical, and housing benefits, while reserving the term “marriage” for rites sanctioned by religious institutions, most of which did not recognize or condone same-sex marriage. This discriminatory practice was legitimized in 1996 when Congress passed the Defense of Marriage Act (DOMA) that defined marriage as a “legal union of one man and one woman as husband and wife” and the word spouse as “a person of the opposite sex who is a husband or wife” (Defense of Marriage Act, 1996).
In 2013, however, President Barack Obama responded to rising opposition to DOMA by declaring it unconstitutional under the Constitution’s Equal Protection Clause. True reform came in the 2015 case of Obergefell v. Hodges when the U.S. Supreme Court voted 5–4 to federally protect same-sex marriage (refer to Figure 14.7). As of 2021, there were more than 710,000 married same-sex households in the United States (U.S. Census Bureau, 2021). These couples are more likely than their opposite-sex married counterparts to be young, well educated, and interracial.
While there has been much progress worldwide to increase marriage equality, only thirty-six countries (fewer than 20 percent of all countries across the globe) have legalized same-sex marriage as of 2024 (refer to Figure 14.8).
Link to Learning
In February 2024, Greece legalized same-sex marriage. Greece is the only Orthodox Christian country in the world to do so. Learn more about the vote and public reaction to Greece legalizing same-sex marriage in this report from DW News.
Division of Labor in Marital Relationships
The dynamics of marital relationships may vary depending on the values, preferences, personality, gender, age, and generational cohort of the partners. Most research on marital dynamics is based on heterosexual couples, and scholars have identified the need for more research on same-sex marriages, as preliminary research suggests that the gendered marital dynamics of same-sex midlife spouses can differ from that of heterosexual couples (Umberson et al., 2018).
In heterosexual marriages, researchers have identified two general approaches to balancing the roles and responsibilities of a marital partnership. Some heterosexual marriages operate within the framework of traditional or conventional gender roles , in which women are more likely to handle domestic work within the home, such as household chores and childcare responsibilities. Men are more likely to provide and control household income as the primary or only breadwinner and person in charge of financial planning and decisions. Although this provides a ready-made and clear division of labor in the household, the arrangement can also limit flexibility and the choices each individual can make, and it can inhibit the need for generative change and growth during middle adulthood, leading to stagnation and dissatisfaction (Saeedi et al., 2024).
In contrast, in an egalitarian marriage , responsibilities are shared equally between partners, and roles are not prescribed according to traditional gender role stereotypes. While this approach theoretically allows for more individual flexibility and shared work, research indicates that when both partners work outside the home, in heterosexual marriages women still complete most household and childcare responsibilities, even when the income from their job makes them a joint or primary breadwinner for their family (Carlson et al., 2016). Recent data on heterosexual marriages show that men are the primary or sole breadwinners in just over half of current heterosexual marriages, while 45 percent of women with opposite-sex spouses are the joint or primary breadwinners. And even though most U.S. adults believe that children are better off when working parents share equally the professional and domestic responsibilities of the household (Fry et al., 2023). Research indicates that when couple's equally share housework, they are more likely to have better relationship quality (Carlson, 2022). Studies consistently find that even in egalitarian dual-earner marriages, women spend significantly more time engaged in childcare and housework than men (Fry et al., 2023) (Figure 14.9). However, whether this unequal delegation of domestic responsibilities produces dissatisfaction appears to depend on the spouses’ beliefs regarding gender roles and how those roles and tasks are discussed among spouses (Magnusson & Marecek, 2012)
Predictors of Marital Satisfaction
So, what is the key to a happy marriage? Many insights into that question have come from a cozy living room that originated on the campus of the University of Washington and is now housed within The Gottman Institute in Seattle, Washington. Illuminated by daylight streaming in through a big picture window, the room is furnished with a comfortable couch, accent tables, a colorful area rug, and a high-tech surveillance system monitored by psychologists to record every detail of the room’s occupants, from conversations and facial expressions to heart rate and skin conductivity.
The room is known as the Gottman Love Lab , and for decades, clinical psychologist John Gottman and colleagues have been collecting observational and self-report data from couples to learn what makes love and marriage successful (Figure 14.10). Longitudinal follow-ups of thousands of couples who have participated in Love Lab research studies have identified several reliable predictors of marital satisfaction. In fact, Gottman claims to predict with over 90% accuracy whether couples will remain together (Gottman & Levenson, 2002).
At the core of the Love Lab findings is the way a couple responds to conflict (rather than avoiding it). Conflict is inevitable in any marriage and often revolves around recurring issues that stem from personality differences (Gottman, 1994a). Therefore, Gottman proposes that a couple’s ability to maintain healthy communication despite conflict is one of the most powerful predictors of marital satisfaction and stability. A couple’s ability to maintain positive affect during and after conflict is key (Driver & Gottman, 2004). In fact, Gottman cites the “5-to-one ratio”: those couples who make at least five positive comments for every one negative comment are most successful in the long run. Not surprisingly, couples who show sustained cycles of negativity are more likely to be dissatisfied with their relationships (Woodin, 2011).
Research found that a couple’s ability to exhibit psychological soothing is crucial to resolving and recovering from conflict (Figure 14.11). Psychological soothing can include expressions of empathy, use of humor, willingness to accept influence (this is especially true for men), and repair behaviors (which can be as simple as apologizing or even offering your partner a cup of coffee) (Gottman et al., 1998; Levenson & Ruef, 1992; Lewis et al., 2015). These behaviors are perhaps best summed up by Gottman’s report of one man’s comment following a particularly heated argument with his partner: “Well, now that we’ve completely destroyed each other’s personalities, do you want a piece of cheesecake?” (Perel, 2023).
Gottman and other researchers assert that spouses who are also friends have the most solid foundation from which to build, repair, and maintain a healthy marriage . Marriage counseling approaches that encourage couples to enhance their friendship are predictive of an increase in marital satisfaction one year later (Babcock et al., 2013). However, recent research has cautioned against a one-size-fits-all, quick-fix view on relationship interventions and therapy, because individual and group differences create complex variations in relationship dynamics. The enduring benefits of marital therapy may depend on the age of the couple and environment in which they live, and while marital counseling may successfully reduce negative communication, it does not consistently increase long-term positive communication or relationship satisfaction (Karney & Bradbury, 2020).
There may also be gender or sexual identity differences in marital functioning. Compared to men, women are more likely to value the role of intimacy in regard to marital satisfaction. Women report slightly less marital satisfaction than men, even when participating in marital counseling, and are somewhat more likely to display a mix of hostility, distress, and intimacy during arguments, whereas men prefer to either withdraw or take a problem-solving approach to resolve arguments (Jackson et al., 2014; Woodin, 2011; Yoo & Joo, 2022). Also, the role of sexual identity in relationship functioning has not yet been adequately explored by current research, particularly within marriages. A study of Italian couples found that same-sex couples reported higher relationship satisfaction than heterosexual couples (Antonelli et al., 2014). Similarly, a longitudinal research study examining the effectiveness of a marital counseling approach guided by principles established at the Gottman Love Lab found that the therapy was actually more effective for same-sex couples than heterosexual couples (Garanzini et al., 2017). This difference between same- and different-sex couples in relationship satisfaction and repair may be related to a previous finding by the Gottman lab, which revealed that same-sex couples are less likely to respond to disagreements with controlling behaviors and more likely to use humor. As a result, same-sex couples experience fewer signs of physiological arousal during an argument, such as increased heart rate, and are better able to employ psychological soothing (Gottman et al., 2003). While psychologists seeking to better understand and support the experiences of those in the LGBTQ+ community say that “available data suggest that many factors that predict relationship satisfaction and disruption for heterosexual couples also do so for same sex couples,” more updated research is needed (Farr & Goldberg, 2018, p. 151).
Divorce
Just as many factors influence whether and how adults form and maintain marital relationships, the experience of ending a marriage can be equally complex. You may have heard people discuss the rising rate of divorce in the United States. But while the United States does have a higher divorce rate than most other countries (thirteenth highest in the world) (United Nations Department of Economic and Social Affairs, 2022), that rate has declined since peaking in 1979 at 22.6 divorces per 1,000 marriages (Figure 14.12). In fact, data from the U.S. Census Bureau’s American Community Survey indicate that divorce is at an all-time low of about 14 divorces per 1,000 marriages (Loo, 2023), though rates are higher among U.S. adults who are Black, have lower incomes, and are less educated (Mayol-García et al., 2021). Research from Sweden, where same-sex marriage has been legally protected since 2009, finds that same-sex marriages between women have a somewhat higher rate of divorce than heterosexual marriages and same-sex marriages between men (Kolk & Anderson, 2020).
Laws related to divorce have clear impacts on the likelihood that adults in unhappy marriages will get divorced. The no-fault divorce laws enacted in the 1970s allowed couples to cite “irreconcilable differences” as grounds for divorce, as opposed to identifying a specific marital transgressions such as adultery or violence. This change is associated with the corresponding rise in divorce rate at that time. In contrast, the legal system in Sri Lanka only accepts fault-based divorce requests and has one of the lowest divorce rates in the world.
Religiosity is also negatively correlated with divorce. Those without religious affiliation are more likely to get divorced, and those with high religious service attendance and conservative religious values are less likely to get divorced (Pew Research Center, 2014). The religion with the lowest divorce rate is Hinduism (Bieber & Ramirez, 2024).
The average length of a first marriage that ends in divorce is approximately eight years (U.S. Census Bureau, 2021). The top reasons for divorce cited by divorced adults over age fifty years are listed in Table 14.1.
| Men | Women |
|---|---|
| 1. We grew apart | 1. Spouse cheated |
| 2. Spouse cheated | 2. Spouse’s use of pornography, alcohol, or drugs |
| 3. Financial difficulties/disagreements | 3. Spouse was verbally or emotionally abusive |
| 4. Spouse’s mental health | 4. We grew apart |
| 5. Problems related to the children | 5. Spouse’s mental health |
The average age of those divorcing is forty-six years for men and forty-four years for women. Divorce rates among those aged fifty years and older have doubled since 1990 (Allred, 2019) (Figure 14.13). Researchers studying the trend of divorce after age fifty years, called gray divorce , point to three likely reasons (Crowley, 2018). First, the purpose of marriage is increasingly conceptualized as a source of happiness. Therefore, when a marriage is negatively affecting a person’s happiness, they are less likely to remain married for other reasons (such as financial stability, children, or reputation). Second, the increase in life expectancy changes the consequences of marriage. As anthropologist Margaret Mead is quoted as saying, “It used to be when we said ‘til death do us part,’ death parted us pretty soon. That’s why marriages used to last forever. Everybody was dead” (Krebs, 1977, pg 41). With increasing numbers of adults living into their eighties, nineties, and even hundreds, not only is marriage a much longer commitment, but the possibility of living a full life after a divorce in middle adulthood is fairly high. The third reason cited is the introduction of no-fault divorce laws, which would not have been available earlier in the marriages of some older adults.
Divorce Processes
Related to the rise of no-fault divorce in the United States and diversification of family and household units, legal scholars and psychologists have advocated for a rejection of the traditional adversarial divorce system in favor of a mediational approach. Within the adversarial divorce approach, one or both spouses have already decided to end their marriage, and the legal system is used to present and dispute the spouses’ opposing views to determine what rights, assets, and support each person will be awarded (i.e., property, spousal or child support, child custody and visitation rights). The adversarial approach employs an argumentative framework that makes reconciliation unlikely. This approach can create drawn-out and expensive proceedings that can cause further financial and emotional damage to the couple (Center for Divorce Mediation, 2024).
When children are involved, an acrimonious divorce can increase their risk of negative emotional, behavioral, and psychological outcomes, such as feelings of humiliation and loneliness, aggressive behavior, poor academic performance, and anxiety (Sarmadi & Kholdabakhshi-Koolaee, 2023). An adversarial divorce can also undermine children’s relationship with their parents during and after the divorce (Kabyn, 2023). The competitive win-lose orientation of an adversarial approach to custodial arrangements and child support can also increase the risk of parental estrangement from their children and nonpayment of support (Murphy & Singer, 2015).
Instead, lawyers and psychologists have advocated for a mediational approach to divorce. This framework employs the assistance of either or both legal and counseling professionals to help the couple collaboratively discuss the state of the marriage and available options that will best serve all involved (Figure 14.14). This process does not require divorce papers to be filed before beginning, which can keep the door open for possible reconciliation. Mediational approaches also tend to be less upsetting, quicker, and less costly (Center for Divorce Mediation, 2024). Mediational approaches to divorce can include the involvement of divorce counselors before, during, and following a divorce. Divorce counselors can assist with helping couples work through the complicated cognitive, psychological, and practical aspects of their separation. Within the cognitive dimension, divorce counseling focuses on improving clients’ self-efficacy in reaching desired goals improved couples’ ability to make calm and thoughtful decisions during divorce mediation (Mahmoodabadi & Zarei, 2018). Within the psychological dimension, divorce counselors can help adults and children to develop effective communication skills, manage stress, and cope with feelings of loss or grief in response to the end of a marriage and preexisting family structure. Divorce counselors can also act as an unbiased third party to assist in practical matters, such as planning how to co-parent following a separation (Birch, 2023). Parents who employ mediational approaches during a divorce report higher satisfaction with custody agreements than those who do not (World Metrics, 2024).
Outcomes of Divorce
Divorce can take a financial, social, and psychological toll. The median legal cost associated with the divorce process is $7,000, and those that go to trial are significantly more expensive than uncontested divorces (Crail & Ramirez, 2024). In the long term, women in heterosexual marriages pay a steeper financial penalty following divorce. In addition to facing an average 45 percent decline in standard of living following a gray divorce (compared to 21 percent for men) (Lin & Brown, 2021), women are also at greater risk of losing more assets, health benefits, and retirement savings than men (Crowley, 2018). While the number of shared-custody arrangements has increased in the last several decades, most children of different-gender parents still end up living primarily with their mothers following a divorce, and most custodial parents do not receive the full amount of the child support from the other parent (Meyer et al., 2022; Eser, 2024).
Divorce can also result in feelings of hopelessness, low self-esteem, loneliness, and alienation (Sarmadi & Kholdabakhshi-Koolaee, 2023). Evidence suggests that in marriages between people of different genders, older men may pay a greater social and psychological toll than women, due to their reliance on the social support network and housework maintained by their spouses. In the years immediately following a divorce, men experience greater initial declines in life satisfaction and mental health compared to women (Leopold, 2018).
However, divorce can have positive outcomes as well. Adult women have been found to exhibit an increase in gregariousness, activity, and positive emotion in the six years following their divorce (Costa et al., 2000). Negative cognitive outcomes of divorce are lower for adults in middle adulthood compared to younger adulthood (Zhang et al., 2022). In the long term, most individuals can recover from the initial negative impacts of divorce (Leopold, 2018) and go on to lead satisfied and fulfilling lives, describing themselves as happy and independent (Crowley, 2019) and optimistic about new roles (Sakraida, 2005).
As you might have noticed in Table 14.1, in a 2018 study, the third most often cited reason women gave for divorcing men was physical or verbal abuse (Crowley, 2018). Domestic abuse is more common than many think. Twenty percent of marriages experience physical abuse (slapping, shoving, hitting, or other assault) and emotional abuse (threats and humiliating or controlling behavior) (American Association for Marriage and Family Therapy, 2023). Leaving an abusive relationship often requires several attempts, as the abuse survivor must often overcome many obstacles, such as threats to one’s safety from the abuser, low self-esteem, and lack of resources. In the immediate aftermath of leaving an abusive relationship, many adults grapple with symptoms of post-traumatic stress disorder. However, over the course of two- and three-year follow-ups, trauma symptoms usually decline, and perceived quality of life increases (Anderson & Saunders, 2003; Blasco-Ros et al., 2010; Flasch et al., 2015).
Link to Learning
If you or someone you know is experiencing domestic violence, reach out to the National Domestic Violence Hotline for help. Call 1-800-799-SAFE, text “START” to 88788, or chat through their website to receive confidential support.
Dating and Remarriage
When seeking out romantic relationships in middle adulthood, men look for commitment, while women desire companionship without the demands of caregiving. Today’s middle-aged adults find themselves needing to adapt to a dating landscape that includes new challenges, such as smaller social networks with fewer eligible partners (McWilliams & Barrett, 2014). These adults are faced with adjusting to modern ways of meeting people, such as online dating. In fact, several online dating sites specifically marketed to adults aged fifty years and older have emerged to meet the demand.
Studies of online dating in middle and older adulthood find that men prefer younger romantic partners, screen for physical attractiveness, and seek a partner who can provide emotional support. Women prioritize intelligence, honesty, companionship, and socioeconomic status in their online dating matches (Hitsch et al., 2010; McWilliams & Barrett, 2014; Watson & Stelle, 2021). Both men and women in middle adulthood are more likely to post dating profiles that emphasize youthfulness, with women more focused on how they look and men focused more on conveying financial and professional success (McWilliams & Barrett, 2014).
Almost 25 percent of currently married couples include at least one person who has been married before (Mayol-García et al., 2021); however, second and third marriages have much higher divorce rates than first marriages, around 70 percent (Bieber & Ramirez, 2024; Brooks, 2023). Individuals who are remarrying are likely starting their relationship under more complex circumstances than in their first marriage. They may still be recovering from the emotional and financial impact of divorce, while possibly managing the challenge of blending families. Seventy percent of children with divorced parents live under shared-custody agreements (Hemez & Washington, 2021).
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Footnotes
- 2 According to the Pew Research Center analysis of the 2021 American Community Survey (IPUMS), “White, Black and Asian adults include those who report being only one race and are not Hispanic; Hispanics are of any race; ‘some college’ includes those with an associate degree and those who attended college but did not obtain a degree.”


4.11: Diversity and Inclusion
- Compare diversity and inclusion
Language can be imprecise and, therefore, ineffective in supporting communication or the transfer of meaning that is essential to collaboration and, in particular, affecting change. Diversity and inclusion speaker and advisor Joe Gerstandt comments “maybe our greatest barrier to further progress [toward achieving diversity] is that [diversity] remains an issue that seems very vague and ambiguous to many people, primarily about platitudes and political correctness.  [1] So true.
In order to get us all on the same page, we’ll start with a minimalist statement that defines and differentiates between diversity and inclusion. To quote Gerstandt: “Diversity means difference and inclusion means our ability to include difference.” Practically speaking, diversity can be understood as a range of human characteristics that differ from our own and/or from those we share with the groups to which we belong. Inclusion is more intuitive; as the Oxford Dictionary defines it, inclusion is “the action or state of including or of being included within a group or structure.” [2] One point worth emphasizing in that definition: inclusion involves “including” as well as “being included.” To that point, Gerstandt emphasizes that “[Inclusion is] activist in nature.” As he puts it, the key question is “what do you do intentionally, and deliberately to be more inclusive?” [3]
A distinction worth noting is that there are generational differences in how diversity and inclusion are interpreted. In their 2019 report “The Bias Barrier: Allyships, Inclusion and Everyday Behaviors,” Deloitte identified that “millennials (aka Generation Y) view inclusion as having a culture of connectedness that facilitates teaming, collaboration, and professional growth.” [4] In contrast, Baby Boomers and Generation X-ers consider diversity and inclusion a matter of representation and assimilation.
| Millennials are more likely to focus on | Nonmillennials are more likely to focus on |
|---|---|
| 32% more likely to focus on respecting identities | 21% more likely to focus on representation |
| 35% more likely to focus on unique experiences | 19% more likely to focus on religion and demographics |
| 29% more likely to focus on ideas, opinions, and thoughts | 25% more likely to focus on equality |
For Millennials, inclusion is primarily about cognitive diversity; specifically, “capitalizing on a variety of perspectives in order to make a stronger business impact.” Deloitte University Leadership Center for Inclusion Managing Principal Christie Smith and Deloitte consultant Dr. Stephanie Turner note that transforming the diversity and inclusion model isn’t just a retention issue, “the millennial viewpoint is simply better for business.” [6]
An IBM study found that 75% of CEOs and executives consider leveraging cognitive diversity fundamental for organizational success.
If you think diversity and inclusion—however its defined or interpreted—is passé, think again. SHRM Senior Legal Editor Lisa Nagele-Piazza lists “improving gender diversity” [7] as one of the Top Ten Workplace Trends for 2019.
Author, researcher and advisor Josh Bersin considers diversity and inclusion “a very hot topic.” [8] In fact, he says it comes up in every client conversation. Why? Follow the hashtags (e.g., #metoo, #blacklivesmatter), political positioning, with the emphasis on income inequality and fairness, and the realities of employee expectations translating into activism or turnover. As Bersin puts it: diversity and inclusion is not [just] an HR program, it’s a business strategy.
For additional perspective on diversity and inclusion, read recruitment automation software provider Ideal’s Diversity and Inclusion: A Beginners Guide . For additional perspective on generational differences in how diversity is perceived, refer to The Radical Transformation of Diversity and Inclusion: The Millennial Influence , a joint project of Deloitte and the Billie Jean King Leadership Initiative (BJKLI).
- Gerstandt, Joe. " What Does Diversity Mean to You? " Joe Gerstandt : The Value of Difference. March 21, 2011. Accessed September 14, 2019. ↵
- " Inclusion ." Lexico. Accessed September 14, 2019. ↵
- Gerstandt, Joe. " Inclusion in Action ." Joe Gerstandt : The Value of Difference. April 11, 2019. Accessed September 14, 2019. ↵
- Smith, Christie and Stephanie Turner. " The Radical Transformation of Diversity and Inclusion: The Millennial Influence ." Deloitte University, The Leadership Center for Inclusion. Accessed September 14, 2019. ↵
- Ibid. ↵
- Ibid. ↵
- Nagele-Piazzam Lisa. " Top 10 Workplace Trends for 2019 ." Society for Human Resource Management. June 27, 2019. Accessed September 14, 2019. ↵
- Bersin, Josh. " Diversity and Inclusion is a Business Stratgey, Not an HR Program ." Josh Bersin. August 29, 2018. Accessed September 14, 2019. ↵
Contributors and Attributions
- Coworkers in a business meeting. Authored by : Rawpixel. Located at : https://flic.kr/p/29ZEMMW . License : CC BY: Attribution


1.20.4: Surfactants and Miceles: Ionics
An intense debate concerns the structure of micelles, particularly those formed by ionic surfactants such as SDS and CTAB. It seems generally agreed that micelles are essentially spherical in shape. The polar head groups ( e.g. \(– \mathrm{N}^{+} \mathrm{Me}_{3}\)) are at the surface of each micelle, having strong interactions with the surrounding solvent. In close proximity in the Stern layer are counterions (e.g. bromide ions in the case of CTAB); the aggregation number \(\mathrm{n}\) describes the number of cations which form each micelle. The total charge on the micelle is determined the aggregation number and a quantity \(\beta\), the latter being the fraction of charge of aggregated ions forming the micelle neutralized by the micelle bound counter ions. The remaining fraction of counter ions exists as ‘free’ ions in aqueous solution. Both \(mathrm{n}\) and \(\beta\) are characteristic of a given surfactant system, and are obtained from analysis of experimental data [1]. The properties of ionic surfactants have been extensively studied [2-14]. Here we examine four thermodynamic descriptions of these systems.
Ionic Surfactant:1:1 salt: Phase Equilibrium: Dry Neutral Micelle
We consider a dilute aqueous solution of an ionic surfactant; e.g. \(\mathrm{AM}^{+} \mathrm{Br}^{-}\). As more surfactant is added a trace amount of micelles appear in the solution when the concentration of surfactant just exceeds the cmc. The trace amount of surfactant is present as micelles constituting a micellar phase. At defined \(\mathrm{T}\) and \(\mathrm{p}\), the following equilibrium is established in the case of the model surfactant \(\mathrm{AM}^{+} \mathrm{Br}^{-}\);
\[\mathrm{AM}^{+} \mathrm{Br}^{-}(\mathrm{aq}) \Leftrightarrow \mathrm{AM}^{+} \mathrm{Br}^{-}(\mathrm{mic}) \nonumber \]
Then,
\[\mu^{\mathrm{cq}}\left[\mathrm{AM}^{+} \mathrm{Br}^{-}(\mathrm{aq})\right]=\mu^{\mathrm{cq}}\left[\mathrm{AM}^{+} \mathrm{Br}^{-}(\mathrm{mic})\right] \nonumber \]
We assume that the micelles carry no charge. The chemical potential of the surfactant in aqueous solution is related to the cmc using the following equation where \(\mathrm{y}_{\pm}\) is the mean ionic activity coefficient. We set \(\mu^{\mathrm{eq}}\left[\mathrm{AM}^{+} \mathrm{Br}^{-} \text {(mic) }\right]\) equal to the chemical potential of the surfactant in the pure micellar state, \(\mu^{*}\left[\mathrm{AM}^{+} \mathrm{Br}^{-} \text {(mic) }\right]\).
\[\begin{aligned}
\mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \mathrm{aq} ; \mathrm{c}-\mathrm{scale}\right)+2 \, \mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{cmc} \, \mathrm{y}_{\pm} \, / \mathrm{c}_{\mathrm{r}}\right) \\
&=\mu^{*}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \text {micellar phase }\right)
\end{aligned} \nonumber \]
Here \(\mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \mathrm{aq} ; \mathrm{c}-\text { scale }\right)\) is the chemical potential of the salt \(\mathrm{AM}^{+} \mathrm{Br}^{-}\) in aqueous solution at unit concentration where the properties of the salt are ideal. Thus \(\mathrm{y}_{\pm}\) describes the role of ion-ion interactions in the solution having salt concentration cmc. Because the model states that there is only a trace amount of micelles in the system, we do not take account of salt-micelle interactions. Then
\[\Delta_{\text {mic }} \mathrm{G}^{0}=\mu^{*}\left(\text { micellar phase; } \mathrm{AM}^{+} \mathrm{Br}^{-}\right)-\mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \text {aq; } \mathrm{c}-\text { scale }\right) \nonumber \]
Hence,
\[\Delta_{\text {mic }} G^{0}(\mathrm{aq} ; \mathrm{c}-\text { scale })=2 \, \mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{cmc} \, \mathrm{y}_{\pm} / \mathrm{c}_{\mathrm{r}}\right) \nonumber \]
If the salt concentration in the aqueous solution at the cmc is quite low, a useful assumption sets \(\mathrm{y}_{\pm}\) equal to unity. Then,
\[\Delta_{\text {mic }} \mathrm{G}^{0}(\mathrm{aq} ; \mathrm{c}-\mathrm{scale})=2 \, \mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{cmc} / \mathrm{c}_{\mathrm{r}}\right) \nonumber \]
The latter equation leads to the calculation of the standard increase in Gibbs energy when one mole of salt \(\mathrm{AM}^{+} \mathrm{Br}^{-}\) passes from the ideal solution, concentration \(1 \mathrm{mol dm}^{-3}\) to the micellar phase.
There is a modest problem with the latter equation which can raise conceptual problems. As normally stated the cmc for a given salt is expressed using the unit ‘\(\mathrm{mol dm}^{-3}\)‘ so that \(\mathrm{c}_{\mathrm{r}} = 1 \mathrm{~mol dm}^{-3}\). This means that when \(\mathrm{cmc} > 1 \mathrm{~mol dm}^{-3}\), \(\Delta_{\operatorname{mic}} G^{0}(\mathrm{aq} ; \mathrm{c}-\text { scale })\) is positive. For solutes where \(\mathrm{cmc} < 1 \mathrm{~mol dm}^{-3}\), the derived quantity is negative.
Another approach expresses the cmc using the mole fractions, cmx such that equation (c) is written as follows.
\[\begin{gathered}
\mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \text {aq } ; \mathrm{x}-\mathrm{scale}\right)+2 \, \mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{cmx} \, \mathrm{f}_{\pm}^{*}\right) \\
=\mu^{*}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \text {micellar phase }\right)
\end{gathered} \nonumber \]
Here \(\mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \mathrm{aq} ; \mathrm{x}-\text { scale }\right)\) is the chemical potential of the salt \(\mathrm{AM}^{+} \mathrm{Br}^{-}\) in an ideal solution where the (asymmetric) activity coefficient \(\mathrm{f}_{\pm}^{*}=1.0\) and \(\mathrm{cmx} = 1.0\). .
By definition \(\operatorname{limit}\left[x\left(\mathrm{AM}^{+} \mathrm{Br}^{-}\right) \rightarrow 0\right] \mathrm{f}_{\pm}^{*}=1.0 \text { at all } \mathrm{T} \text { and } \mathrm{p}\).} The analogue of equation (f) takes the following form.
\[\Delta_{\text {mic }} \mathrm{G}^{0}(\mathrm{aq} ; \mathrm{x}-\text { scale })=2 \, \mathrm{R} \, \mathrm{T} \, \ln (\mathrm{cm} \mathrm{x}) \nonumber \]
Because cmx is always less than unity, \(\Delta_{\text {mic }} G^{0}(a q ; x-\text { scale })\) is always negative. It is important in these calculations to note the definitions of reference and standard states for solutes and micelles otherwise false conclusions can be drawn [14]. The analysis proceeds to use the Gibbs-Helmholtz equation. Hence,
\[\Delta_{\text {mic }} \mathrm{H}^{0}(\mathrm{aq} ; \mathrm{x}-\text { scale })=-2 \, \mathrm{R} \, \mathrm{T}^{2} \,\{\partial \ln (\mathrm{cmx}) / \partial \mathrm{T}\}_{\mathrm{p}} \nonumber \]
The term \(\left\{\partial \ln (\mathrm{cmx}) / \partial \mathrm{T}_{\mathrm{P}}\right.\) is conveniently obtained by expressing the dependence of cmx on temperature using the following polynomial.
\[\ln (c m x)=a_{1}+a_{2} \, T+a_{3} \, T^{2}+\ldots \nonumber \]
Equation (h) is straightforward, the stoichiometric factor ‘2’ emerging from the fact that each mole of salt \(\mathrm{AM}^{+} \mathrm{Br}^{-}\) produces on complete dissociation 2 moles of ions. A key assumption in this analysis is that the micelles carry no electric charge. In other words a micelle is formed by \(\mathrm{n}\) moles of cation \(\mathrm{AM}^{+}\), \(\mathrm{n}\) moles of counter ions \(\mathrm{Br}^{-}\) being bound within the Stern layer such that the charge on each micelle is zero. This model is a little unrealistic.
Ionic Surfactant: 1:1 salt: Phase Equilibrium: Dry Charged Micelle
A cationic surfactant \(\mathrm{AM}^{+} \mathrm{Br}^{-}\) in aqueous solution forms micelles when \(\mathrm{n}\) cations come together to form a micellar phase. Bearing in mind that \(\mathrm{n}\) might be greater than 20, the idea that there exists micro-phases of macro-cations in a system with an electric charge at least +20 is not attractive. In practice the charge is partially neutralised by bromide ions in the Stern layer. The quantity \(\beta\) refers to the fraction of counter ions bound to cations. Thus the formal charge number on each micelle is \([n \,(1-\beta)]\). In the model developed here we represent the formation of the micro-phase comprising the micelles as follows where n is the number of cation monomers which cluster, the remaining bromide ions being present in the aqueous solution (phase).
\[\begin{aligned}
\mathrm{nAM}^{+}(\mathrm{aq}) &+\mathrm{n} \,(1-\beta+\beta) \mathrm{Br}^{-}(\mathrm{aq}) \\
& \Leftrightarrow\left[\mathrm{nAM}^{+} \mathrm{n} \, \beta \mathrm{Br}^{-}\right]^{\mathrm{n} \,(1-\beta)}(\mathrm{mic})+\mathrm{n} \,(1-\beta) \mathrm{Br}^{-}(\mathrm{aq})
\end{aligned} \nonumber \]
We re-express this equilibrium in terms of equilibrium chemical potentials for a system at fixed \(\mathrm{T}\) and \(\mathrm{p}\).
\[\begin{aligned}
&\mathrm{n} \, \mu^{\mathrm{cq}}\left(\mathrm{AM}^{+} ; \mathrm{aq}\right)+\mathrm{n} \,(1-\beta+\beta) \, \mu^{\mathrm{eq}}\left(\mathrm{Br}^{-} ; \mathrm{aq}\right) \\
&=\mu^{\mathrm{eq}}\left\{\left[\mathrm{nAM}^{+} \mathrm{n} \, \beta \mathrm{Br}^{-}\right]^{\mathrm{n}(1-\beta)} ; \text { micelle }\right\}+\mathrm{n} \,(1-\beta) \mu^{\mathrm{cq}}\left(\mathrm{Br}^{-} ; \mathrm{aq}\right)
\end{aligned} \nonumber \]
We define the chemical potential of the micelle microphase which contains 1 mole of \(\mathrm{AM}^{+}\). This is a key extrathermodynamic step. We also describe the micelle as a pure ‘phase’.
\[\begin{aligned}
\mu^{\mathrm{eq}}\left\{\left[\mathrm{AM}^{+} \beta \mathrm{Br}^{*}\right]^{(1-\beta)} ; \text { micelle }\right\} \\
&=\mu^{\mathrm{cq}}\left\{\left[\mathrm{nAM}^{+} \mathrm{n} \, \beta \mathrm{Br}^{-}\right]^{\mathrm{n}(1-\beta)} ; \text { micelle }\right\} / \mathrm{n}
\end{aligned} \nonumber \]
Hence,
\[\begin{aligned}
&\mu^{\mathrm{eq}}\left(\mathrm{AM}^{+} ; \mathrm{aq}\right)+\mu^{\mathrm{eq}}\left(\mathrm{Br}^{-} ; \mathrm{aq}\right) \\
&=\mu^{*}\left\{\left[\mathrm{AM}^{+} \beta \mathrm{Br}^{*}\right]^{(1-\beta)} ; \text { micelle }\right\}+(1-\beta) \mu^{\mathrm{eq}}\left(\mathrm{Br}^{-} ; \mathrm{aq}\right)
\end{aligned} \nonumber \]
Or,
\[\begin{aligned}
&\mu^{\mathrm{cq}}\left(\mathrm{AM}^{+} \mathrm{Br}^{-1} ; \mathrm{aq}\right)= \\
&\mu^{\mathrm{eq}}\left\{\left[\mathrm{AM}^{+} \beta \mathrm{Br}^{-}\right]^{(1-\beta)} ; \text { micelle\} }+(1-\beta) \mu^{\mathrm{cq}}\left(\mathrm{Br}^{-} ; \mathrm{aq}\right)\right.
\end{aligned} \nonumber \]
The term \(\mu^{थ}\left(\mathrm{AM}^{+} \mathrm{Br}^{-1} ; \mathrm{aq}\right)\) is the equilibrium chemical potential of a 1:1 salt in solution at the cmc. The term \(\mu^{\mathrm{eq}}\left(\mathrm{Br}^{-} ; \mathrm{aq}\right)\) is the equilibrium chemical potential of the bromide ion in the solution at the cmc of the surfactant. In any event the system is electrically neutral.
\[\begin{aligned}
&\mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-1} ; \mathrm{aq}\right)+2 \, \mathrm{R} \, \mathrm{T} \, \ln \left[\mathrm{cmc} \, \mathrm{y}\left(\mathrm{AM}^{+} \mathrm{Br}^{-}\right) / \mathrm{c}_{\mathrm{r}}\right] \\
&=\mu^{*}\left\{\left[\mathrm{AM}^{+} \beta \mathrm{Br}^{*}\right]^{(1-\beta)} ; \text { micelle }\right\} \\
&+(1-\beta) \,\left\{\mu^{0}\left(\mathrm{Br}{ }^{-} ; \mathrm{aq}\right)+\mathrm{R} \, \mathrm{T} \, \ln \left[\mathrm{cmc} \, \mathrm{y}\left(\mathrm{Br}^{-}\right) / \mathrm{c}_{\mathrm{r}}\right]\right\}
\end{aligned} \nonumber \]
By definition,
\[\begin{aligned}
\Delta_{\text {mic }} \mathrm{G}^{0}=\mu^{*} &\left\{\left[\mathrm{AM}^{+} \beta \mathrm{Br}^{*}\right]^{(1-\beta)} ; \text { micelle }\right\} \\
&+(1-\beta) \, \mu^{0}\left(\mathrm{Br}^{-} ; \mathrm{aq}\right)-\mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-1} ; \mathrm{aq}\right)
\end{aligned} \nonumber \]
Assuming both \(\mathrm{y}\left(\mathrm{AM}^{+} \mathrm{Br}^{-}\right)\) and \(\mathrm{y}\left(\mathrm{Br}^{-}\right)\) are unity,
\[\Delta_{\text {mic }} \mathrm{G}^{0}=2 \, \mathrm{R} \, \mathrm{T} \, \ln \left[\mathrm{cmc} / \mathrm{c}_{\mathrm{r}}\right]-(1-\beta) \, \mathrm{R} \, \mathrm{T} \, \ln \left[\mathrm{cmc} / \mathrm{c}_{\mathrm{r}}\right] \nonumber \]
or
\[\Delta_{\text {mic }} \mathrm{G}^{0}=(1+\beta) \, \mathrm{R} \, \mathrm{T} \, \ln \left[\mathrm{cmc} / \mathrm{c}_{\mathrm{r}}\right] \nonumber \]
The latter equation closely resembles that for non-ionic surfactants for which \(\beta\) is unity. For ionic surfactants it is not justified to assume that \(\beta\) is also unity.
Ionic Surfactant: 1:1 salt: Dry Charged Micelle:Mixed Salt Solutions
As more ionic surfactant is added to a solution having the concentration of surfactant equal to the cmc, so the solution increasingly resembles a mixed salt solution, simple salt, charged micelles and counter ions. Analysis of the properties of such solutions was described by Burchfield and Woolley [2-5]. We might develop the analysis from equation (k). An advantage of writing the equation in this form stems from the observation that both sides of the equation describe an electrically neutral system. Woolley and co-- workers [4,5] prefer a form which removes a contribution \(\mathrm{n} \,(1-\beta) \mathrm{Br}^{-}(\mathrm{aq})\) from each side of equation (k).
\[\mathrm{nAM}^{+}(\mathrm{aq})+\mathrm{n} \, \beta \mathrm{Br}^{-}(\mathrm{aq}) \Leftrightarrow\left[\mathrm{nAM}^{+} \mathrm{n} \, \beta \mathrm{Br}^{-}\right]^{\mathrm{a} \,(1-\beta)}(\mathrm{aq}) \nonumber \]
Nevertheless one might argue that equation (k) does have the merit in comparing two salts whereas equation (t) describes the links between three ions. In terms of equation (k) , there are two salts in solution.
-
\(\mathrm{AM}^{+} \mathrm{Br}^{-}\) where \(v_{+}=1, v_{-}=1, v=2, Q=\left(v_{+}^{v+} \, v_{-}^{v-}\right)^{1 / v}=1, y_{\pm}^{v}=y_{+}^{v+} \, y_{-}^{v-}, \text { or } y_{\pm}^{2}=y_{+} \, y_{-}\) But
\[\begin{aligned}
&\mu\left(\mathrm{AM}^{+} \mathrm{Br}^{-}\right)= \\
&\mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-}\right)+2 \, \mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{c}\left(\mathrm{AM}^{+} \mathrm{Br}^{-}\right) \, \mathrm{y}_{\pm}\left(\mathrm{AM}^{+} \mathrm{Br}^{-}\right) / \mathrm{c}_{\mathrm{r}}\right)
\end{aligned} \nonumber \] -
For the micellar salt, \(\left[\mathrm{nAM}^{+} \mathrm{n} \, \beta \mathrm{Br}^{-}\right]^{\mathrm{n} \,(1-\beta)} \mathrm{n} \,(1-\beta) \mathrm{Br} \mathrm{r}^{-}\)
\(\mathrm{v}_{+}=1, \mathrm{v}_{-}=\mathrm{n} \,(1-\beta),\) and \(v=n \,(1-\beta)+1\) and \(\mathrm{Q}^{\mathrm{n}(1-\beta)+1}=\left[1 \,\{\mathrm{n} \,(1-\beta)\}^{\mathrm{n}(1-\beta)}\right]\) with \(\mathrm{y}_{\pm}^{\mathrm{n} \,(1-\beta)+1}=\mathrm{y}_{+}^{1} \, \mathrm{y}_{-}^{\mathrm{n} \,(1-\beta)}\)
Then,\[\begin{aligned}
&\mu(\text { mic. salt }) \\
&\left.=\mu^{0} \text { (mic. salt }\right)+[n \,(1-\beta)+1] \, R \, T \, \ln \left[Q \, c(\text { mic.salt }) \, y_{\pm} / c_{r}\right]
\end{aligned} \nonumber \]
At equilibrium,
\[\mathrm{n} \, \mu^{\mathrm{eq}}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \mathrm{aq}\right)=\mu^{\mathrm{eq}}(\text { mic. salt; aq }) \nonumber \]
Hence,
\[\Delta_{\text {mics slt }} \mathrm{G}^{0}=-\mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{K}_{0}\right)=\mu^{0}(\text { mic.salt })-\mathrm{n} \, \mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-}\right) \nonumber \]
The total concentration of salt ctot in the system is given by equation (y).
\[\operatorname{ctot}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \text {system }\right)=\mathrm{n} \, \mathrm{c}(\text { ch arg ed micelles })+\mathrm{c}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \mathrm{aq}\right) \nonumber \]
The analysis makes no explicit reference to a cmc. Instead the micellar system is described as a mixed salt solution. Application of these equations requires careful computer –based curve fitting for multi-parametric equations. The latter include equations relating mean ionic activity coefficients for salts to the composition of a given solution. A shielding factor \(\delta\) was use by Burchfield and Woolley to reduce the impact of micellar charge of the cationic micelles on calculated ionic strength [2]. Thus the effective charge on the cationic micelles was written as \(n \,(1-\beta) \, \delta\) where \(\delta\) is approx. 0.5.
Ionic Surfactant: Mass Action Model
In general terms the equilibrium between surfactant monomers \(\mathrm{Z}^{+}\), counter anions \(\mathrm{X}^{-}\) and micelles \(\mathrm{M}\) can be represented by the following equation.
\[\mathrm{n} Z^{+}(\mathrm{aq})+\mathrm{mX} \mathrm{X}^{-}(\mathrm{aq}) \Leftrightarrow \mathrm{M}^{(\mathrm{n}-\mathrm{m})+}(\mathrm{aq}) \nonumber \]
Then in terms of the mass action model, the concentration equilibrium constant,
\[\mathrm{K}_{\mathrm{c}}^{0}=\left[\mathrm{M}^{(\mathrm{n}-\mathrm{m})+}\right] /\left\{\left[\mathrm{Z}^{+}\right]^{\mathrm{n}} \,\left[\mathrm{X}^{-}\right]^{\mathrm{m}}\right\} \nonumber \]
By definition,
\[\Delta_{\text {mic }} \mathrm{G}^{0}=-(\mathrm{n})^{-1} \, \mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{K}_{\mathrm{c}}^{0}\right) \nonumber \]
Then,
\[\Delta_{\text {mic }} \mathrm{G}^{0} /(\mathrm{R} \, \mathrm{T})=-(\mathrm{n})^{-1} \, \ln \left[\mathrm{M}^{(\mathrm{n}-\mathrm{m})+}\right]+\ln \left[\mathrm{Z}^{+}\right]+(\mathrm{m} / \mathrm{n}) \, \ln \left[\mathrm{X}^{-}\right] \nonumber \]
Footnotes
[1] N. M. van Os, J. R. Haak and L. A. M. Rupert, Physico – Chemical Properties of Selected Anionic, Cationic and Non-ionic Surfactants, Elsevier, Amsterdam 1993.
[2] T. E. Burchfield, and E. M. Woolley, J. Phys. Chem.,1984, 88 ,2149.
[3] T. E. Burchfield and E. M. Woolley, in Surfactants in Solution, ed. K. L. Mittal and P. Bothorel, Plenum Press, New Yok, 1987, volume 4 , 69.
[4] E. M. Woolley and T. E. Burchfield, J. Phys. Chem.,1984, 88 ,2155.
[5] T. E. Burchfield and E.M.Wooley, Fluid Phase Equilib., 1985, 20 ,207.
[6] D. F.Evans, M. Allen, B.W. Ninham and A. Fouda, J. Solution Chem.,1984, 13 ,87.
[7] D. G. Archer, J. Solution Chem.,1986, 15 ,727
[8]
- L. Espada, M. N. Jones and G. Pilcher, J.Chem. Thermodyn., 1970, 2 ,1, 333; and references therein.
- M. N. Jones, G. Pilcher and L.Espada, J. Chem.Thermodyn,.,1970, 2 ,333
[9] M. J. Blandamer, P. M. Cullis, L. G. Soldi and M. C. S. Subha, J. Therm. Anal.,1996, 46 ,1583.
[10] R. Zana, Langmuir, 1996, 12 ,1208.
[11] M. J. Blandamer, K. Bijma, J. B. F. N. Engberts, P. M. Cullis, P. M. Last, K. D. Irlam and L. G. Soldi, J. Chem.Soc. Faraday Trans.,1997, 93 ,1579; and references therein.
[12] M. J. Blandamer, W. Posthumnus, J. B. F. N. Engberts and K. Bijma, J. Mol. Liq., 1997, 73-74 ,91.
[13] R. DeLisi, E. Fiscaro, S. Milioto, E. Pelizetti and P. Savarino, J. Solution Chem.,1990, 19 , 247.
[14] M. J. Blandamer, P. M. Cullis, L. G. Soldi, J. B. F. N. Engberts, A. Kacperska, N. M. van Os and M. C. S. Subha, Adv. Colloid Interface Sci.,1995, 58 ,171.
[15] For further references concerning the Stern Layer, see N. J. Buurma, P. Serena, M. J. Blandamer and J. B. F. N. Engberts, J. Org. Chem., 2004, 69 , 3899.


7.3.6B: Productive Life Cycle with Possible Latency
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- Ying Liu
- City College of San Francisco
State the major difference between the productive life cycle of animal viruses and the latent life cycle.
Define provirus.
Name 3 herpes viruses that may have a latent cycle, state in what cell types they become latent, and name the diseases each cause.
Some animal viruses, such as the herpes viruses and a group of viruses known as the retroviruses, are able to remain latent within infected host cells for long periods of time without replicating or causing harm. Some of these viruses remain latent within the cytoplasm of the host cell while others are able to insert or integrate their DNA into the host cell's chromosomes. When the viral DNA is incorporated into the host cell's DNA, it is called a provirus.
In many instances, viral latency, as well as viral persistence, is thought to be due to a process called RNA interference (RNAi) where small non-coding regulatory RNAs (ncRNAs) such as microRNAs (miRNAs) regulate gene expression. Certain viruses that infect humans are able to establish persistent infection by using their own miRNAs and/or miRNAs produced by their human host.
For example, viral and/or host miRNAs may bind to certain viral messenger RNA ( mRNA ) molecules and block translation of viral proteins required for rapid viral replication, or they may bind to the mRNA of human genes that produce proteins used in viral replication. The resulting low viral levels may then minimize immune responses against that virus. In addition, these miRNAs may directly affect host immune defenses by turning off the production of antiviral cytokines or by blocking apoptosis of infected host cells. Examples include the herpesviruses , retroviruses , and anelloviruses .
Herpes viruses, for example, are often latent in some cell types but productive in others. Herpes viruses include herpes simplex type 1 (HSV-1) which usually causes fever blisters or oral herpes, herpes simplex type 2 (HSV-2) which usually causes genital herpes, Epstein-Barr virus (EBV) which causes infectious mononucleosis and plays a role in certain cancers, varicella-zoster virus (VZV) which causes chickenpox and shingles, and cytomegalovirus (CMV) which causes a variety of infections in immunosuppressed persons and is also a leading cause of birth defects.
For more on HSV and CMV, see the AIDS Pathology Tutorial at the University of Utah.
Herpesviruses use both host and viral miRNAs to switch between the productive life cycle in infected epithelial cells whereby large numbers of viruses are produced and the infected host cells are killed (as in the case of fever blisters) and the persistent latent state in nerve cells where low levels of viruses are produced and the infected host cells are not killed by apoptosis.
With EBV, the virus is productive in epithelial cells but latent in B-lymphocytes.
In the case of HSV-1, HSV-2, and VZV, primary infection causes the virus to replicate within epithelial cells. However, some of the viruses enter and migrate down neurons where they become latent in the body of sensory neurons. Subsequent activation of the latently infected neurons by a variety of extracellular stimuli enables the viruses to migrate back up the nerve cell and replicate again in the epithelial cells. With EBV, the virus is productive in epithelial cells but latent in B-lymphocytes.
- Scanning electron micrograph of HSV ; courtesy of Dennis Kunkel's Microscopy .
In the case of HIV, the viral genome eventually becomes a provirus. After integration, the HIV proviral DNA can exist in either a latent or productive state, which is determined by genetic factors of the viral strain, the type of cell infected, and the production of specific host cell proteins.
The majority of the proviral DNA is integrated into the chromosomes of activated T4-lymphocytes. These generally comprise between 93% and 95% of infected cells and are productively infected, not latently infected. However, a small percentage of HIV-infected memory T4-lymphocytes persists in a resting state because of a latent provirus. Subsequent activation of the host cell by extracellular stimuli, however, causes the needed proteins to be made and the virus again replicates via the productive life cycle. These memory T4-lymphocytes, along with infected monocytes, macrophages, and dendritic cells, provide stable reservoirs of HIV capable of escaping host defenses and antiretroviral chemotherapy.
In the next section we will now look at the life cycle of HIV.
Study the material in this section and then write out the answers to these questions. Do not just click on the answers and write them out. This will not test your understanding of this tutorial.
Summary
Questions


1.5.4: Chemical Potentials- Solutions- Composition
A given aqueous solution at temperature \(\mathrm{T}\) and pressure \(\mathrm{p}\) (both near ambient) was prepared using \(\mathrm{n}_{1}\) moles of water and \(\mathrm{n}_{j}\) moles of urea (i.e. chemical substance \(j\)). The Gibbs energy \(\mathrm{G}(\mathrm{aq})\), an extensive property (variable), is given by the sum of products of amounts of each chemical substance and chemical potentials [1].
\[\mathrm{G}(\mathrm{aq})=\mathrm{n}_{1} \, \mu_{1}(\mathrm{aq})+\mathrm{n}_{\mathrm{j}} \, \mu_{\mathrm{j}}(\mathrm{aq}) \label{a} \]
Equation \ref{a} is key although we cannot put number values to \(\mathrm{G}(\mathrm{aq})\), \(\mu_{1}(\mathrm{aq})\) and \(\mu_{j}(\mathrm{aq}\). The latter two quantities are, respectively, the chemical potentials of the solvent, water and solute \(j\) in the aqueous solution at the same temperature and pressure. Equation \ref{a} seems a strange starting point granted it contains three quantities which we can never know. Matters can only improve.
There is merit in turning attention to an intensive property describing the Gibbs energy of a solution prepared using \(1 \mathrm{~kg}\) of solvent, \(\mathrm{G}\left(\mathrm{aq} ; \mathrm{w}_{1}=1.0 \mathrm{~kg}\right)\). Therefore, we do not have to worry about the size of the flask containing the solution. The same descriptor applies to \(0.1 \mathrm{~cm}^{3}\) or \(10 \mathrm{m}^{3}\) of a given solution [2,3].
\[\text { By definition } \quad \mathrm{G}\left(\mathrm{aq} ; \mathrm{w}_{1}=1.0 \mathrm{~kg}\right)=\mathrm{G}(\mathrm{aq}) / \mathrm{w}_{1} \nonumber \]
\[\mathrm{G}\left(\mathrm{aq} ; \mathrm{w}_{1}=1.0 \mathrm{~kg}\right)=\left(1 / \mathrm{M}_{1}\right) \, \mu_{1}(\mathrm{aq})+\mathrm{m}_{\mathrm{j}} \, \mu_{\mathrm{j}}(\mathrm{aq}) \nonumber \]
\(\mathrm{M}_{1}\) is the molar mass of solvent, water, and mj is the molality of solute \(j\). Again we cannot put number values to \(\mathrm{G}\left(\mathrm{aq} ; \mathrm{w}_{1}=1.0 \mathrm{~kg}\right)\), \(\mu_{1}(\mathrm{aq})\) and \(\mu_{\mathrm{j}}(\mathrm{aq})\). Faced with this situation, the well-established approach involves an examination of differences. With respect to \(\mu_{1}(a q)\), the properties of water in an aqueous solution are compared with the properties of water at the same temperature and pressure. In these terms, we compare \(\mu_{1}(\mathrm{aq}, \mathrm{T}, \mathrm{p})\) with \(\mu_{1}^{*}(\ell, T, p)\). The superscript * in the latter term indicates that the chemical substance is pure and the symbol '\(\ell\)' indicates that this substance is a liquid. Hence, comparison is drawn with the chemical potential of pure liquid water at the same \(\mathrm{T}\) and \(\mathrm{p}\). In one sense we regard the solute as a controlled impurity perturbing the properties of the solvent. [We use the subscript '1' to indicate chemical substance 1 which in the convention used here refers to the solvent; water in the case of aqueous solutions.]
In considering the properties of, for example, urea in this aqueous solution molality \(\mathrm{m}_{j}\), we need a reference state against which to compare the properties of urea in the real solution prepared by dissolving \(\mathrm{n}_{j}\) moles of urea in \(\mathrm{n}_{1}\) moles of water. There is little point in comparing the properties of solute, urea with those of solid urea, a hard crystalline solid. Instead, we identify a reference solution state.
In general terms chemists explore how the chemical potentials of solvent and solute in an aqueous solution are related to the composition of the solution. Equations which offer such relationships should satisfy two criteria [4]: in the limit of infinite dilution (i) the partial molar volumes \(\mathrm{V}_{\mathrm{j}}(\mathrm{aq})\) and \(\mathrm{V}_{1}(\mathrm{aq})\) are meaningful and (ii) the partial molar enthalpies \(\mathrm{H}_{\mathrm{j}}(\mathrm{aq}\) and \(\mathrm{H}_{1}(\mathrm{aq})\) are meaningful. In other words, these properties do not approach an asymptotic limit of either \(+ \infty\) or \(– \infty\) with increasing dilution. For this reason physical chemists usually favour expressing the composition of solutions in molalities.
In summary analysis of the properties of solutions and liquid mixtures is built around the somewhat abstract concept of the chemical potential introduced by J. Willard Gibbs and by Pierre Duhem. The task of showing chemists the significance and application of this concept was left to Lewis and Randall in their classic monograph [5] published in 1923 [6]. Chemical potentials are one example of a class of properties called partial molar which provide the key link between macroscopic thermodynamic descriptions of systems and molecular properties [7].
Footnotes
[1] \(\mathrm{G}(\mathrm{aq})=[\mathrm{mol}] \,\left[\mathrm{J} \mathrm{mol}{ }^{-1}\right]+[\mathrm{mol}] \,\left[\mathrm{J} \mathrm{mol}^{-1}\right]=[\mathrm{J}]\)
[2] \(\begin{aligned}
&\mathrm{G}\left(\mathrm{aq} ; \mathrm{w}_{1}=1.0 \mathrm{~kg}\right)= \\
&\quad\left[1 / \mathrm{kg} \mathrm{mol}^{-1}\right] \,\left[\mathrm{J} \mathrm{mol}^{-1}\right]+\left[\mathrm{mol} \mathrm{kg}^{-1}\right] \,\left[\mathrm{J} \mathrm{mol}^{-1}\right]=\left[\mathrm{J} \mathrm{kg}^{-1}\right]
\end{aligned}\)
[3] With reference to equations (a) and (c), we must avoid the temptation to write “at constant temperature and pressure”. This condition is implicit in the description of the system using the independent variables \(\left[\mathrm{T}, \mathrm{p}, \mathrm{n}_{1}, \mathrm{n}_{\mathrm{j}}\right]\) for the aqueous solution containing the solute with the added condition that \(\mathrm{T}\) and \(\mathrm{p}\) are intensive variables; i.e. the set of independent variables is Gibbsian. Nonetheless there is often merit in using a complete set of descriptions of a system even if we over-define the variable under discussion. In describing the Gibbs energy defined by equation (a), we might write \(\mathrm{G}(\mathrm{T} ; \mathrm{p} ; \mathrm{aq})\). Similarly for the system described by equation (b) it is often helpful to write \(\mathrm{G}\left(\mathrm{T} ; \mathrm{p} ; \mathrm{aq} ; \mathrm{w}_{1}=1 \mathrm{~kg} ; \mathrm{m}_{\mathrm{j}}\right)\). In reviewing the properties of solutions our interest, unless otherwise stated, centres on solutions at equilibrium where the affinity \(\mathrm{A}\) is zero and the organisation characteristic of the equilibrium system, \(\xi^{e q}\). We may find it helpful to write \(\mathrm{G}\left(\mathrm{T} ; \mathrm{p} ; \mathrm{aq} ; \mathrm{w}_{1}=1 \mathrm{~kg} ; \mathrm{m}_{\mathrm{j}} ; \mathrm{A}=0 ; \xi^{\mathrm{eq}}\right)\), replacing \(\mathrm{G}\) by \(\mathrm{H}\), \(\mathrm{S}\) and \(\mathrm{V}\) for the corresponding enthalpy, entropy and volume of this solution. Clearly this over-definition is somewhat silly. Nevertheless it is often preferable to over-define a system rather than under-define when mistakes can arise.
[4] J. E. Garrod and T. M. Herrington, J. Chem. Educ., 1969, 46 , 165.
[5] G. N. Lewis and M. L. Randall, Thermodynamics and the Free Energy of Chemical Substances, McGraw-Hill, New York, 1923.
[6] See also, G. N. Lewis, Proc. Am. Acad. Arts Sci.,1907, 43 ,259.
[7] L. Hepler, Thermochim. Acta, 1986, 100 , 171.


1.9: Scales and Scale Degrees
A scale is a succession of pitches ascending or descending in steps. There are two types of steps: half steps and whole steps . A half step (H) consists of two adjacent pitches on the keyboard. A whole step (W) consists of two half steps. Usually, the pitches in a scale are each notated with different letter names, though this isn’t always possible or desirable.
The Chromatic Scale
The chromatic scale consists entirely of half steps, and uses every pitch on the keyboard within a single octave. Here is the chromatic scale that spans the pitches C4 through C5.
The major scale
A major scale, a sound with which you are undoubtedly familiar, consists of seven whole (W) and half (H) steps in the following succession: W-W-H-W-W-W-H. The first pitch of the scale, called the tonic , is the pitch upon which the rest of the scale is based. When the scale ascends, the tonic is repeated at the end an octave higher.
Here is the D major scale. It is called the “D major scale” because the pitch D is the tonic and is heard at both ends of the scale.
Scale degrees and solfège
While ISO notation allows us to label a pitch in its specific register, it is often useful to know where that pitch fits within a given scale. For example, the pitch class D is the first (and last) note of the D-major scale. The pitch class A is the fifth note of the D-major scale. When described in this way, we call the notes scale degrees , because they’re placed in context of a specific scale. Solfège syllables, a centuries-old method of teaching pitch and sight singing , can also be used to represent scale degrees (when used in this way, this system is specifically called movable- do solfège).
Scale degrees are labeled with Arabic numerals and carets (^). The illustration below shows a D-major scale and corresponding ISO notation, scale degrees, and solfège syllables.
The minor scale
Another scale with which you are likely very familiar is the minor scale. There are several scales that one might describe as minor , all of which have a characteristic third scale degree that is lower than the one found in the major scale. The minor scale most frequently used in tonal music from the Common Practice period is based on the aeolian mode (you’ll read more about modes later), which is sometimes referred to as the natural minor scale.
The natural minor scale consists of seven whole (W) and half (H) steps in the following succession: W-H-W-W-H-W-W. Note the changes in solfège syllables.
If you sing through the above example, you’ll notice that the ending lacks the same sense of closure you heard in the major scale. This closure is created in the major scale, in part, by the ascending semitone between ti and do . Composers often want to have this sense of closure when using the minor mode, too. They’re able to achieve this by applying an accidental to the seventh scale degree, raising it by a semitone. If you do this within the context of the natural minor scale, you get something called the harmonic minor scale.
Now the last two notes of the scale sound much more conclusive, but you might have found it difficult to sing le to ti . When writing melodies in a minor key, composers often “corrected” this by raising le by a semitone to become la when approaching the note ti . When the melody descended from do , the closure from ti to do isn’t needed; likewise, it is no longer necessary to “correct” le , so the natural form of the minor scale is used again. Together, these different ascending and descending versions are called the melodic minor scale.
When ascending, the melodic minor scale uses la and ti .
When descending, the melodic minor scale uses the “natural” te and le .
Truth be told, most composers don’t really think about three different “forms” of the minor scale. The harmonic minor scale simply represents composers’ tendency to use ti when building harmonies that include the seventh scale degree in the minor mode. Likewise, the melodic minor scale is derived from composers’ desire to avoid the melodic augmented second interval (more on this in the intervals section) between le and ti (and some chose not to avoid this!). In reality, there is only one “version” of the minor scale. Context determines when a composer might use la and ti when writing music in a minor key.