Blood quantum laws

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Blood_quantum_laws 

 

Members of the Muscogee (Creek) Nation in Oklahoma around 1877, including some with partial European and African ancestry

Blood quantum laws or Indian blood laws are laws in the United States that define Native American status by fractions of Native American ancestry. These laws were enacted by the federal government and state governments as a way to establish legally defined racial population groups. By contrast, many tribes do not include blood quantum as part of their own enrollment criteria.

A person's blood quantum is defined as the fraction of their ancestors, out of their total ancestors, who are documented as full-blood Native Americans. For instance, a person who has one parent who is a full-blood Native American and one who has no Native ancestry has a blood quantum of 1/2. Nations that use blood quantum often do so in combination with other criteria. For instance, the Omaha Tribe of Nebraska requires a blood quantum of 1/4 Native American and descent from a registered ancestor for enrollment, while the Cherokee Nation of Oklahoma has no BQ requirement, and only requires lineal descent from a documented Cherokee ancestor listed on the Dawes Rolls, a specific census roll that still upheld racist stereotypes and blood quantum theories, and that supersedes other older rolls. Other Nations have a tiered system, with the Choctaw Nation of Oklahoma using lineal descent for general enrollment, but requiring a BQ of "at least one-fourth" of anyone who would run for tribal council.

The Indian Removal Act and the Trail of Tears led to a major enumeration of Native Americans, and many controversies and misunderstandings about blood quantum that persist to this day. As they were being forcibly driven out of their ancestral homelands and subjected to genocide, many Natives understandably feared and distrusted the government and tried to avoid being enumerated. But the only way to do this was to completely flee the Indian community, during a time of persecution and war. Indians who tried to refuse, if they were not already in a prison camp, had warrants issued for their arrests; they were forcibly rounded up and documented against their will. It is a modern-day misconception that this enumeration was the equivalent of contemporary tribal "enrollment" and in any way optional.

The concept of blood quantum was not widely applied by the United States government until the Indian Reorganization Act of 1934. At that time, the federal government required persons to have a certain blood quantum to be recognized as Native American and be eligible for financial and other benefits under treaties or sales of land.

Native American nations have continued to assert sovereignty and treaty rights, including their own criteria for tribal membership, which vary among them. In the early 21st century, some nations, such as the Wampanoag, tightened their membership rules and excluded persons who had previously been considered members. Challenges to such policies have been pursued by those excluded.

Origin of blood quantum law

In 1705 the Colony of Virginia adopted the "Indian Blood law" that limited civil rights of Native Americans and persons of one-half or more Native American ancestry. This also had the effect of regulating who would be classified as Native American. In the 19th and 20th centuries, the US government believed tribal members had to be defined, for the purposes of federal benefits or annuities paid under treaties resulting from land cessions. According to the Pocahontas Clause of the Racial Integrity Act of 1924, a white person in Virginia could have a maximum blood quantum of one-sixteenth Indian ancestry without losing his or her legal status as white.

Native American tribes did not formally use blood quantum law until the government introduced the Indian Reorganization Act of 1934, instead determining tribal status on the basis of kinship, lineage and family ties. Some tribes, such as the Navajo Nation, did not adopt the type of written constitution suggested in that law until the 1950s. Given intermarriage among tribes, particularly those that are closely related and have settled near each other, critics object to the federal requirement that individuals identify as belonging to only one tribe when defining blood quantum. They believe this reduces an individual's valid membership in more than one tribe, as well as costing some persons their qualification as Native American because of having ancestry from more than one tribe but not 1/4 or more from one tribe. Overall, the numbers of registered members of many Native American tribes have been reduced because of tribal laws that define and limit the definition of acceptable blood quantum.

The National Research Council noted in 1996, "The U.S. census decennial enumerations indicate a Native American population growth for the United States that has been nearly continuous since 1900 (except for an influenza epidemic in 1918 that caused serious losses), to 1.42 million by 1980 and to over 1.9 million by 1990." In the 2000 census, there were 2.5 million American Indians. Since 1960, people may self-identify their ancestry on the US Census. Indian activism and a rising interest in Native American history appear to have resulted in more individuals identifying as having Native American ancestry on the census.

Prior to colonization, individual tribes had established their own requirements for membership, including the practice of banishment for those who had committed unforgivable crimes. Some traditional communities still hold to these precontact standards. Tribes that follow lineal descent may require a Native American ancestor who is listed on a prior tribal rations-issue roll, such as the Dawes Rolls for the Five Civilized Tribes in Oklahoma, or a late 19th-century census. In some cases they may also require a certain percentage of Native American ancestry, and demonstrated residence with a tribe or commitment to the community. Few tribes allow members to claim ancestry in more than one tribe. The Little Traverse Bay Bands of Odawa Indians accept persons of 1/4 Native American ancestry, plus documented descent from an ancestor listed in specific records. In part, this recognizes that the Odawa people historically had a territory on both sides of what is now the border between the US and Canada.

Each federally recognized tribe has established its own criteria for membership. Given the new revenues that many tribes are realizing from gambling casinos and other economic development, or from settlement of 19th-century land claims, some have established more restrictive rules to limit membership. Between 1904 and 1919, tribal members of mixed African and Native American ancestry were disenrolled from the Chitimacha tribe of Louisiana, and their descendants have since then been denied tribal membership.

In 2007 the Cherokee Nation voted in the majority to exclude as members those Cherokee Freedmen who had no documented ancestors on the Cherokee-by-blood list of the Dawes Rolls. However, the Cherokee Supreme Court ruled in 2005 that they were legitimate members of the tribe at that time. After the Civil War, the US required the Cherokee and other Native American tribes that had supported the Confederacy to make new treaties. They also required them to emancipate their slaves, and to give full tribal membership to those freedmen who wanted to stay in tribal territory. The Cherokee Freedmen often had intermarried and some had Cherokee ancestry at the time of the Dawes Rolls, qualifying as Cherokee by blood, but registrars typically classified them as Freedmen.

Similarly, in 2000, the Seminole Nation of Oklahoma attempted to exclude two bands of Seminole Freedmen from membership to avoid including them in settlement of land claims in Florida, where Seminole Freedmen had also owned land taken by the US government.

Since 1942, the Seminole have at times tried to exclude Black Seminoles from the tribe. The freedmen were listed separately on the Dawes Rolls and suffered segregation in Oklahoma. More recently, the Seminole refused to share with them the revenues of 20th-century US government settlements of land claims. The Center for Constitutional Rights has filed an amicus brief, taking up the legal case of the Black Seminoles and criticizing some officials of the Bureau of Indian Affairs for collaborating in this discrimination by supporting tribal autonomy in lawsuits. By treaty, after the American Civil War, the Seminole were required to emancipate slaves and provide Black Seminoles with all the rights of full-blood Indian members.

American Indian tribes located on reservations tend to have higher blood quantum requirements for membership than those located off reservation....[reference to table] [O]ver 85 percent of tribes requiring more than a one-quarter blood quantum for membership are reservation based, as compared with less than 64 percent of those having no minimum requirement. Tribes on reservations have seemingly been able to maintain exclusive membership by setting higher blood quanta, since the reservation location has generally served to isolate the tribe from non-Indians and intermarriage with them.

Issues related to blood quantum laws

Many Native Americans have become used to the idea of "blood quantum". The blood quantum laws have caused problems in Native American families whose members were inaccurately recorded as having differing full or partial descent from particular tribes.

At certain times, some state governments classified persons with African American and Native American admixture solely as African American, largely because of racial discrimination related to slavery history and the concept of the one drop rule. This was prevalent in the South after Reconstruction, when white-dominated legislatures imposed legal segregation, which classified the entire population only as white or colored (Native Americans, some of whom were of mixed race, were included in the latter designation). It related to the racial caste system of slavery before the American Civil War.

Some critics argue that blood quantum laws helped create racism among tribal members. The historian Tony Seybert contends that was why some members of the so-called Five Civilized tribes were slaveholders. The majority of slave owners were of mixed-European ancestry. Some believed they were of higher status than full-blood Indians and people of African ancestry. Other historians contend that the Cherokee and other tribes held slaves because it was in their economic interest and part of the general southeastern culture. Cherokee and other tribes had also traditionally taken captives in warfare to use as slaves, though their institution differed from what developed in the southern colonies.

Issues with DNA ancestry testing

No federally recognized tribe enrolls members solely based on DNA testing, as it generally cannot distinguish among tribes. Some tribes may require DNA testing only to document that a child is related to particular parents. Many researchers have published articles that caution that genetic ancestry DNA testing has limitations and should not be depended on by individuals to answer all their questions about heritage.

Many African Americans believe they have some Native American ancestry. But, in the PBS series led by historian Henry Louis Gates Jr., called African American Lives, geneticists said DNA evidence shows that Native American ancestry is far less common than previously believed; of the group tested in the series, only two of the people showed likely Native ancestry. Gates summarized the data:

Only 5 percent of African Americans have at least one-eighth Native American ancestry (equivalent to one great-grandparent). On the other hand, nearly 78 percent of African Americans have at least one-eighth European ancestry (the equivalent to one great-grandparent), and nearly 20 percent have at least one-quarter European ancestry (the equivalent to one grandparent.)

In response, one critic asserted the percentage must be higher because there are so many family stories (the reasons for which Gates and, notably, Chris Rock explored in the documentary), but felt that many people didn't always talk about it because to acknowledge it would be to deny their African heritage.

Some critics thought the PBS series African American Lives did not sufficiently explain such limitations of DNA testing for assessment of heritage. In terms of persons searching for ethnic ancestry, they need to understand that Y-chromosome and mtDNA (mitochondrial DNA) testing looks only at "direct" line male and female ancestors, and thus can fail to pick up many other ancestors' heritage. Newer DNA tests can survey all the DNA that can be inherited from either parent of an individual, but at a cost of precision. DNA tests that survey the full DNA strand focus on "single nucleotide polymorphisms" or SNPs, but SNPs might be found in Africans, Asians, and people from every other part of the world. Full survey DNA testing cannot accurately determine an individual's full ancestry. Though DNA testing for ancestry is limited more recent genetic testing research of 2015, have found that varied ancestries show different tendencies by region and sex of ancestors. These studies found that on average, African Americans have 73.2-82.1% West African, 16.7%-29% European, and 0.8–2% Native American genetic ancestry, with large variation between individuals.

A notable debate in 2019 over the validity of DNA testing for Native American ancestry arose over the controversies surrounding Elizabeth Warren's ancestry.

Issues with tribal rolls

Basing citizenship off specific enrollment rolls, like the Dawes Roll (that were taken after more than 80 years after Removal, after the Civil War, and after tribal government restructuring), is what scholar Fay A. Yarbrough calls "dramatically different from older conceptions" of tribal identity based on clan relationships, "in which individuals could be fully," for example, "Cherokee without possessing any Cherokee ancestry." And that by the tribe later "developing a quantifiable definition of Cherokee identity based on ancestry," this "would dramatically affect the process of enrollment late in the nineteenth century and the modern procedure of obtaining membership in the Cherokee Nation, both of which require tracing and individuals’ lineage to a ‘Cherokee by blood.’" Thus, the Dawes Roll still upholds "by blood" language and theory of its time even though the tribe does not require blood quantum. Author Robert J. Conley has stated that if a tribe like the Cherokee Nation are "really serious about exercising its sovereignty and determining its membership," then it should not use the roll that "was put together by the U.S. government and then closed by the U.S. government," meaning that a tribal nation is still subject to the settler definitions of its members when other outside nations do not require rolls, ethnicity, race, or blood quantum for citizenship, but rather birth location and descendance.

Implementation

Many Native American tribes continue to employ blood quantum in current tribal laws to determine who is eligible for membership or citizenship in the tribe or Native American nation. These often require a minimum degree of blood relationship and often an ancestor listed in a specific tribal census from the late 19th century or early 20th century. The Eastern Band of Cherokee Indians of North Carolina, for example, require an ancestor listed in the 1924 Baker census and a minimum of 1/16 Cherokee blood inherited from their ancestor(s) on that roll. Meanwhile, the Cherokee Nation requires applicants to descend from an ancestor in the 1906 Dawes roll (direct lineal ancestry), but does not impose minimum blood quantum requirement. The United Keetoowah Band requires a minimum 1/4 blood quantum.

The Mashantucket Pequot tribe on the other hand, base their tribal membership on an individual proving descent, by recognized genealogical documentation from one or more members of the eleven families included on the 1900 US census of the tribe.

The Northern Ute Tribe require a 5/8 blood quantum, the highest requirement of any American tribe. The Miccosukee of Florida, the Mississippi Choctaw, and the St. Croix Chippewa of Wisconsin all require one-half "tribal blood quantum", also among the higher percentages.

At the other end of the scale, some tribes, such as the Kaw Nation, have no blood quantum requirement.

Many tribes, such as Alabama-Quassarte Tribal Town and the Wyandotte Nation, require an unspecified amount of Indian ancestry (known as "lineal descendancy") documented by descent from a recognized member. Others require a specified degree of Indian ancestry but an unspecified share of ancestry from the ancestral tribe or tribes from which the contemporary tribal entity is derived, such as the Grand Traverse Band of Ottawa and Chippewa Indians and the Poarch Band of Creek Indians. Many tribes today are confederations of different ethnic groups joined into a single political entity making the determination of blood quantum challenging.

Other tribes require a minimum blood degree only for tribal members born "off" (outside) the nominal reservation. This is a concept comparable to the legal principles of Jus soli and Jus sanguinis in the nationality laws of modern sovereign states.

The Red Lake Nation of Minnesota declared in 2019 that all original enrollees on the tribe's 1958 roll were to be "considered full-bloods", regardless of their actual blood quantum as recorded on the roll. Since the tribal blood requirement for membership was (and still is) 1/4, the implication of this "resetting" of the original tribal members' blood quantum is that the grandchild of a person on the 1958 roll who was recorded as 1/4 Chippewa is now eligible for tribal membership, thus effectively setting the requirement at 1/16.

Radical polymerization

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Radical_polymerization

In polymer chemistry, free-radical polymerization (FRP) is a method of polymerization by which a polymer forms by the successive addition of free-radical building blocks (repeat units). Free radicals can be formed by a number of different mechanisms, usually involving separate initiator molecules. Following its generation, the initiating free radical adds (nonradical) monomer units, thereby growing the polymer chain.

Free-radical polymerization is a key synthesis route for obtaining a wide variety of different polymers and materials composites. The relatively non-specific nature of free-radical chemical interactions makes this one of the most versatile forms of polymerization available and allows facile reactions of polymeric free-radical chain ends and other chemicals or substrates. In 2001, 40 billion of the 110 billion pounds of polymers produced in the United States were produced by free-radical polymerization.

Free-radical polymerization is a type of chain-growth polymerization, along with anionic, cationic and coordination polymerization.

IUPAC definition

A chain polymerization in which the kinetic-chain carriers are radicals.

Note: Usually, the growing chain end bears an unpaired electron.

Initiation

Initiation is the first step of the polymerization process. During initiation, an active center is created from which a polymer chain is generated. Not all monomers are susceptible to all types of initiators. Radical initiation works best on the carbon–carbon double bond of vinyl monomers and the carbon–oxygen double bond in aldehydes and ketones. Initiation has two steps. In the first step, one or two radicals are created from the initiating molecules. In the second step, radicals are transferred from the initiator molecules to the monomer units present. Several choices are available for these initiators.

Types of initiation and the initiators

Thermal decomposition

The initiator is heated until a bond is homolytically cleaved, producing two radicals (Figure 1). This method is used most often with organic peroxides or azo compounds.

Figure 1: Thermal decomposition of dicumyl peroxide

 

Photolysis

Radiation cleaves a bond homolytically, producing two radicals (Figure 2). This method is used most often with metal iodides, metal alkyls, and azo compounds.

Figure 2: Photolysis of azoisobutylnitrile (AIBN)

 

Photoinitiation can also occur by bi-molecular H abstraction when the radical is in its lowest triplet excited state. An acceptable photoinitiator system should fulfill the following requirements:

• High absorptivity in the 300–400 nm range.
• Efficient generation of radicals capable of attacking the alkene double bond of vinyl monomers.
• Adequate solubility in the binder system (prepolymer + monomer).
• Should not impart yellowing or unpleasant odors to the cured material.
• The photoinitiator and any byproducts resulting from its use should be non-toxic.

Redox reactions

Reduction of hydrogen peroxide or an alkyl hydrogen peroxide by iron (Figure 3). Other reductants such as Cr²⁺, V²⁺, Ti³⁺, Co²⁺, and Cu⁺ can be employed in place of ferrous ion in many instances.

${\displaystyle {\text{H}}_2^{}{\text{O}}_2^{}+{\text{Fe}}^{2+}⟶{\text{Fe}}^{3+}+{\text{HO}}^{-}+{\text{HO}}^{\cdot }}$ Figure 3: Redox reaction of hydrogen peroxide and iron.

Persulfates

The dissociation of a persulfate in the aqueous phase (Figure 4). This method is useful in emulsion polymerizations, in which the radical diffuses into a hydrophobic monomer-containing droplet.

Figure 4: Thermal degradation of a persulfate

 

Ionizing radiation

α-, β-, γ-, or x-rays cause ejection of an electron from the initiating species, followed by dissociation and electron capture to produce a radical (Figure 5).

Figure 5: The three steps involved in ionizing radiation: ejection, dissociation, and electron-capture

 

Electrochemical

Electrolysis of a solution containing both monomer and electrolyte. A monomer molecule will receive an electron at the cathode to become a radical anion, and a monomer molecule will give up an electron at the anode to form a radical cation (Figure 6). The radical ions then initiate free radical (and/or ionic) polymerization. This type of initiation is especially useful for coating metal surfaces with polymer films.

Figure 6: (Top) Formation of radical anion at the cathode; (bottom) formation of radical cation at the anode

Plasma

A gaseous monomer is placed in an electric discharge at low pressures under conditions where a plasma (ionized gaseous molecules) is created. In some cases, the system is heated and/or placed in a radiofrequency field to assist in creating the plasma.

Sonication

High-intensity ultrasound at frequencies beyond the range of human hearing (16 kHz) can be applied to a monomer. Initiation results from the effects of cavitation (the formation and collapse of cavities in the liquid). The collapse of the cavities generates very high local temperatures and pressures. This results in the formation of excited electronic states, which in turn lead to bond breakage and radical formation.

Ternary initiators

A ternary initiator is the combination of several types of initiators into one initiating system. The types of initiators are chosen based on the properties they are known to induce in the polymers they produce. For example, poly(methyl methacrylate) has been synthesized by the ternary system benzoyl peroxide-3,6-bis(o-carboxybenzoyl)-N-isopropylcarbazole-di-η⁵-indenylzicronium dichloride (Figure 7).

Figure 7: benzoyl peroxide-3,6-bis(o-carboxybenzoyl)-N-isopropylcarbazole-di-η⁵-indenylzicronium dichloride

 

This type of initiating system contains a metallocene, an initiator, and a heteroaromatic diketo carboxylic acid. Metallocenes in combination with initiators accelerate polymerization of poly(methyl methacrylate) and produce a polymer with a narrower molecular weight distribution. The example shown here consists of indenylzirconium (a metallocene) and benzoyl peroxide (an initiator). Also, initiating systems containing heteroaromatic diketo carboxylic acids, such as 3,6-bis(o-carboxybenzoyl)-N-isopropylcarbazole in this example, are known to catalyze the decomposition of benzoyl peroxide. Initiating systems with this particular heteroaromatic diket carboxylic acid are also known to have effects on the microstructure of the polymer. The combination of all of these components—a metallocene, an initiator, and a heteroaromatic diketo carboxylic acid—yields a ternary initiating system that was shown to accelerate the polymerization and produce polymers with enhanced heat resistance and regular microstructure.

Initiator efficiency

Due to side reactions and inefficient synthesis of the radical species, chain initiation is not 100%. The efficiency factor f is used to describe the effective radical concentration. The maximal value of f is 1, but typical values range from 0.3 to 0.8. The following is a list of reactions that decrease the efficiency of the initiator.

Primary recombination

Two radicals recombine before initiating a chain (Figure 8). This occurs within the solvent cage, meaning that no solvent has yet come between the new radicals.

Figure 8: Primary recombination of BPO; brackets indicate that the reaction is happening within the solvent cage

Other recombination pathways

Two radical initiators recombine before initiating a chain, but not in the solvent cage (Figure 9).

Figure 9: Recombination of phenyl radicals from the initiation of BPO outside the solvent cage

Side reactions

One radical is produced instead of the three radicals that could be produced (Figure 10).

${\displaystyle \text{R}\cdot +{\text{R}}^{\prime }-\text{O}-\text{O}-{\text{R}}^{\prime }⟶{\text{ROR}}^{\prime }+{\text{R}}^{\prime }{\text{O}}^{\prime }}$ Figure 10: Reaction of polymer chain R with other species in reaction

Propagation

During polymerization, a polymer spends most of its time in increasing its chain length, or propagating. After the radical initiator is formed, it attacks a monomer (Figure 11). In an ethene monomer, one electron pair is held securely between the two carbons in a sigma bond. The other is more loosely held in a pi bond. The free radical uses one electron from the pi bond to form a more stable bond with the carbon atom. The other electron returns to the second carbon atom, turning the whole molecule into another radical. This begins the polymer chain. Figure 12 shows how the orbitals of an ethylene monomer interact with a radical initiator.

Figure 11: Phenyl initiator from benzoyl peroxide (BPO) attacks a styrene molecule to start the polymer chain.

 

Figure 12: An orbital drawing of the initiator attack on ethylene molecule, producing the start of the polyethylene chain.

Once a chain has been initiated, the chain propagates (Figure 13) until there are no more monomers (living polymerization) or until termination occurs. There may be anywhere from a few to thousands of propagation steps depending on several factors such as radical and chain reactivity, the solvent, and temperature. The mechanism of chain propagation is as follows:

Figure 13: Propagation of polystyrene with a phenyl radical initiator.

Termination

Chain termination is inevitable in radical polymerization due to the high reactivity of radicals. Termination can occur by several different mechanisms. If longer chains are desired, the initiator concentration should be kept low; otherwise, many shorter chains will result.

• Combination of two active chain ends: one or both of the following processes may occur.
  • Combination: two chain ends simply couple together to form one long chain (Figure 14). One can determine if this mode of termination is occurring by monitoring the molecular weight of the propagating species: combination will result in doubling of molecular weight. Also, combination will result in a polymer that is C₂ symmetric about the point of the combination.
    

Figure 14: Termination by the combination of two poly(vinyl chloride) (PVC) polymers.

Radical disproportionation: a hydrogen atom from one chain end is abstracted to another, producing a polymer with a terminal unsaturated group and a polymer with a terminal saturated group (Figure 15).

• Figure 15: Termination by disproportionation of poly(methyl methacrylate).

Combination of an active chain end with an initiator radical (Figure 16).

Figure 16: Termination of PVC by reaction with radical initiator.

Interaction with impurities or inhibitors. Oxygen is the common inhibitor. The growing chain will react with molecular oxygen, producing an oxygen radical, which is much less reactive (Figure 17). This significantly slows down the rate of propagation.

Figure 17: Inhibition of polystyrene propagation due to reaction of polymer with molecular oxygen.

 

Nitrobenzene, butylated hydroxyl toluene, and diphenyl picryl hydrazyl (DPPH, Figure 18) are a few other inhibitors. The latter is an especially effective inhibitor because of the resonance stabilization of the radical.

• Figure 18: Inhibition of polymer chain, R, by DPPH.

Chain transfer

Contrary to the other modes of termination, chain transfer results in the destruction of only one radical, but also the creation of another radical. Often, however, this newly created radical is not capable of further propagation. Similar to disproportionation, all chain-transfer mechanisms also involve the abstraction of a hydrogen or other atom. There are several types of chain-transfer mechanisms.

• To solvent: a hydrogen atom is abstracted from a solvent molecule, resulting in the formation of radical on the solvent molecules, which will not propagate further (Figure 19).
  

Figure 19: Chain transfer from polystyrene to solvent.

 

The effectiveness of chain transfer involving solvent molecules depends on the amount of solvent present (more solvent leads to greater probability of transfer), the strength of the bond involved in the abstraction step (weaker bond leads to greater probability of transfer), and the stability of the solvent radical that is formed (greater stability leads to greater probability of transfer). Halogens, except fluorine, are easily transferred.

To monomer: a hydrogen atom is abstracted from a monomer. While this does create a radical on the affected monomer, resonance stabilization of this radical discourages further propagation (Figure 20).

Figure 20: Chain transfer from polypropylene to monomer.

To initiator: a polymer chain reacts with an initiator, which terminates that polymer chain, but creates a new radical initiator (Figure 21). This initiator can then begin new polymer chains. Therefore, contrary to the other forms of chain transfer, chain transfer to the initiator does allow for further propagation. Peroxide initiators are especially sensitive to chain transfer.

Figure 21: Chain transfer from polypropylene to di-t-butyl peroxide initiator.

To polymer: the radical of a polymer chain abstracts a hydrogen atom from somewhere on another polymer chain (Figure 22). This terminates the growth of one polymer chain, but allows the other to branch and resume growing. This reaction step changes neither the number of polymer chains nor the number of monomers which have been polymerized, so that the number-average degree of polymerization is unaffected.

• Figure 22: Chain transfer from polypropylene to backbone of another polypropylene.

Effects of chain transfer: The most obvious effect of chain transfer is a decrease in the polymer chain length. If the rate of transfer is much larger than the rate of propagation, then very small polymers are formed with chain lengths of 2-5 repeating units (telomerization). The Mayo equation estimates the influence of chain transfer on chain length (x_n): ${\displaystyle \frac{1}{x_n}={\left(\frac{1}{x_n}\right)}_o+\frac{k_{tr}[solvent]}{k_p[monomer]}}$. Where k_tr is the rate constant for chain transfer and k_p is the rate constant for propagation. The Mayo equation assumes that transfer to solvent is the major termination pathway.

Methods

There are four industrial methods of radical polymerization:

• Bulk polymerization: reaction mixture contains only initiator and monomer, no solvent.
• Solution polymerization: reaction mixture contains solvent, initiator, and monomer.
• Suspension polymerization: reaction mixture contains an aqueous phase, water-insoluble monomer, and initiator soluble in the monomer droplets (both the monomer and the initiator are hydrophobic).
• Emulsion polymerization: similar to suspension polymerization except that the initiator is soluble in the aqueous phase rather than in the monomer droplets (the monomer is hydrophobic, and the initiator is hydrophilic). An emulsifying agent is also needed.

Other methods of radical polymerization include the following:

• Template polymerization: In this process, polymer chains are allowed to grow along template macromolecules for the greater part of their lifetime. A well-chosen template can affect the rate of polymerization as well as the molar mass and microstructure of the daughter polymer. The molar mass of a daughter polymer can be up to 70 times greater than those of polymers produced in the absence of the template and can be higher in molar mass than the templates themselves. This is because of retardation of the termination for template-associated radicals and by hopping of a radical to the neighboring template after reaching the end of a template polymer.
• Plasma polymerization: The polymerization is initiated with plasma. A variety of organic molecules including alkenes, alkynes, and alkanes undergo polymerization to high molecular weight products under these conditions. The propagation mechanisms appear to involve both ionic and radical species. Plasma polymerization offers a potentially unique method of forming thin polymer films for uses such as thin-film capacitors, antireflection coatings, and various types of thin membranes.
• Sonication: The polymerization is initiated by high-intensity ultrasound. Polymerization to high molecular weight polymer is observed but the conversions are low (<15%). The polymerization is self-limiting because of the high viscosity produced even at low conversion. High viscosity hinders cavitation and radical production.

Reversible deactivation radical polymerization

Main article: Reversible-deactivation radical polymerization

Also known as living radical polymerization, controlled radical polymerization, reversible deactivation radical polymerization (RDRP) relies on completely pure reactions, preventing termination caused by impurities. Because these polymerizations stop only when there is no more monomer, polymerization can continue upon the addition of more monomer. Block copolymers can be made this way. RDRP allows for control of molecular weight and dispersity. However, this is very difficult to achieve and instead a pseudo-living polymerization occurs with only partial control of molecular weight and dispersity. ATRP and RAFT are the main types of complete radical polymerization.

• Atom transfer radical polymerization (ATRP): based on the formation of a carbon-carbon bond by atom transfer radical addition. This method, independently discovered in 1995 by Mitsuo Sawamoto and by Jin-Shan Wang and Krzysztof Matyjaszewski, requires reversible activation of a dormant species (such as an alkyl halide) and a transition metal halide catalyst (to activate dormant species).
• Reversible Addition-Fragmentation Chain-Transfer Polymerization (RAFT): requires a compound that can act as a reversible chain-transfer agent, such as dithio compound.
• Stable Free Radical Polymerization (SFRP): used to synthesize linear or branched polymers with narrow molecular weight distributions and reactive end groups on each polymer chain. The process has also been used to create block co-polymers with unique properties. Conversion rates are about 100% using this process but require temperatures of about 135 °C. This process is most commonly used with acrylates, styrenes, and dienes. The reaction scheme in Figure 23 illustrates the SFRP process.
  

Figure 23: Reaction scheme for SFRP.

• Figure 24: TEMPO molecule used to functionalize the chain ends.
  Because the chain end is functionalized with the TEMPO molecule (Figure 24), premature termination by coupling is reduced. As with all living polymerizations, the polymer chain grows until all of the monomer is consumed.

Kinetics

In typical chain growth polymerizations, the reaction rates for initiation, propagation and termination can be described as follows:

${\displaystyle v_i=\mathrm{d}[M\cdot ]/\mathrm{d}t=2k_{d}f[I]}$

${\displaystyle v_p=k_p[M][M\cdot ]}$

${\displaystyle v_t=-\mathrm{d}[M\cdot ]/\mathrm{d}t=2k_t[M\cdot {]}^2}$

where f is the efficiency of the initiator and k_d, k_p, and k_t are the constants for initiator dissociation, chain propagation and termination, respectively. [I] [M] and [M•] are the concentrations of the initiator, monomer and the active growing chain.

Under the steady-state approximation, the concentration of the active growing chains remains constant, i.e. the rates of initiation and of termination are equal. The concentration of active chain can be derived and expressed in terms of the other known species in the system.

${\displaystyle [M\cdot ]={\left(\frac{k_d[I]f}{k_t}\right)}^{1/2}}$

In this case, the rate of chain propagation can be further described using a function of the initiator and monomer concentrations

${\displaystyle v_p=k_p{\left(\frac{f{k}_d}{k_t}\right)}^{1/2}[I{]}^{1/2}[M]}$

The kinetic chain length v is a measure of the average number of monomer units reacting with an active center during its lifetime and is related to the molecular weight through the mechanism of the termination. Without chain transfer, the kinetic chain length is only a function of propagation rate and initiation rate.

${\displaystyle \nu =\frac{v_p}{v_i}=\frac{k_p[M][M\cdot ]}{2f{k}_d[I]}=\frac{k_p[M]}{2(f{k}_d{k}_t[I]{)}^{1/2}}}$

Assuming no chain-transfer effect occurs in the reaction, the number average degree of polymerization P_n can be correlated with the kinetic chain length. In the case of termination by disproportionation, one polymer molecule is produced per every kinetic chain:

${\displaystyle x_n=\nu }$

Termination by combination leads to one polymer molecule per two kinetic chains:

${\displaystyle x_n=2\nu }$

Any mixture of both these mechanisms can be described by using the value δ, the contribution of disproportionation to the overall termination process:

${\displaystyle x_n=\frac{2}{1+\delta }\nu }$

If chain transfer is considered, the kinetic chain length is not affected by the transfer process because the growing free-radical center generated by the initiation step stays alive after any chain-transfer event, although multiple polymer chains are produced. However, the number average degree of polymerization decreases as the chain transfers, since the growing chains are terminated by the chain-transfer events. Taking into account the chain-transfer reaction towards solvent S, initiator I, polymer P, and added chain-transfer agent T. The equation of P_n will be modified as follows:

${\displaystyle \frac{1}{x_n}=\frac{2k_{t,d}+k_{t,c}}{{k_p}^2[M{]}^2}{v}_p+C_M+C_S\frac{[S]}{[M]}+C_I\frac{[I]}{[M]}+C_P\frac{[P]}{[M]}+C_T\frac{[T]}{[M]}}$

It is usual to define chain-transfer constants C for the different molecules

${\displaystyle C_M=\frac{k_{tr}^M}{k_p}}$, ${\displaystyle C_S=\frac{k_{tr}^S}{k_p}}$, ${\displaystyle C_I=\frac{k_{tr}^I}{k_p}}$, ${\displaystyle C_P=\frac{k_{tr}^P}{k_p}}$, ${\displaystyle C_T=\frac{k_{tr}^T}{k_p}}$

Thermodynamics

In chain growth polymerization, the position of the equilibrium between polymer and monomers can be determined by the thermodynamics of the polymerization. The Gibbs free energy (ΔG_p) of the polymerization is commonly used to quantify the tendency of a polymeric reaction. The polymerization will be favored if ΔG_p < 0; if ΔG_p > 0, the polymer will undergo depolymerization. According to the thermodynamic equation ΔG = ΔH – TΔS, a negative enthalpy and an increasing entropy will shift the equilibrium towards polymerization.

In general, the polymerization is an exothermic process, i.e. negative enthalpy change, since addition of a monomer to the growing polymer chain involves the conversion of π bonds into σ bonds, or a ring–opening reaction that releases the ring tension in a cyclic monomer. Meanwhile, during polymerization, a large amount of small molecules are associated, losing rotation and translational degrees of freedom. As a result, the entropy decreases in the system, ΔS_p < 0 for nearly all polymerization processes. Since depolymerization is almost always entropically favored, the ΔH_p must then be sufficiently negative to compensate for the unfavorable entropic term. Only then will polymerization be thermodynamically favored by the resulting negative ΔG_p.

In practice, polymerization is favored at low temperatures: TΔS_p is small. Depolymerization is favored at high temperatures: TΔS_p is large. As the temperature increases, ΔG_p become less negative. At a certain temperature, the polymerization reaches equilibrium (rate of polymerization = rate of depolymerization). This temperature is called the ceiling temperature (T_c). ΔG_p = 0.

Stereochemistry

The stereochemistry of polymerization is concerned with the difference in atom connectivity and spatial orientation in polymers that has the same chemical composition.

Hermann Staudinger studied the stereoisomerism in chain polymerization of vinyl monomers in the late 1920s, and it took another two decades for people to fully appreciate the idea that each of the propagation steps in the polymer growth could give rise to stereoisomerism. The major milestone in the stereochemistry was established by Ziegler and Natta and their coworkers in 1950s, as they developed metal based catalyst to synthesize stereoregular polymers. The reason why the stereochemistry of the polymer is of particular interest is because the physical behavior of a polymer depends not only on the general chemical composition but also on the more subtle differences in microstructure. Atactic polymers consist of a random arrangement of stereochemistry and are amorphous (noncrystalline), soft materials with lower physical strength. The corresponding isotactic (like substituents all on the same side) and syndiotactic (like substituents of alternate repeating units on the same side) polymers are usually obtained as highly crystalline materials. It is easier for the stereoregular polymers to pack into a crystal lattice since they are more ordered and the resulting crystallinity leads to higher physical strength and increased solvent and chemical resistance as well as differences in other properties that depend on crystallinity. The prime example of the industrial utility of stereoregular polymers is polypropene. Isotactic polypropene is a high-melting (165 °C), strong, crystalline polymer, which is used as both a plastic and fiber. Atactic polypropene is an amorphous material with an oily to waxy soft appearance that finds use in asphalt blends and formulations for lubricants, sealants, and adhesives, but the volumes are minuscule compared to that of isotactic polypropene.

When a monomer adds to a radical chain end, there are two factors to consider regarding its stereochemistry: 1) the interaction between the terminal chain carbon and the approaching monomer molecule and 2) the configuration of the penultimate repeating unit in the polymer chain. The terminal carbon atom has sp² hybridization and is planar. Consider the polymerization of the monomer CH₂=CXY. There are two ways that a monomer molecule can approach the terminal carbon: the mirror approach (with like substituents on the same side) or the non-mirror approach (like substituents on opposite sides). If free rotation does not occur before the next monomer adds, the mirror approach will always lead to an isotactic polymer and the non-mirror approach will always lead to a syndiotactic polymer (Figure 25).

Figure 25: (Top) formation of isotactic polymer; (bottom) formation of syndiotactic polymer.

However, if interactions between the substituents of the penultimate repeating unit and the terminal carbon atom are significant, then conformational factors could cause the monomer to add to the polymer in a way that minimizes steric or electrostatic interaction (Figure 26).

Figure 26: Penultimate unit interactions cause monomer to add in a way that minimizes steric hindrance between substituent groups. (P represents polymer chain.)

Reactivity

Traditionally, the reactivity of monomers and radicals are assessed by the means of copolymerization data. The Q–e scheme, the most widely used tool for the semi-quantitative prediction of monomer reactivity ratios, was first proposed by Alfrey and Price in 1947. The scheme takes into account the intrinsic thermodynamic stability and polar effects in the transition state. A given radical ${\displaystyle M_i^o}$ and a monomer ${\displaystyle M_j}$ are considered to have intrinsic reactivities P_i and Q_j, respectively. The polar effects in the transition state, the supposed permanent electric charge carried by that entity (radical or molecule), is quantified by the factor e, which is a constant for a given monomer, and has the same value for the radical derived from that specific monomer. For addition of monomer 2 to a growing polymer chain whose active end is the radical of monomer 1, the rate constant, k₁₂, is postulated to be related to the four relevant reactivity parameters by

${\displaystyle k_{12}=P_1{Q}_2\exp (-e_1{e}_2)}$

The monomer reactivity ratio for the addition of monomers 1 and 2 to this chain is given by

${\displaystyle r_1=\frac{k_{11}}{k_{12}}=\frac{Q_1}{Q_2}\exp (-e_1(e_1-e_2))}$

For the copolymerization of a given pair of monomers, the two experimental reactivity ratios r₁ and r₂ permit the evaluation of (Q₁/Q₂) and (e₁ – e₂). Values for each monomer can then be assigned relative to a reference monomer, usually chosen as styrene with the arbitrary values Q = 1.0 and e = –0.8.

Applications

Free radical polymerization has found applications including the manufacture of polystyrene, thermoplastic block copolymer elastomers, cardiovascular stents, chemical surfactants and lubricants. Block copolymers are used for a wide variety of applications including adhesives, footwear and toys.

Free radical polymerization has uses in research as well, such as in the functionalization of carbon nanotubes. CNTs intrinsic electronic properties lead them to form large aggregates in solution, precluding useful applications. Adding small chemical groups to the walls of CNT can eliminate this propensity and tune the response to the surrounding environment. The use of polymers instead of smaller molecules can modify CNT properties (and conversely, nanotubes can modify polymer mechanical and electronic properties). For example, researchers coated carbon nanotubes with polystyrene by first polymerizing polystyrene via chain radical polymerization and subsequently mixing it at 130 °C with carbon nanotubes to generate radicals and graft them onto the walls of carbon nanotubes (Figure 27). Chain growth polymerization ("grafting to") synthesizes a polymer with predetermined properties. Purification of the polymer can be used to obtain a more uniform length distribution before grafting. Conversely, “grafting from”, with radical polymerization techniques such as atom transfer radical polymerization (ATRP) or nitroxide-mediated polymerization (NMP), allows rapid growth of high molecular weight polymers.

Figure 27: Grafting of a polystyrene free radical onto a single-walled carbon nanotube.

Radical polymerization also aids synthesis of nanocomposite hydrogels. These gels are made of water-swellable nano-scale clay (especially those classed as smectites) enveloped by a network polymer. They are often biocompatible and have mechanical properties (such as flexibility and strength) that promise applications such as synthetic tissue. Synthesis involves free radical polymerization. The general synthesis procedure is depicted in Figure 28. Clay is dispersed in water, where it forms very small, porous plates. Next the initiator and a catalyst are added, followed by adding the organic monomer, generally an acrylamide or acrylamide derivative. The initiator is chosen to have stronger interaction with the clay than the organic monomer, so it preferentially adsorbs to the clay surface. The mixture and water solvent is heated to initiate polymerization. Polymers grow off the initiators that are in turn bound to the clay. Due to recombination and disproportionation reactions, growing polymer chains bind to one another, forming a strong, cross-linked network polymer, with clay particles acting as branching points for multiple polymer chain segments. Free radical polymerization used in this context allows the synthesis of polymers from a wide variety of substrates (the chemistries of suitable clays vary). Termination reactions unique to chain growth polymerization produce a material with flexibility, mechanical strength and biocompatibility.

Figure 28: General synthesis procedure for a nanocomposite hydrogel.

Electronics

The radical polymer glass PTMA is about 10 times more electrically conductive than common semiconducting polymers. PTMA is in a class of electrically active polymers that could find use in transparent solar cells, antistatic and antiglare coatings for mobile phone displays, antistatic coverings for aircraft to protect against lightning strikes, flexible flash drives, and thermoelectric devices, which convert electricity into heat and the reverse. Widespread practical applications require increasing conductivity another 100 to 1,000 times.

The polymer was created using deprotection, which involves replacing a specific hydrogen atom in the pendant group with an oxygen atom. The resulting oxygen atom in PTMA has one unpaired electron in its outer shell, making it amenable to transporting charge. The deprotection step can lead to four distinct chemical functionalities, two of which are promising for increasing conductivity.