6.2: Half Steps and Whole Steps
- The pitch of a note is how high or low it sounds. The distance between two pitches can be measured in half steps and whole steps.
The pitch of a note is how high or low it sounds. Musicians often find it useful to talk about how much higher or lower one note is than another. This distance between two pitches is called the interval between them. In Western music, the small interval from one note to the next closest note higher or lower is called a half step or semi-tone.
Half Steps
Listen to the half steps in Figure 1.
The intervals in Figure 1 look different on a staff; sometimes they are on the same line, sometimes not. But it is clear at the keyboard that in each case there is no note in between them.
So a scale that goes up or down by half steps, a chromatic scale, plays all the notes on both the white and black keys of a piano. It also plays all the notes easily available on most Western instruments. (A few instruments, like trombone and violin, can easily play pitches that aren't in the chromatic scale, but even they usually don't.)
One Octave Chromatic Scale
Listen to a chromatic scale.
If you go up or down two half steps from one note to another, then those notes are a whole step, or whole tone apart.
Whole Steps
A whole tone scale, a scale made only of whole steps, sounds very different from a chromatic scale.
Whole Tone Scale
Listen to a whole tone scale.
You can count any number of whole steps or half steps between notes; just remember to count all sharp or flat notes (the black keys on a keyboard) as well as all the natural notes (the white keys) that are in between.
The interval between C and the F above it is 5 half steps, or two and a half steps.
Identify the intervals below in terms of half steps and whole steps. If you have trouble keeping track of the notes, use a piano keyboard, a written chromatic scale, or the chromatic fingerings for your instrument to count half steps.
Solution
Fill in the second note of the interval indicated in each measure. If you need staff paper for this exercise, you can print out this staff paper PDF file.


7.14D: Shuttle Vectors and Expression Vectors
An expression vector is generally a plasmid that is used to introduce a specific gene into a target cell.
LEARNING OBJECTIVES
Explain the structure and function of shuttle and expression vectors
Key Takeaways
An expression vector, otherwise known as an expression construct, is generally a plasmid that is used to introduce a specific gene into a target cell. Once the expression vector is inside the cell, the protein that is encoded by the gene is produced by the cellular-transcription and translation machinery ribosomal complexes. The plasmid is frequently engineered to contain regulatory sequences that act as enhancer and promoter regions and lead to efficient transcription of the gene carried on the expression vector. The goal of a well-designed expression vector is the production of large amounts of stable messenger RNA, and in extension, proteins. Expression vectors are basic tools for biotechnology and the production of proteins such as insulin, which is important for the treatment of diabetes.
After expression of the gene product, the purification of the protein is required; but since the vector is introduced to a host cell, the protein of interest should be purified from the proteins of the host cell. Therefore, to make the purification process easy, the cloned gene should have a tag. This tag could be histidine (His) tag or any other marker peptide.
Expression vectors are used for molecular biology techniques such as site-directed mutagenesis. Cloning vectors, which are very similar to expression vectors, involve the same process of introducing a new gene into a plasmid, but the plasmid is then added into bacteria for replication purposes. In general, DNA vectors that are used in many molecular-biology gene-cloning experiments need not result in the expression of a protein.
Expression vectors must have expression signals such as a strong promoter, a strong termination codon, adjustment of the distance between the promoter and the cloned gene, and the insertion of a transcription termination sequence and a PTIS (portable translation initiation sequence).
A shuttle vector is a vector that can propagate in two different host species, hence, inserted DNA can be tested or manipulated in two different cell types. The main advantage of these vectors is that they can be manipulated in E. coli and then used in a system which is more difficult or slower to use.
Shuttle vectors can be used in both eukaryotes and prokaryotes. Shuttle vectors are frequently used to quickly make multiple copies of the gene in E. coli (amplification). They can also be used for in vitro experiments and modifications such as mutagenesis and PCR. One of the most common types of shuttle vectors is the yeast shuttle vector that contains components allowing for the replication and selection in both E. coli cells and yeast cells. The E. coli component of a yeast shuttle vector includes an origin of replication and a selectable marker, such as an antibiotic resistance like beta lactamase. The yeast component of a yeast shuttle vector includes an autonomously replicating sequence (ARS), a yeast centromere (CEN), and a yeast selectable marker.
Key Points
- The plasmid is frequently engineered to contain regulatory sequences that act as enhancer and promoter regions and lead to efficient transcription of the gene carried on the expression vector.
- Expression vectors must have expression signals such as a strong promoter, a strong termination codon, adjustment of the distance between the promoter and the cloned gene, and the insertion of a transcription termination sequence and a portable translation initiation sequence.
- Expression vectors are used for molecular biology techniques such as site-directed mutagenesis.
Key Terms
- plasmid : A circle of double-stranded DNA that is separate from the chromosomes, which is found in bacteria and protozoa.
- expression vector : An expression vector, otherwise known as an expression construct, is generally a plasmid that is used to introduce a specific gene into a target cell.
- transcription : The synthesis of RNA under the direction of DNA.


5.5: Answers to exercises
Two sample tests, effect sizes
Answer to the sign test question. It is enough to write:
Code \(\PageIndex{1}\) (R):
Here the sign test failed to find obvious differences because (like t-test and Wilcoxon test) it considers only central values.
Answer to the ozone question. To know if our data are normally distributed, we can apply the Normality() function:
Code \(\PageIndex{2}\) (R):
(Here we applied unstack() function which segregated our data by months.)
Answer to the argon question. First, we need to check assumptions:
Code \(\PageIndex{3}\) (R):
It is clear that in this case, nonparametric test will work better:
Code \(\PageIndex{4}\) (R):
(We used jitter() to break ties. However, be careful and try to check if this random noise does not influence the p-value. Here, it does not.)
And yes, boxplots (Figure 5.2.4) told the truth: there is a statistical difference between two set of numbers.
Answer to the cashiers question. Check normality first:
Code \(\PageIndex{5}\) (R):
Now, we can compare means:
Code \(\PageIndex{6}\) (R):
It is likely that first cashier has generally bigger lines:
Code \(\PageIndex{7}\) (R):
The difference is not significant.
Answer to the grades question. First, check the normality:
Code \(\PageIndex{8}\) (R):
(Function split() created three new variables in accordance with the grouping factor; it is similar to unstack() from previous answer but can accept groups of unequal size.)
Check data (it is also possible to plot boxplots):
Code \(\PageIndex{9}\) (R):
It is likely that the first class has results similar between exams but in the first exam, the second group might have better grades. Since data is not normal, we will use nonparametric methods:
Code \(\PageIndex{10}\) (R):
For the first class, we applied the paired test since grades in first and second exams belong to the same people. To see if differences between different classes exist, we used one-sided alternative hypothesis because we needed to understand not if the second class is different, but if it is better .
As a result, grades of the first class are not significantly different between exams, but the second class performed significantly better than first. First confidence interval includes zero (as it should be in the case of no difference), and second is not of much use.
Now effect sizes with suitable nonparametric Cliff’s Delta:
Code \(\PageIndex{11}\) (R):
Therefore, results of the second class are only slightly better which could even be negligible since confidence interval includes 0.
Answer to the question about ground elder leaves (Figure \(\PageIndex{1}\)).
First, check data, load it and check the object:
Code \(\PageIndex{12}\) (R):
(We also converted SUN variable into factor and supplied the proper labels.)
Let us check the data for the normality and for the most different character (Figure \(\PageIndex{2}\)):
Code \(\PageIndex{13}\) (R):
TERM.L (length of the terminal leaflet, it is the rightmost one on Figure \(\PageIndex{1}\)), is likely most different between sun and shade. Since this character is normal, we will run more precise parametric test:
Code \(\PageIndex{14}\) (R):
To report t-test result, one needs to provide degrees of freedom, statistic and p-value, e.g., like “in a Welch test, t statistic is 14.85 on 63.69 degrees of freedom, p-value is close to zero, thus we rejected the null hypothesis”.
Effect sizes are usually concerted with p-values but provide additional useful information about the magnitude of differences:
Code \(\PageIndex{15}\) (R):
Both Cohen’s d and Lyubishchev’s K (coefficient of divergence) are large.
ANOVA
Answer to the height and color questions. Yes on both questions:
Code \(\PageIndex{16}\) (R):
There are significant differences between all three groups.
Answer to the question about differences between cow-wheats (Figure \(\PageIndex{3}\)) from seven locations.
Load the data and check its structure:
Code \(\PageIndex{17}\) (R):
Plot it first (Figure \(\PageIndex{4}\)):
Code \(\PageIndex{18}\) (R):
Check assumptions:
Code \(\PageIndex{19}\) (R):
Consequently, leaf length must be analyzed with non-parametric procedure, and plant height—with parametric which does not assume homogeneity of variance (one-way test):
Code \(\PageIndex{20}\) (R):
Now the leaf length:
Code \(\PageIndex{21}\) (R):
All in all, location pairs 2–4 and 4–6 are divergent statistically in both cases. This is visible also on boxplots (Figure \(\PageIndex{5}\)). There are more significant differences in plant heights, location #6, in particular, is quite outstanding.
Contingency tables
Answer to the seedlings question. Load data and check its structure:
Code \(\PageIndex{22}\) (R):
Now, what we need is to examine the table because both variables only look like numbers; in fact, they are categorical. Dotchart (Figure \(\PageIndex{5}\)) is a good way to explore 2-dimensional table:
Code \(\PageIndex{23}\) (R):
To explore possible associations visually, we employ vcd package:
Code \(\PageIndex{24}\) (R):
Both table output and vcd association plot (Figure \(\PageIndex{6}\)) suggest some asymmetry (especially for CID80) which is a sign of possible association. Let us check it numerically, with the chi-squared test:
Code \(\PageIndex{25}\) (R):
Yes, there is an association between fungus (or their absence) and germination. How to know differences between particular samples? Here we need a post hoc test:
Code \(\PageIndex{26}\) (R):
(Exact Fisher test was used because some counts were really small.)
It is now clear that germination patterns form two fungal infections, CID80 and CID105, are significantly different from germination in the control (CID0). Also, significant association was found in the every comparison between three infections; this means that all three germination patterns are statistically different. Finally, one fungus, CID63 produces germination pattern which is not statistically different from the control.
Answer to the question about multiple comparisons of toxicity. Here we will go the slightly different way. Instead of using array, we will extract p-values right from the original data, and will avoid warnings with the exact test:
Code \(\PageIndex{27}\) (R):
(We cannot use pairwise.Table2.test() from the previous answer since our comparisons have different structure. But we used exact test to avoid warnings related with small numbers of counts.)
Now we can adjust p-values:
Code \(\PageIndex{28}\) (R):
Well, now we can say that Caesar salad and tomatoes are statistically supported as culprits. But why table tests always show us two factors? This could be due to the interaction: in simple words, it means that people who took the salad, frequently took tomatoes with it.
Answer to the scurvy-grass question. Check the data file, load and check result:
Code \(\PageIndex{29}\) (R):
(In addition, we converted LOC and IS.CREEPING to factors and provided new level labels.)
Next step is the visual analysis (Figure \(\PageIndex{7}\)):
Code \(\PageIndex{30}\) (R):
Some locations look different. To analyze, we need contingency table:
Code \(\PageIndex{31}\) (R):
Now the test and effect size:
Code \(\PageIndex{32}\) (R):
( Run pairwise.Table2.test(cc.lc) yourself to understand differences in details.)
Yes, there is a large, statistically significant association between locality and life form of scurvy-grass.
Answer to the question about equality of proportions of LOBES character in two birch localities. First, we need to select these two localities (1 and 2) and count proportions there. The shortest way is to use the table() function:
Code \(\PageIndex{33}\) (R):
Spine plot (Figure \(\PageIndex{8}\)) helps to make differences in the table even more apparent:
Code \(\PageIndex{34}\) (R):
(Please also note how to create two colors intermediate between black and dark green.)
The most natural choice is prop.test() which is applicable directly to the table() output:
Code \(\PageIndex{35}\) (R):
Instead of proportion test, we can use Fisher exact:
Code \(\PageIndex{36}\) (R):
... or chi-squared with simulation (note that one cell has only 4 cases), or with default Yates’ correction:
Code \(\PageIndex{37}\) (R):
All in all, yes, proportions of plants with different position of lobes are different between location 1 and 2.
And what about effect size of this association?
Code \(\PageIndex{38}\) (R):
Answer to the question about proportion equality in the whole betula dataset. First, make table:
Code \(\PageIndex{39}\) (R):
There is no apparent asymmetry. Since betula.lw is \(2\times2\) table, we can apply fourfold plot. It shows differences not only as different sizes of sectors, but also allows to check 95% confidence interval with marginal rings (Figure \(\PageIndex{9}\)):
Code \(\PageIndex{40}\) (R):
Also not suggestive... Finally, we need to test the association, if any. Noe that samples are related . This is because LOBES and WINGS were measured on the same plants . Therefore, instead of the chi-squared or proportion test we should run McNemar’s test:
Code \(\PageIndex{41}\) (R):
We conclude that proportions of two character states in each of characters are not statistically different.


10.1.4: Health Care in the U.S.
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Health Care in the U.S.
Healthcare in the United States is provided by separate legal entities, often private facilities with governmental insurance for citizens.
Learning Objectives
Outline the problems with American health care, primarily due to privatization
Key Points
- Healthcare facilities are largely owned and operated by the private sector.
- The United States is alone among developed nations with the notable absence of a universal healthcare system.
- Publicly-funded insurance is provided to the public through programs, such as Medicare, Medicaid, TRICARE, the Children’s Health Insurance Program, and the Veterans Health Administration.
- Active debate about healthcare reform in the United States concerns questions of a right to healthcare, access, fairness, efficiency, cost, choice, value, and quality.
- Many of the uninsured are the working poor or are unemployed. Although some are healthy and choose to go without it, others have been rejected by insurance companies and are considered “uninsurable”.
Key Terms
- the Children’s Health Insurance Program : The Children’s Health Insurance Program (CHIP) is a program administered by the United States Department of Health and Human Services that provides matching funds to states for health insurance to families with children. The program was designed to cover uninsured children in families with incomes that are modest but too high to qualify for Medicaid.
- private insurance : Private insurance refers to health insurance provided by a non-governmental organization, usually a privately owned or publicly traded corporation.
- TRICARE : is a health care program of the United States Department of Defense Military Health System. TRICARE provides civilian health benefits for military personnel, military retirees, and their dependents, including some members of the Reserve Component.
Healthcare in the United States is provided by many separate legal entities. Healthcare facilities are largely owned and operated by the private sector. Health insurance is now primarily provided by the government in the public sector, with 60-65% of healthcare provision and spending coming from programs, such as Medicare, Medicaid, TRICARE, the Children’s Health Insurance Program, and the Veterans Health Administration.
The United States is alone among developed nations with the notable absence of a universal healthcare system. Current estimates put U.S. healthcare spending at approximately 16% of GDP, second highest to East Timor (Timor-Leste) among all United Nations member nations. The U.S. system is primarily one of private insurance, with governmental insurance provided for citizens on the healthcare fringe. Insurance is provided by large-risk bearing corporate entities, which organize healthcare delivery by negotiating pricing and services with provider (physicians and hospitals) organizations. Most Americans under age 65 (59.3%) receive their health insurance coverage through an employer (which includes both private, as well as civilian public-sector employers) under group coverage, although this percentage is declining.
Debates about Healthcare in the United States
Active debate about healthcare reform in the United States concerns questions of a right to health care, access, fairness, efficiency, cost, choice, value, and quality. Some have argued that the system does not deliver equivalent value for the money spent. The United States pays twice as much, yet lags behind other wealthy nations in such measures as infant mortality and life expectancy. Currently, the United States has a higher infant mortality rate than most of the world’s industrialized nations. Around 84.7% of Americans have some form of health insurance; either through their employer or the employer of their spouse or parent (59.3%), purchased individually (8.9%), or provided by government programs (27.8%; there is some overlap in these figures).
Furthermore, the number of persons without health insurance coverage in the United States is one of the primary concerns raised by advocates of healthcare reform. According to the United States Census Bureau, in 2009, there were 50.7 million people in the United States (16.7% of the population) who were without health insurance. Some Americans who do not qualify for government-provided health insurance are not provided health insurance by an employer, and are unable to afford, cannot qualify for, or choose not to purchase private health insurance. Many of the uninsured are the working poor or are unemployed. Although some are healthy and choose to go without it, others have been rejected by insurance companies and are considered “uninsurable.”
Physicians, Nurses, and Patients
The interactions between physicians, nurses, and patients are central to healthcare.
Learning Objectives
Evaluate the importance of positive interactions between physicians, nurses and patients, in terms of satisfaction with health care services
Key Points
- Physicians in the United States include both physicians trained by medical education in the United States, and physicians that are international medical graduates who have progressed through the necessary steps to acquire a medical license to practice in a state.
- Patient’s satisfaction is favored by a good doctor-patient relationship.
- Nursing is a healthcare profession focused on the care of individuals, families, and communities so they may attain, maintain, or recover optimal health and quality of life.
Key Terms
- patient’s satisfaction : Patients’ satisfaction with an encounter with health care service is mainly dependent on the duration and efficiency of care, and how empathetic and communicable the health care providers are.
- doctor-patient relationship : The doctor-patient relationship is central to the practice of healthcare and is essential for the delivery of high-quality health care in the diagnosis and treatment of disease.
- medical education : Medical education is education related to the practice of being a medical practitioner, either the initial training to become a doctor (i.e., medical school and internship), additional training thereafter (e.g., residency and fellowship), or Physician Assistant education.
Physicians
A physician is a health care provider who practices the profession of medicine, which is concerned with promoting, maintaining or restoring human health through the study, diagnosis, and treatment of disease, injury and other physical and mental impairments. They may focus their practice on certain disease categories, types of patients, or methods of treatment; such physicians are known as specialist medical practitioners. They may also assume responsibility for the provision of continuing comprehensive medical care to individuals, families and communities; these physicians are known as general practitioners.
Medical practice properly requires both a detailed knowledge of the academic disciplines (such as anatomy and physiology) underlying diseases and their treatment, and also a decent competence in its applied practice. Physicians in the United States include both physicians trained by medical education in the United States, and physicians that are international medical graduates who have progressed through the necessary steps to acquire a medical license to practice in a state. The U.S. physicians are an important part of the health care in the United States. Currently, the American College of Physicians uses the term physician to describe all medical practitioners holding a professional medical degree.
Nurses
Nursing is a healthcare profession focused on the care of individuals, families, and communities so they may attain, maintain, or recover optimal health and quality of life. There are a number of educational paths to becoming a professional nurse, which vary greatly worldwide, but all involve extensive study of nursing theory and practice, and training in clinical skills. Nursing Science is a field of knowledge based on the contributions of nursing scientists through peer-reviewed scholarly journals and evidenced-based practice. Nurses care for individuals of all ages and cultural backgrounds, who are healthy and ill, in a holistic manner based on the individual’s physical, emotional, psychological, intellectual, social, and spiritual needs. The profession combines physical science, social science, nursing theory, and technology in caring for those individuals.
Patients
A patient is any recipient of health care services. The patient is most often ill or injured and in need of treatment by a physician, advanced practice registered nurse, or other health care provider. Patients’ satisfaction with an encounter with health care service is mainly dependent on the duration and efficiency of care, and how empathetic and communicable the health care providers are. It is favored by a good doctor-patient relationship. Also, patients that are well informed of the necessary procedures in a clinical encounter, and the time it is expected to take, are generally more satisfied even if there is a longer waiting time.
Alternatives to Traditional Health Care
Alternative medicine is any practice claiming to heal “that does not fall within the realm of conventional medicine.”
Learning Objectives
Break down the various types of alternative medicine and how they fit into the health care system
Key Points
- Alternative medicine is frequently grouped with complementary medicine or integrative medicine, which, in general, refers to the same interventions when used in conjunction with mainstream techniques, under the umbrella term complementary and alternative medicine, or CAM.
- Whole medical systems cut across more than one of the other groups; examples include traditional Chinese medicine, naturopathy, homeopathy, and Ayurveda.
- Mind-body medicine takes a holistic approach to health that explores the interconnection between the mind, body, and spirit.
- Biology-based practices use substances found in nature such as herbs, foods, vitamins, and other natural substances.
- Manipulative and body-based practices feature manipulation or movement of body parts, such as is done in chiropractic and osteopathic manipulation.
- Integrative medicine is the combination of the practices and methods of alternative/complementary medicine with conventional medicine.
Key Terms
- mind-body medicine : Mind-body medicine takes a holistic approach to health that explores the interconnection between the mind, body, and spirit.
- manipulative and body-based practices : Manipulative and body-based practices feature manipulation or movement of body parts, such as is done in chiropractic and osteopathic manipulation.
- integrative medicine : Integrative medicine is the combination of the practices and methods of alternative/complementary medicine with conventional medicine. It may include preventive medicine and patient-centered medicine.
Non-Conventional and Conventional Medicine
Alternative medicine methods are diverse in their foundations and methodologies, and they may be based on historical or cultural traditions, rather than on scientific evidence. Methods may incorporate or base themselves on traditional medicine, folk knowledge, spiritual beliefs, or newly conceived approaches to healing. Alternative medicine is frequently grouped with complementary medicine or integrative medicine, which, in general, refers to the same interventions when used in conjunction with mainstream techniques, under the umbrella term complementary and alternative medicine, or CAM.
There is no clear and consistent definition for either alternative or complementary medicine. In Western culture, it is often defined as any healing practice “that does not fall within the realm of conventional medicine,” or “that which has not been shown consistently to be effective. ” There is a debate among medical researchers over whether any therapy may be properly classified as “alternative medicine. ” Some claim that there is only medicine that has been adequately tested and that which has not. They feel that healthcare practices should be classified based solely on scientific evidence.
The U.S. National Center for Complementary and Alternative Medicine (NCCAM) has developed one of the most widely used classification systems for the branches of complementary and alternative medicine. It classifies complementary and alternative therapies into five major groups, which have some overlap. Whole medical systems cut across more than one of the other groups; examples include traditional Chinese medicine, naturopathy, homeopathy, and Ayurveda. Mind-body medicine takes a holistic approach to health that explores the interconnection between the mind, body, and spirit. Biology-based practices use substances found in nature, such as herbs, foods, vitamins, and other natural substances. Manipulative and body-based practices feature manipulation or movement of body parts, such as is done in chiropractic and osteopathic manipulation.
Integrative medicine is the combination of the practices and methods of alternative/complementary medicine with conventional medicine. It may include preventive medicine and patient-centered medicine. It may also include practices not normally referred to as medicine, such as using prayer, meditation, socializing, and recreation as therapies. Its academic proponents sometimes recommend misleading patients by using known placebo treatments in order to achieve a placebo effect.
The Role of Government
Publicly funded health care is a form of healthcare financing designed to meet the cost of healthcare needs from a publicly managed fund.
Learning Objectives
Analyze the role of the government in the provision of health care
Key Points
- Most developed countries, with the exception of the United States, have partially or fully, publicly funded health systems.
- Publicly funded healthcare systems are usually financed in one of two ways: through taxation or via compulsory national health insurance.
- In compulsory insurance models, healthcare is financed from some combination of employees’ salary deductions, employers’ contributions, and possibly additional state funds. Insurance may cover other benefits, as well as health.
- When taxation is the primary means of financing healthcare, all eligible people receive the same level of cover regardless of their financial circumstances or risk factors.
- Most western industrial countries have a system of social insurance based on the principle of social solidarity covers eligible people from bearing the direct burden of most healthcare expenditure, funded by taxation during their working life.
- A range of measures, such as better payment methods, has improved the microeconomic incentives facing healthcare providers.
Key Terms
- social solidarity : Most western industrial countries have a system of social insurance based on the principle of social solidarity covers eligible people from bearing the direct burden of most healthcare expenditure, funded by taxation during their working life.
- compulsory insurance models : In compulsory insurance models, healthcare is financed from some combination of employees’ salary deductions, employers’ contributions, and possibly additional state funds. Insurance may cover other benefits as well as health.
- Publicly funded health care : Publicly funded healthcare is a form of healthcare financing designed to meet the cost of all or most healthcare needs from a publicly managed fund.
Government and Healthcare
Publicly funded health care is a form of healthcare financing designed to meet the cost of all or most healthcare needs from a publicly managed fund. The fund may be a not-for-profit trust, which pays out for health care according to common rules established by the members or by some other democratic form. In some countries, the fund is controlled directly by the government or by an agency of the government for the benefit of the entire population. This distinguishes it from other forms of private medical insurance. In the private model, the rights of access are subject to contractual obligations between an insurer and an insurance company. The latter seeks to make a profit by managing the flow of funds between funders and providers of health care services.
Publicly funded healthcare systems are usually financed in one of two ways: through taxation or via compulsory national health insurance. In compulsory insurance models, healthcare is financed from some combination of employees’ salary deductions, employers’ contributions, and possibly additional state funds. Insurance may cover other benefits as well as health. When taxation is the primary means of financing healthcare, all eligible people receive the same level of cover regardless of their financial circumstances or risk factors.
Most developed countries, with the exception of the United States, have partially or fully publicly funded health systems. Most western industrial countries have a system of social insurance based on the principle of social solidarity covers eligible people from bearing the direct burden of most healthcare expenditure, funded by taxation during their working life. Many OECD countries have implemented reforms to achieve policy goals of ensuring access to healthcare, improving the quality of healthcare and health outcomes, allocating an appropriate level of public sector other resources to healthcare, while at the same time ensuring that services are provided in a cost-efficient and cost-effective manner (microeconomic efficiency). A range of measures, such as better payment methods, has improved the microeconomic incentives facing providers. However, introducing improved incentives through a more competitive environment among providers and insurers has proved difficult.
Contributors and Attributions
CC licensed content, Specific attribution


3.1.18: Yi Sang (1910-1937)
Phantom Illusion Korean Modernism / Postcolonialism Yi Sang (a.k.a. Lee Sang, with the surname being Yi or Lee) is the pen name of Kim Hae-kyeong—a notable avant-garde Korean writer when Korea was a colony of Japan; the Japanese colonial rule of Korea lasted from 1910 to 1945. Even though his biological father was still alive, Yi (born in Seoul in 1910) was adopted at around age two by his eldest uncle who didn't have a son; this was due to the residual tradition of primogeniture. For Yi, however, having been separated from his own family and raised in his uncle's family was a source of life-long trauma. Although initially trained as an architect, Yi later joined Guinhoe, a circle of Korean writers that was formed in 1933. He first began writing poems and later wrote short stories. His work, suggesting the influence of existentialism, Dadaism, and surrealism, is considered modernist in the ways in which it employs language, numbers, and geometric shapes as well as the motif of fragmented and alienated selves. After Yi moved to Tokyo, Japan, in 1936, he was soon arrested by the Japanese police for his "unsound" ideas. Although he was released because of illness, he soon died of tuberculosis in 1937. His best-known work is "Nalgae [The Wings]" (1936), a short story that invites multiple interpretations, such as those from postcolonial, biographical, and psychoanalytical perspectives. He also wrote many experimental poems. "Phantom Illusion" (Korean title: "Hwansigi"), published posthumously in 1938, is a semi-autobiographical short story. It displays many of Yi's signature styles and motifs, including modern alienated men and women, a new modern educated woman, questions about human/romantic relationships, and a sense of nausea. Consider while reading:
- How might the narrator reflect the author's biography or his psychology ?
- How does the style of the story reflect the themes of alienation and isolation?
- In what ways does the short story reflect the historical context of colonial Korea?
- In what specific ways does the short story reflect modernist literary characteristics?
Written by Kyounghye Kwon


2.3: Cell wall, Vacuoles, and Plasmodesmata
Among eukaryotic cells, plant cells are largest. Some of them (for example, cells from green pepper and grapefruit) are well visible with the naked eye. Plant cells do not have well-developed internal cytoskeleton, but cell wall provides an external one. There are two kinds (or, better, two stages of development) of cell walls, the primary and the secondary . The primary cell wall is typically flexible, frequently thin and is made of cellulose, different carbohydrates and proteins. The secondary cell wall contains also lignin and highly hydrophobic suberin . These chemicals completely block the exchange between the cell and the environment which means that the cell with secondary wall will soon die. Dead cells can still be useful to plants in many ways, for example as a defense against herbivores, support and water transport. In fact, more than 90% of wood is dead.
Since every plant cell is surrounded with a cell wall, they need a specific way of communication. This is done through plasmodestata —thin cytoplasmic bridges between neighbor cells. A symplast is the name of continuous cytoplasm inside of cells. An apoplast is cell walls and space outside the cell where communication and considerable metabolic activity take place. Both the symplast and apoplast are important to the transportation of nutrients needed by the cell (Figure \(\PageIndex{1}\)).
If cells are surrounded by a smaller concentration of salts than in the cytoplasm, the water will flow into the cell. This process is called osmosis . In plant cells, most of the water with diluted chemicals is concentrated in vacuole(s). Turgor pressure is the combined pressure of the cell and vacuoles wall that supports the shape of cell (Figure 3.1.4).
You may think of plant tissue as about staked cardboard boxes where every box is made from wet cardboard paper (cell wall) but has the inflated balloon (vacuole) inside, and when the pressure of vacuole decreases (water deficit), plant organs droop. Please see the video http://ashipunov.info/shipunov/school/biol_154/mov/balloon.mp4 to understand this better.
Comparing with animal cells, plant cells have chloroplasts, vacuoles, cell walls, and plasmodesmata but they hardly have any phagocytosis and true cytoskeleton (Figure \(\PageIndex{2}\)). They are easy to explain: animals do not photosynthesize (no chloroplasts), instead, they need to move quickly (no cell walls and plasmodesmata); animals will support the shape of cell from cytoskeleton (no need for vacuole turgor system) and use molecular pumps to counterpart the osmosis.


2.2: Molecular Weight Determination
Solution Molecular Weight of Small Molecules
The cryoscopic method was formally introduced in the 1880’s when François-Marie Raoult published how solutes depressed the freezing points of various solvents such as benzene, water, and formic acid. He concluded from his experimentation “if one molecule of a substance can be dissolved in one-hundred molecules of any given solvent then the solvent temperature is lowered by a specific temperature increment”. Based on Raoult’s research, Ernst Otto Beckmann invented the Beckmann thermometer and the associated freezing - point apparatus, which was a significant improvement in measuring freezing - point depression values for a pure solvent. The simplicity, ease, and accuracy of this apparatus has allowed it to remain as a current standard with few modifications for molecular weight determination of unknown compounds.
The historical significance of Raoult and Beckmann’s research, among many other investigators, has revolutionized a physical chemistry technique that is currently applied to a vast range of disciplines from food science to petroleum fluids. For example, measured cryoscopic molecular weights of crude oil are used to predict the viscosity and surface tension for necessary fluid flow calculations in pipeline.
Freezing Point Depression
Freezing point depression is a colligative property in which the freezing temperature of a pure solvent decreases in proportion to the number of solute molecules dissolved in the solvent. The known mass of the added solute and the freezing point of the pure solvent information permit an accurate calculation of the molecular weight of the solute.
In Equation \ref{1} the freezing point depression of a non-ionic solution is described. Where ∆T f is the change in the initial and final temperature of the pure solvent, K f is the freezing point depression constant for the pure solvent, and m (moles solute/kg solvent) is the molality of the solution.
\[\Delta T _ { f } = K _ { f } m \label{1} \]
For an ionic solution shown in Figure \(\PageIndex{2}\), the dissociation particles must be accounted for with the number of solute particles per formula unit, \(i\) (the van’t Hoff factor ).
\[\Delta T _ { f } = K _ { f } m i\ \label{2} \]
Cryoscopic Procedures
Cryoscopic Apparatus
For cryoscopy, the apparatus to measure freezing point depression of a pure solvent may be representative of the Beckmann apparatus previously shown in Figure \(\PageIndex{3}\). The apparatus consists of a test tube containing the solute dissolved in a pure solvent, stir bar or magnetic wire and closed with a rubber stopper encasing a mercury thermometer. The test tube component is immersed in an ice-water bath in a beaker. An example of the apparatus is shown in Figure \(\PageIndex{4}\). The rubber stopper and stir bar/wire stirrer are not shown in the figure.
Sample and Solvent Selection
The cryoscopic method may be used for a wide range of samples with various degrees of polarity. The solute and solvent selection should follow the premise of like dissolved like or in terms of Raoult’s principle of the dissolution of one molecule of solute in one-hundred molecules of a solvent. The most common solvents such as benzene are generally selected because it is unreactive, volatile, and miscible with many compounds.Table \(\PageIndex{1}\) shows the cryoscopic constants (K f ) for the common solvents used for cryoscopy. A complete list of K f values are available in Knovel Critical Tables.
| Compound | K f |
|---|---|
| Acetic Acid | 3.90 |
| Benzene | 5.12 |
| Camphor | 39.7 |
| Carbon disulfide | 3.8 |
| Carbon tetrachloride | 30 |
| Chloroform | 4.68 |
| Cyclohexane | 20.2 |
| Ethanol | 1.99 |
| Naphthalene | 6.8 |
| Phenol | 7.27 |
| Water | 1.86 |
Cryoscopic Method
The detailed information about the procedure used for cryoscopy is shown below:
Allow the solution to stir continuously to avoid supercooling
- Weigh (15 to 20 grams) of the pure solvent in a test tube and record the measured weight value of the pure solvent.
- Place a stir bar or wire stirrer in the test tube and close with a rubber stopper that has a hole to encase a mercury thermometer.
- Place a mercury thermometer in the rubber stopper hole.
- Immerse the test tube apparatus in an ice-water bath.
- Allow the solvent to stir continuously and equilibrate to a few degrees below the freezing point of the solvent.
- Record the temperature at which the solvent reaches the freezing point, which remains at a constant temperature reading.
- Repeat the freezing point data collection for at least two more measurements without a difference less than 0.5 °C between the measurements.
- Weigh a quantity of the solute for investigation and record the measured value.
- Add the weighed solute to the test tube containing the pure solvent.
- Re - close the test tube with a rubber stopper encasing a mercury thermometer.
- Re-immerse the test tube in an ice water bath and allow the mixture to stir to fully dissolve the solute in the pure solvent.
- Measure the freezing point and record the temperature value.
The observed freezing point of the solution is when the temperature reading remains constant.
Sample calculation to determine molecular weight
Sample Data Set
Table \(\PageIndex{2}\) represents an example of a data set collection for cryoscopy.
| Parameter | Trial 1 | Trial 2 | Trial 3 | Avg. |
|---|---|---|---|---|
| Mass of cyclohexane (g) | 9.05 | 9.00 | 9.04 | 9.03 |
| Mass of unknown solute (g) | 0.4000 | 0.41010 | 0.4050 | 0.4050 |
| Freezing point of cyclohexane (°C) | 6.5°C | 6.5°C | 6.5°C | 6.5°C |
| Freezing point of cyclohexane mixed with unknown solute (°C) | 4.2°C | 4.3°C | 4.2°C | 4.2°C |
Calculation of molecular weight using the freezing point depression equation
Calculate the freezing point (Fpt) depression of the solution (TΔ f ) from Equation \ref{3}
\[T \Delta _{f} =\ (Fpt\ of\ pure\ solvent)\ -\ (Fpt\ of\ solution)\ \label{3} \]
\[T \Delta_{f} = \ 6.5^{\circ}C-4.2^{\circ}C \nonumber \]
\[T \Delta_{f} =\ 2.3^{\circ} \nonumber \]
Calculate the molal concentration, m, of the solution using the freezing point depression and K f (see \label{4})
\[ T \Delta_{f} = K_{f}m\ \label{4} \]
\[m = (2.3^{\circ}C)/(20.2^{\circ}C/molal) \nonumber \]
\[m = 0.113 molal \nonumber \]
\[m = g(solute)/kg(solvent) \nonumber \]
Calculate the M W of the unknown sample.
i = 1 for covalent compounds in \ref{2}
\[M_{W} =\frac{K_{f}(g\ solute)}{\Delta T_{f} (kg solvent)} \nonumber \]
\[M_{W} = \frac{20.2^{\circ}C*kg/moles \times 0.405\ g}{2.3^{\circ}C \times 0.00903\ kg} \nonumber \]
\[M_{W} =\ 393\ g/mol \nonumber \]
Problems
1. Nicotine (Figure \(\PageIndex{5}\) is an extracted pale yellow oil from tobacco leaves that dissolves in water at temperatures less than 60°C. What is the molality of nicotine in an aqueous solution that begins to freeze at -0.445°C? See Table \(\PageIndex{1}\) for K f values.
2. If the solution used in Problem 1 is obtained by dissolving 1.200 g of nicotine in 30.56 g of water, what is the molar mass of nicotine?
3. What would be the freezing point depression when 0.500 molal of Ca(NO 3 ) 2 is dissolved in 60 g of water?
4. Calculate the number of weighted grams of Ca(NO 3 ) 2 added to the 60 g of water to achieve the freezing point depression from Problem 3.
Answers
1.
2.
3.
4.
Molecular Weight of Polymers
Knowledge of the molecular weight of polymers is very important because the physical properties of macromolecules are affected by their molecular weight. For example, shown in Figure \(\PageIndex{6}\) the interrelation between molecular weight and strength for a typical polymer. Dependence of mechanical strength on polymer molecular weight. Adapted from G. Odian, Principles of Polymerization, 4 th edition, Willey-Interscience, New York (2004).
The melting point of polymers are also slightly depend on their molecular weight. Figure \(\PageIndex{7}\) shows relationship between molecular weight and melting temperatures of polyethylene (Figure \(\PageIndex{8}\) ) Most linear polyethylenes have melting temperatures near 140 °C. The approach to the theoretical asymptote, that is a line whose distance to a given curve tends to zero, indicative that a theoretical polyethylene of infinite molecular weight (i.e., M = ∞) would have a melting point of 145 °C.
The molecular weight-melting temperature relationship for the alkane series. Adapted from L. H. Sperling, Introduction to physical polymer science , 4th edition, Wiley-Interscience, New York (2005).
There are several ways to calculate molecular weight of polymers like number average of molecular weight, weight average of molecular weight, Z-average molecular weight, viscosity average molecular weight, and distribution of molecular weight.
Molecular Weight Calculations
Number average of molecular weight (M n )
Number average of molecular weight is measured to determine number of particles. Number average of molecular weight is the total weight of polymer, \ref{5}, divided by the number of polymer molecules, \ref{6} . The number average molecular weight (M n ) is given by \ref{7} , where M i is molecular weight of a molecule of oligomer n, and N i is number of molecules of that molecular weight.
\[ Total\ weight =\ \Sigma _{i=1} ^{∞} M_{i} N_{i} \label{5} \]
\[ Total\ number = \ \Sigma _{i=1} ^{∞} N _{i} \label{6} \]
\[ M_{n} =\frac{ \Sigma _{i=1} ^{∞} M_{i} N_{i}}{\Sigma _{i=1} ^{∞} N _{i}} \label{7} \]
Consider a polymer sample comprising of 5 moles of polymer molecules having molecular weight of 40.000 g/mol and 15 moles of polymer molecules having molecular weight of 30.000 g/mol.
Weight average of molecular weight (M W )
Weight average of molecular weight (M W ) is measured to determine the mass of particles. M W defined as \ref{8} , where M i is molecular weight of oligomer n, and N i is number of molecules of that molecular weight.
\[ M_{W} =\frac{\Sigma _{i=1} ^{∞} N_{i} (M_{i})^{2}}{\Sigma _{i=1} ^{∞} N_{i} M_{i}} \label{8} \]
Example:
Consider the polymer described in the previous problem.
Calculate the M W for a polymer sample comprising of 9 moles of polymer molecules having molecular weight of 30.000 g/mol and 5 moles of polymer molecules having molecular weight of 50.000 g/mol.
Answer:
Z-average molecular weight (M Z )
The Z-average molecular weight (M z ) is measured in some sedimentation equilibrium experiments. M z isn’t common technique for molecular weight of polymers. The molar mass depends on size and mass of the molecules. The ultra centrifugation techniques employ to determine M z . M z emphasizes large particles and it defines the EQ, where M i is molecular weight and N i is number of molecules.
\[ M_{W} =\frac{\Sigma N_{i} M_{i}^{3}}{\Sigma N_{i} M{i}^{2}} \nonumber \]
Consider the polymer described in the previous problem.
Viscosity average molecular weight (M V )
One of the ways to measure the average molecular weight of polymers is viscosity of solution. Viscosity of a polymer depend on concentration and molecular weight of polymers. Viscosity techniques is common since it is experimentally simple. Viscosity average molecular weight defines as \ref{9} , where M i is molecular weight and N i is number of molecules, a is a constant which depend on the polymer-solvent in the viscosity experiments. When a is equal 1, M v is equal to the weight average molecular weight, if it isn’t equal 1 it is between weight average molecular weight and the number average molecular weight.
\[(\frac{\Sigma N_{i} M_{i} ^{1+a}}{\Sigma N_{i} M_{i}})^{\frac{1}{2}} \label{9} \]
Distribution of molecular weight
Molecular weight distribution is one of the important characteristic of polymer because it affects polymer properties. A typical molecular distribution of polymers show in \(\PageIndex{6}\). There are various molecular weights in the range of curve. The distribution of sizes in a polymer sample isn't totally defined by its central tendency. The width and shape of distribution must be known. It is always true that the various range molecular weight is \ref{10} . The equality is occurring when all polymer in the sample have the same molecular weight.
\[ M_{N} \geq M_{V} \geq M_{W} \geq M_{Z} \geq M_{Z+1} \label{10} \]
Molecular weight analysis of polymers
Gel permeation chromatography (GPC)
Gel permeation chromatography is also called size exclusion chromatography. It is widely used method to determine high molecular weight distribution. In this technique, substances separate according to their molecule size. Firstly, large molecules begin to elute then smaller molecules are eluted Figure \(\PageIndex{7}\). The sample is injected into the mobile phase then the mobile phase enters into the columns. Retention time is the length of time that a particular fraction remains in the column. As shown in Figure \(\PageIndex{7}\), while the mobile phase passes through the porous particles, the area between large molecules and small molecules is getting increase. GPC gives a full molecular distribution, but its cost is high.
According to basic theory of GPC, the basic quantity measured in chromatography is the retention volume, \ref{11}, where V 0 is mobile phase volume and V p is the volume of a stationary phase. K is a distribution coefficient related to the size and types of the molecules.
\[V_{e} = V_{0} + V_{p} K \label{11} \]
The essential features of gel permeation chromatography are shown in Figure \(\PageIndex{8}\). Solvent leaves the solvent supply, then solvent is pumped through a filter. The desired amount of flow through the sample column is adjusted by sample control valves and the reference flow is adjusted that the flow through the reference and flow through the sample column reach the detector in common front. The reference column is used to remove any slight impurities in the solvent. In order to determine the amount of sample, a detector is located at the end of the column. Also, detectors may be used to continuously verify the molecular weight of species eluting from the column. The flow of solvent volume is as well monitored to provide a means of characterizing the molecular size of the eluting species.
As an example, consider the block copolymer of ethylene glycol (PEG, Figure \(\PageIndex{9}\) ) and poly(lactide) (PLA, Figure \(\PageIndex{10}\) ), i.e., Figure \(\PageIndex{11}\). In the first step starting with a sample of PEG with a M n of 5,700 g/mol. After polymerization, the molecular weight increased because of the progress of lactide polymerization initiated from end of PEG chain. Varying composition of PEG-PLA shown in Table \(\PageIndex{3}\) can be detected by GPC (Figure \(\PageIndex{12}\) ).
| Polymer | M n of PEG | M w /M n of PEG | M n of PLA | M w /M n of block copolymer | Weight ratio of PLA to PEG |
| PEG-PLA (41-12) | 4100 | 1.05 | 1200 | 1.05 | 0.29 |
| PEG-PLA (60-30) | 6000 | 1.03 | 3000 | 1.08 | 0.50 |
| PEG-PLA (57-54) | 5700 | 1.03 | 5400 | 1.08 | 0.95 |
| PEG-PLA (61-78) | 6100 | 1.03 | 7800 | 1.11 | 1.28 |
Light-scattering
One of the most used methods to characterize the molecular weight is light scattering method. When polarizable particles are placed in the oscillating electric field of a beam of light, the light scattering occurs. Light scattering method depends on the light, when the light is passing through polymer solution, it is measure by loses energy because of absorption, conversion to heat and scattering. The intensity of scattered light relies on the concentration, size and polarizability that is proportionality constant which depends on the molecular weight. Figure \(\PageIndex{13}\) shows light scattering off a particle in solution.
A schematic laser light-scattering is shown in Figure \(\PageIndex{14}\). A major problem of light scattering is to prepare perfectly clear solutions. This problem is usually accomplished by ultra-centrifugation. A solution should be as possible as clear and dust free to determine absolute molecular weight of polymer. The advantages of this method, it doesn’t need calibration to obtain absolute molecular weight and it can give information about shape and M w information. Also, it can be performed rapidly with less amount of sample and absolute determinations of the molecular weight can be measured. The weaknesses of the method is high price and most times it requires difficult clarification of the solutions.
The weight average molecular weight value of scattering polymers in solution related to their light scattering properties that define by \ref{12} , where K is the wave vector, that defined by \ref{13} . C is solution concentration, R(θ) is the reduced Rayleigh ratio, P(θ) the particle scattering function, θ is the scattering angle, A is the osmotic virial coefficients, where n 0 solvent refractive index, λ the light wavelength and N a Avagadro’s number. The particle scattering function is given by \ref{14} , where R z is the radius of gyration.
\[ KC / R( \theta )\ = \ 1/M_{W} ( P( \theta) \ +\ 2A_{2}C\ +\ 3A_{3}C_{2}\ +\ ...) \label{12} \]
\[ K\ =\ 2 \pi ^{2}n_{0}^{2}(dn/dC)^{2}/N_{a} \lambda ^{2} \label{13} \]
\[ 1/(P(\theta )) \ =\ 1+16 \pi ^{2} n_{0} ^{2} ( R _{z} ^{2} )sin ^{2} ( \theta /2) 3 \lambda ^{2} \label{14} \]
Weight average molecular weight of a polymer is found from extrapolation of data in the form of a Zimm plot ( Figure \(\PageIndex{15}\) ). Experiments are performed at several angles and at least at 4 different concentrations. The straight line extrapolations provides M w .
X-ray Scattering
X-rays are a form of electromagnetic wave with wavelengths between 0.001 nm and 0.2 nm. X-ray scattering is particularly used for semicrystalline polymers which includes thermoplastics, thermoplastic elastomers, and liquid crystalline polymers. Two types of X-ray scattering are used for polymer studies:
- Wide-angle X-ray scattering (WAXS) which is used to study orientation of the crystals and the packing of the chains.
- Small-angle X-ray scattering (SAXS) which is used to study the electron density fluctuations that occur over larger distances as a result of structural inhomogeneities.
Schematic representation of X-ray scattering shows in Figure \(\PageIndex{16}\).
At least two SAXS curves are required to determine the molecular weight of a polymer. The SAXS procedure to determine the molecular weight of polymer sample in monomeric or multimeric state solution requires the following conditions.
a. The system should be monodispersed.
b. The solution should be dilute enough to avoid spatial correlation effects.
c. The solution should be isotropic.
d. The polymer should be homogenous.
Osometer
Osmometry is applied to determine number average of molecular weight (M n ). There are two types of osmometer:
- Vapor pressure osmometry (VPO).
- Membrane osmometry.
Vapor pressure osmometry measures vapor pressure indirectly by measuring the change in temperature of a polymer solution on dilution by solvent vapor and is generally useful for polymers with M n below 10,000–40,000 g/mol. When molecular weight is more than that limit, the quantity being measured becomes very small to detect. A typical vapor osmometry shows in the Figure \(\PageIndex{17}\). Vapor pressure is very sensitive because of this reason it is measured indirectly by using thermistors to measure voltage changes caused by changes in temperature.
Membrane osmometry is absolute technique to determine M n (Figure \(\PageIndex{18}\) ). The solvent is separated from the polymer solution with semipermeable membrane that is strongly held between the two chambers. One chamber is sealed by a valve with a transducer attached to a thin stainless steel diaphragm which permits the measurement of pressure in the chamber continuously. Membrane osmometry is useful to determine M n about 20,000-30,000 g/mol and less than 500,000 g/mol. When M n of polymer sample more than 500,000 g/mol, the osmotic pressure of polymer solution becomes very small to measure absolute number average of molecular weight. In this technique, there are problems with membrane leakage and symmetry. The advantages of this technique is that it doesn’t require calibration and it gives an absolute value of M n for polymer samples.
Summary
Properties of polymers depend on their molecular weight. There are different kind of molecular weight and each can be measured by different techniques. The summary of these techniques and molecular weight is shown in the Table \(\PageIndex{4}\).
| Method | Type of Molecular Weight | Range of Application |
| Light Scattering | M W | ∞ |
| Membrane Osmometry | Mn | 10 4 -10 6 |
| Vapor Phase Osmometry | M n | 40,000 |
| X-ray scattering | M w, n, z | 10 2 |
Size Exclusion Chromatography and its Application in Polymer Science
Size exclusion chromatography (SEC) is a useful technique that is specifically applicable to high-molecular-weight species, such as polymer. It is a method to sort molecules according to their sizes in solution. The sample solution is injected into the column, which is filled with rigid, porous, materials, and is carried by the solvent through the packed column. The sizes of molecules are determined by the pore size of the packing particle in the column within which the separation occurs.
For polymeric materials, the molecular weight (M w ) or molecular size plays a key role in determining the mechanical, bulk, and solution properties of materials. It is known that the sizes of polymeric molecules depend on their molecular weights, side chain configurations, molecular interaction, and so on. For example, the exclusion volume of polymers with rigid side group is larger than those with soft long side chains. Therefore, in order to determine the molecular weight and molecular weight distribution of a polymer, one of the most widely applied methods is gel-permeation chromatography.
Gel permeation chromatography (GPC) is a term used for when the separation technique size exclusion chromatography (SEC) is applied to polymers.
The primary purpose and use of the SEC technique is to provide molecular weight distribution information about a particular polymeric material. Typically, in about 30 minutes using standard SEC, the complete molecular weight distribution of a polymer as well as all the statistical information of the distribution can be determined. Thus, SEC has been considered as a technique essentially supplanting classical molecular weight techniques. To apply this powerful technique, there is some basic work that needs to be done before its use. The selection of an appropriate solvent and the column, as well as the experimental conditions, are important for proper separation of a sample. Also, it is necessary to have calibration curves in order to determine the relative molecular weight from a given retention volume/time.
It is well known that both the majority of natural and synthetic polymers are polydispersed with respect to molar mass. For synthetic polymers, the more mono-dispersed a polymer can be made, the better the understanding of its inherent properties will be obtained.
Polymer Properties
A polymer is a large molecule (macromolecule) composed of repeating structural units typically connected by covalent chemical bonds. Polymers are common materials that are widely used in our lives. One of the most important features which distinguishes most synthetic polymers from simple molecular compounds is the inability to assign an exact molar mass to a polymer. This is a consequence of the fact that during the polymerization reaction the length of the chain formed is determined by several different events, each of which have different reaction rates. Hence, the product is a mixture of chains of different length due to the random nature of growth. In addition, some polymers are also branched (rather than linear) as a consequence of alternative reaction steps. The molecular weight (M w ) and molecular weight distribution influences many of the properties of polymers:
- Processability - the suitability of the polymer to physical processing.
- Glass-transition temperature - refers to the transformation of a glass-forming liquid into a glass.
- Solution viscosity - measure of the resistance of a fluid which is being deformed by either shear stress or tensile stress.
- Hardness - a measure of how resistant a polymer is to various kinds of permanent shape change when a force is applied.
- Melt viscosity - the rate of extrusion of thermoplastics through an orifice at a prescribed temperature and load.
- Tear strength - a measure of the polymers resistance to tearing.
- Tensile strength - as indicated by the maxima of a stress-strain curve and, in general, is the point when necking occurs upon stretching a sample.
- Stress-crack resistance - the formation of cracks in a polymer caused by relatively low tensile stress and environmental conditions.
- Brittleness - the liability of a polymer to fracture when subjected to stress.
- Impact resistance - the relative susceptibility of polymers to fracture under stresses applied at high speeds.
- Flex life - the number of cycles required to produce a specified failure in a specimen flexed in a prescribed manner.
- Stress relaxation - describes how polymers relieve stress under constant strain.
- Toughness - the resistance to fracture of a polymer when stressed.
- Creep strain - the tendency of a polymer to slowly move or deform permanently under the influence of stresses.
- Drawability - The ability of fiber-forming polymers to undergo several hundred percent permanent deformation, under load, at ambient or elevated temperatures.
- Compression - the result of the subjection of a polymer to compressive stress.
- Fatigue - the failure by repeated stress.
- Tackiness - the property of a polymer being adhesive or gummy to the touch.
- Wear - the erosion of material from the polymer by the action of another surface.
- Gas permeability - the permeability of gas through the polymer.
Consequently, it is important to understand how to determine the molecular weight and molecular weight distribution.
Molecular Weight
Simpler pure compounds contain the same molecular composition for the same species. For example, the molecular weight of any sample of styrene will be the same (104.16 g/mol). In contrast, most polymers are not composed of identical molecules. The molecular weight of a polymer is determined by the chemical structure of the monomer units, the lengths of the chains and the extent to which the chains are interconnected to form branched molecules. Because virtually all polymers are mixtures of many large molecules, we have to resort to averages to describe polymer molecular weight.
The polymers produced in polymerization reactions have lengths which are distributed according to a probability function which is governed by the polymerization reaction. To define a particular polymer weight average, the average molecular weight M avg is defined by \ref{15} Where N i is the number of molecules with molecular weight M i .
\[ M_{avg} \ =\ \frac{\Sigma N_{i} M_{i}^{a}}{\Sigma N_{i} M_{i} ^{a-1}} \label{15} \]
There are several possible ways of reporting polymer molecular weight. Three commonly used molecular weight descriptions are: the number average (M n ), weight average (M w ), and z-average molecular weight (M z ). All of three are applicable to different constant a in \ref{16} and are shown in Figure \(\PageIndex{19}\).
When a = 1, the number average molecular weight, \ref{16} .
\[ M_{n,\ avg} \ =\ \frac{\Sigma N_{i}M_{i}}{\Sigma N_{i}}\ =\ \frac{w}{N} \label{16} \]
When a = 2, the number average molecular weight, \ref{17} .
\[ M_{n,\ avg} \ =\ \frac{\Sigma N_{i}M_{i}^{2}}{\Sigma N_{i}M_{i}}\ =\ \frac{\Sigma N_{i}M_{i}}{w} \label{17} \]
When a = 2, the number average molecular weight, \ref{18} .
\[ M_{n,\ avg} \ =\ \frac{\Sigma N_{i}M_{i}^{3}}{\Sigma N_{i}M_{i}^{2}}\ =\ \frac{\Sigma N_{i}M_{i}^{2}}{\Sigma N_{i}M_{i}} \label{18} \]
Bulk properties weight average molecular weight, M w is the most useful one, because it fairly accounts for the contributions of different sized chains to the overall behavior of the polymer, and correlates best with most of the physical properties of interest.
There are various methods published to detect these three different primary average molecular weights respectively. For instance, a colligative method, such as osmotic pressure, effectively calculates the number of molecules present and provides a number average molecular weight regardless of their shape or size of polymers. The classical van’t Hoff equation for the osmotic pressure of an ideal, dilute solution is shown in \ref{19} .
\[ \frac{\pi }{c}\ =\ \frac{RT}{M_{n}} \label{19} \]
The weight average molecular weight of a polymer in solution can be determined by either measuring the intensity of light scattered by the solution or studying the sedimentation of the solute in an ultracentrifuge. From light scattering method which is depending on the size rather than the number of molecules, weight average molecular weight is obtained. This work requires concentration fluctuations which are the main source of the light scattered by a polymer solution. The intensity of the light scattering of polymer solution is often expressed by its turbidity τ which is given in Rayleigh’s law in \ref{20} . Where i θ is scattered intensity at only one angle θ, r is the distance from the scattering particle to the detection point, and I 0 is the incident intensity.
\[ \tau\ =\ \frac{16\pi i_{\Theta} r^{2}}{3I_{0}(1+cos^{2}\Theta )} \label{20} \]
The intensity scattered by molecules (N i ) of molecular weight (M i ) is proportional to N i M i 2 . Thus, the total light scattered by all molecules is described in \ref{21} , where c is the total weight of the sample ∑N i M i .
\[ \frac{\pi}{c} ~ \frac{\Sigma N_{i}M_{i}^{2}}{\Sigma N_{i}M_{i}}\ =\ M_{W,\ avg} \label{21} \]
Poly-disperse index (PDI)
The polydispersity index (PDI), is a measure of the distribution of molecular mass in a given polymer sample. As shown in Figure \(\PageIndex{19}\), it is the result of the definitions that M w ≥ M n . The equality of M w and M n would correspond with a perfectly uniform (monodisperse) sample. The ratio of these average molecular weights is often used as a guide to the dispersity of the chain lengths in a polymer sample. The greater M w / M n is, the greater the dispersity is.
The properties of a polymer sample are strongly dependent on the way in which the weights of the individual molecules are distributed about the average. The ratio M w /M n gives sufficient information to characterize the distribution when the mathematical form of the distribution curve is known.
Generally, the narrow molecular weight distribution materials are the models for much of work aimed at understanding the materials’ behaviors. For example, polystyrene and its block copolymer polystyrene-b-polyisoprene have quite narrow distribution. As a result, narrow molecular weight distribution materials are a necessary requirement when people study their behavior, such as self-assembly behavior for block copolymer. Nonetheless, there are still lots of questions for scientists to explore the influence of polydispersity. For example, research on self-assembly which is one of the interesting fields in polymer science shows that we cannot throw polydispersity away.
Setup of SEC Equipment
In SEC, sample components migrate through the column at different velocities and elute separately from the column at different times. In liquid chromatography and gas chromatography, as a solute moves along with the carrier fluid, it is at times held back either by surface of the column packing, by stationary phase, or by both. Unlike gas chromatography (GC) and liquid chromatography (LC), molecular size, or more precisely, molecular hydrodynamic volume governs the separation process of SEC, not varied by the type of mobile phase. The smallest molecules are able to penetrate deeply into pores whereas the largest molecules are excluded by the smaller pore sizes. Figure \(\PageIndex{20}\) shows the regular instrumental setup of SEC.
The properties of mobile phase are still important in that it is supposed to be strong affinity to stationary phase and be a good solubility to samples. The purpose of well soluble of sample is to make the polymer be perfect coil suspending in solution. Thus, as a mixture of solutes of different size passes through a column packed with porous particles. As shown in Figure \(\PageIndex{21}\), it clearly depicts the general idea for size separation by SEC. the main setup of SEC emphasizes three concepts: stationary phase (column), mobile phase (solvent) and sample preparation.
Solvent Selection
Solvent selection for SEC involves a number if considerations, such as convenience, sample type, column packing, operating variables, safety, and purity.
For samples concern, the solvents used for mobile phase of SEC are limited to those follows following criteria:
- The solvent must dissolve the sample completely.
- The solvent has different properties with solute in the eluent: typically with solvent refractive index (RI) different from the sample RI by ± 0.05 unit of more, or more than 10% of incident energy for UV detector.
- The solvent must not degrade the sample during use. Otherwise, the viscosity of eluent will gradually increase over times.
- The solvent is not corrosive to any components of the equipment.
Therefore, several solvents are qualified to be solvents such as THF, chlorinated hydrocarbons (chloroform, methylene chloride, dichloroethane, etc), aromatic hydrocarbons (benzene, toluene , trichlorobenzene, etc).
Normally, high purity of solvent (HPLC-grade) is recommended. The reasons are to avoid suspended particulates that may abrade the solvent pumping system or cause plugging of small-particle columns, to avoid impurities that may generate baseline noise, and to avoid impurities that are concentrated due to evaporation of solvent.
Column Selection
Column selection of SEC depends mainly on the desired molecular weight range of separation and the nature of the solvents and samples. Solute molecules should be separated solely by the size of gels without interaction of packing materials. Better column efficiencies and separations can be obtained with small particle packing in columns and high diffusion rates for sample solutes. Furthermore, optimal performance of an SEC packing materials involves high resolution and low column backpressure. Compatible solvent and column must be chosen because, for example, organic solvent is used to swell the organic column packing and used to dissolve and separate the samples.
It is convenient that columns are now usually available from manufacturers regarding the various types of samples. They provide the information such as maximum tolerant flow rates, backpressure tolerances, recommended sample concentration, and injection volumes, etc. Nonetheless, users have to notice a few things upon using columns:
- Vibration and extreme temperatures should be avoided because these will post irreversible damage on columns.
- For aqueous mobile phase, it is unwise to allow the extreme pH solutions staying in the columns for a long period of time.
- The columns should be stored with some neat organic mobile phase, or aqueous mobile phase with pH range 2 - 8 to prevent degradation of packing when not in use.
Sample Preparation
The sample solutions are supposed to be prepared in dilute concentration (less than 2 mg/mL) for several concerns. For polymer samples, samples must be dissolved in the solvent same as used for mobile phase except some special cases. A good solvent can dissolve a sample in any proportion in a range of temperatures. It is a slow process for dissolution because the rate determining step is solvent diffusion into polymers to produce swollen gels. Then, gradual disintegration of gels makes sample-solvent mixture truly become solution. Agitation and warming the mixtures are useful methods to speed up sample preparation.
It is recommended to filter the sample solutions before injecting into columns or storing in sample vials in order to get rid of clogging and excessively high pressure problems. If unfortunately the excessively high pressure or clogging occur due to higher concentration of sample solution, raising the column temperature will reduce the viscosity of the mobile phase, and may be helpful to redissolve the precipitated or adsorbed solutes in the column. Back flushing of the columns should only be used as the last resort.
Analysis of SEC Data
The size exclusion separation mechanism is based on the effective hydrodynamic volume of the molecule, not the molecular weight, and therefore the system must be calibrated using standards of known molecular weight and homogeneous chemical composition. Then, the curve of sample is used to compare with calibration curve and obtain information relative to standards. The further step is required to covert relative molecular weight into absolute molecular weight of a polymer.
Calibration
The purpose of calibration in SEC is to define the relationship between molecular weight and retention volume/time in the chosen permeation range of column set and to calculate the relative molecular weight to standard molecules. There are several calibration methods are commonly employed in modern SEC: direct standard calibration, poly-disperse standard calibration, universal calibration.
The most commonly used calibration method is direct standard calibration. In the direct standard calibration method, narrowly distributed standards of the same polymer being analyzed are used. Normally, narrow-molecular weight standards commercially available are polystyrene (PS). The molecular weight of standards are measured originally by membrane osmometry for number-average molecular weight, and by light scattering for weight-average molecular weight as described above. The retention volume at the peak maximum of each standard is equated with its stated molecular weight.
Relative M w versus absolute M w
The molecular weight and molecular weight distribution can be determined from the calibration curves as described above. But as the relationship between molecular weight and size depends on the type of polymer, the calibration curve depends on the polymer used, with the result that true molecular weight can only be obtained when the sample is the same type as calibration standards. As Figure \(\PageIndex{23}\) depicted, large deviations from the true molecular weight occur in the instance of branched samples because the molecular density of these is higher than in the linear chains.
Light-scattering detector is now often used to overcome the limitations of conventional SEC. These signals depend only on concentration, not on molecular weight or polymer size. For instance, for LS detector, \ref{22} applies:
\[LS\ Signal\ =\ K_{LS} \cdot (dn/dc)^{2}\cdot M_{W} \cdot c \label{22} \]
Where K LS is an apparatus-specific sensitivity constant, dn/dc is the refractive index increment and c is concentration. Therefore, accurate molecular weight can be determined while the concentration of the sample is known without calibration curve.
A Practical Example
The syntheses of poly(3-hexylthiophene) are well developed during last decade. It is an attractive polymer due to its potential as electronic materials. Due to its excellent charge transport performances and high solubility, several studies discuss its further improvement such as making block copolymer even triblock copolymer. The details are not discussed here. However, the importance of molecular weight and molecular weight distribution is still critical.
As shown in Figure \(\PageIndex{24}\), they studied the mechanism of chain-growth polymerization and successfully produced low polydispersity P3HT. The figure also demonstrates that the molecule with larger molecular size/ or weight elutes out of the column earlier than those which has smaller molecular weight.
The real molecular weight of P3HT is smaller than the molecular weight relative to polystyrene. In this case, the backbone of P3HT is harder compared with polystyrenes’ backbone because of the position of aromatic groups. It results in less flexibility. We can briefly judge the authentic molecular weight of the synthetic polymer according to its molecular structure.


2.3.2: Patient Bill of Rights
(Adapted from the American Hospital Association, 1992).
Remember, the patient is the most important member of the health care team. They have rights that all members of the health care team must respect and uphold.
- The patient has the right to considerate and respectful care.
- The patient has the right to obtain understandable information about their diagnosis, treatment, and prognosis. They have a right to be informed about the risks and benefits of all services and treatments received. Patients also have a right to know the identity (name, license, and health care provider role) of all people involved in their care (doctors, nurses, home health aides/personal care aides).
- The patient has a right to make decisions about the plan of care before receiving treatment. The patient also has the right to refuse any treatment, and to be informed about the medical consequences of refusing treatment. If the patient refuses a specific treatment or care, they still have the right to receive other care services, or to be provided with referrals to services outside of the agency or organization. The patient has the right to participate in the planning of their healthcare and to be informed of any changes in the plan of care prior to the change being made.
- The patient has the right to have an advanced directive or to designate a health care proxy to make decisions for them if they are unable to do so themselves.
- The patient has a right to privacy.
- The patient has a right to expect that all communications and records pertaining to their health and health care will be kept confidential by their healthcare providers, except in cases of suspected abuse and public health hazards when reporting is permitted or required by law.
- The patient has a right to review their health care records and to have the information explained, except when restricted by law.
- The patient has a right to expect that within its capabilities an agency will make reasonable responses to a patient’s requests for medically indicated care and services. If an organization is unable to accommodate such requests, the patient has the right to transfer to another organization which may be able to provide such requests.
- The patient has the right to ask and be informed of any business or financial relationships that exist within the organization which may influence their care.
- The patient has the right to consent or decline participation in research studies, and to be provided with a full explanation about participation in such studies.
- The patient has the right to receive continuity of care and to be informed when such care cannot be provided.
- The patient has the right to be informed of policies and procedures that relate to their care. The patient has the right to be informed of the method they should use to resolve any discrepancies, conflicts, or grievances they may have. They have the right to know the procedure for making complaints if they feel they have not been given the care they deserve. The patient has the right to make complaints without fear of discrimination or negative repercussions for doing so. The patient also has the right to be informed of any charges for services and available payment methods and insurances accepted. This includes being made aware of services not covered by Medicare and Medicaid, and what charges they may be liable for.


32.5: Chapter Summary
This chapter discussed the differences between overweight and obesity and their pathophysiology. Clinical manifestations were also explained. A variety of pharmacological methods of weight management were discussed, including anorexiants, lipase inhibitors, and other drugs. The chapter also described various supplements and herbal remedies for weight loss.
Despite the availability of OTC and prescribed weight-loss drugs and supplements, the chapter discussed how the best strategy for weight loss is lifestyle modifications, such as exercise and caloric restriction, as a proven effective treatment in obesity. However, lifestyle modifications do not always promote optimal weight loss. Often supplements and/or medications are required. Once a healthy weight is achieved, clients must continue to practice healthy habits to maintain weight management.


4.6: Managing Long Documents in Google Docs
By the end of this section, you will be able to:
- Utilize Paint format to apply formatting in a long document
- Insert and modify a table of contents
- Use linked bookmarks and hyperlinks
Google Docs has tools that can help users construct and navigate through long documents. The market trends report will have multiple sections containing information that is best presented in varied ways. There are three tools in Docs that this section will cover that are especially helpful: Paint format, Table of contents, and Hyperlinks.
Paint Format
The Paint format command in Docs is the equivalent of the Format Painter in Microsoft Word. You use it in the same way: selecting a format you want to copy from the original source, choosing the Paint format icon from the action bar (it looks like a small paint roller), and using the cursor to apply it on the target text.
In Docs, you can even copy and apply the same original source format multiple times. Once you make your selection, you are able to apply it many times in different areas of the document. To do this, you need to double-click the Paint format icon, after which it will stay locked, as shown in Figure 4.101. (Word’s Format Painter behaves the same way.) After you are done formatting all the text you need, you can unlock it by clicking once on the icon again; then, the mouse pointer will return to normal.
It is not advised to use the Paint format tool to apply a style to an entire document with multiple different features, such as tables and multilevel lists. The Paint format tool may not apply the style in exactly the way you want with these kinds of special formatting. Additionally, note that in Docs, you can use the Paint format tool with one open document only.
Table of Contents
As in Word, a table of contents in Docs requires that you have your headings properly styled, your section breaks in place, and page numbers.
Headings for Tables of Contents
What Word calls Styles is called Paragraph Styles in Docs. We previously touched on the importance of these styles in Docs in the Creating and Working in Documents chapter when we discussed the use of the View menu to activate or hide the document outline. Moreover, we carefully went over headings and their significance for the document when we described the font formatting, and how it can be accelerated with the use of styles. Here, we will discuss how the use of styles helps you manage long documents by helping to structure your table of contents.
Docs will automatically read your styles and headings and autogenerate the table of contents from that. For instance, you may have an H1 (Heading 1) for a chapter title, and H2 and H3 headings for subsections. You can see Google’s default heading styles in Figure 4.102. We can add the table of contents to our WorldCorp market trends report because we have already formatted the various sections of the report with headings.
All of these styles can be modified using the Options menu. You can modify any of the heading styles, or even the Normal style. If you like these styles and will use them frequently, select Save as my default styles. These will be the default styles for every new document you create.
Changing your styles can be useful when working with long documents. Say that you want to change the font type of all the document’s Normal style text. The first thing to do is to change a particular paragraph by selecting it, and then changing its font type to your desired font. While the text is still selected, go to Styles and hover over Normal text. Then, click Update ‘Normal text’ to match, as Figure 4.103 shows. That will change all the document’s Normal paragraphs to have the new font type. Labeling the text Normal every time gives the user the power to automatize the font formatting.
Once you have labeled your headings and styled your document properly, the headings will appear in the document outline. This is a good place to check that your headings are correct before you create a table of contents. You can preview all the headings and should be able to quickly catch if something is styled incorrectly. If you see a mistake, simply select that heading and Docs will take you there. From there, you can select the incorrectly styled text and make it the correct heading style.
Inserting Section Breaks for Tables of Contents
We stressed the importance of section breaks in the chapter Creating and Working in Documents. Section breaks are necessary when creating a table of contents if you want to have different page numbering in different sections. If your page numbering is continuous throughout the entire document, you would not need section breaks to create a table of contents. You only need the section titles to be formatted as a Heading Style . However, if you want the page numbering to restart with each section of the document, you would need to also include a break at the end of each section.
Once you have applied correct formatting to all of your headings and placed your section breaks, inserting your table of contents is easy. Go to the Insert menu and choose Table of contents . There are two types: one with page numbers and one with blue links and no page numbers. The option with page numbers is a good choice for either print or digital publishing. If you plan on printing out your report, you want your readers to be able to use the table of contents effectively and be able to flip to the correct page. Digital readers can still click on the page number and be taken there automatically. The option with only blue links and no page numbers is a good choice if your document will only be used by digital readers.
Let’s now add the table of contents to the WorldCorp report in Docs. First, go to Insert, then go to the bottom of the menu and choose Table of contents (see Figure 4.104). Select a type, and the table of contents will be inserted at the location of your cursor (Figure 4.105).
Normally, business report writers add the table of contents when they are finished with the report. But in Docs, it is easy to add the table of contents at the beginning and update it as you go along. For example, each collaborator might add new headings to the document as they write or revise, which you would want to see reflected in the table of contents. Once their work is complete, you would simply select the refresh button (“Update table of contents”) or right-click to “Update table of contents,” to update the table of contents (Figure 4.106). This will tell Docs to recheck the document, and reread for new, modified, or deleted headings. The table of contents will automatically update with the new document structure.
If you want to change the table of content’s appearance, just select it, and then use the action bar to apply formatting changes as you would to normal text. You can change the font type, change the size of the font, or choose to bold or italicize the font.
Hyperlinks, Bookmarks, and Links to Other Files
Hyperlinks can be input in various ways in Docs. As in Word, these help with citations and navigation in long documents. First, you need to select the text you want to make into a link, then you can choose to use the menus or the right-click context menu to create the link. You can see both methods in Figure 4.107. They both lead to a dialog box that asks for the web address, which you input, and then click Apply.
If you want to add a link to another part of the same document, you can create a link to a specific heading. Use the Headings and bookmarks option that comes up in the Link dialog box. Select the text that will be the link, then right-click to Link, and you will see all the titles that the user styled to be headings, as Figure 4.108 displays. You will choose the part of the document that you want to link to.
You may also link to a certain part of the document that is not a heading. This requires first creating a bookmark. For example, suppose you want to reference a table or figure in your document. You must first add a bookmark next to the table or figure, then you can link to that bookmark. To add the bookmark, place your cursor next to the table or figure you want to link to, then go to the Insert menu and click Bookmark (Figure 4.109). Then, when you want to link to that bookmark later on in the document, you do the same steps you did for creating a link to a heading: Select the text you want to turn into a link and right-click to Link. The dialog box will show the Headings and the bookmarks option. You can choose the pertaining bookmark, as Figure 4.110 shows. (To undo the bookmark you just made, click on it to select it, and then click Remove.)
For linking to another document, you need to already have the document in Google Drive. Go to Drive’s file options to make a public shareable link. The linked document will not be accessible to someone unless they have access to the document, meaning that the document has been shared with them. Copy this link address. Next, open the document where the link will be placed, and select the text to be linked, then right-click to Link. In the dialog box, paste the public shareable address of the other document, and click Apply. Or, skip the pasting method, and select one that has been shared already in the link dialog box, as in Figure 4.111.