5.2: Crown Classes - Biology

Crown class is a term used to describe the position of an individual tree in the forest canopy. 1997 and Helms 1998 modified for clarity):

  • Dominant Trees These crowns extend above the general level of the canopy. They receive full light from above and some light from the sides. Generally, they have the largest, fullest crowns in the stand (Figure 5.4).
  • Codominant Trees These crowns make up the general level of the canopy. They receive direct light from above, but little or no light from the sides. Generally they are shorter than the dominant trees.
  • Intermediate Trees These crowns occupy a subordinate position in the canopy. They receive some direct light from above, but no direct light from the sides. Crowns are generally narrow and/or one-sided, and shorter than the dominant and codominant trees.
  • Suppressed Trees (Overtopped Trees) These crowns are below the general level of the canopy. They receive no direct light. Crowns are generally short, sparse, and narrow.

Figure 5.4. An illustration of crown classes. “D” = Dominant; “C” = Codominant; “I” = Intermediate and “S” = Suppressed.

“General layer of the canopy” refers to the size class or cohort being examined. Crown classes are most easily determined in evenaged stands, as depicted in Figure 5.4. In an unevenaged stand, a tree would be compared to other trees in the same layer. Crown classes are a function of tree vigor, tree growing space, access to sunlight (functions of stand density), and species shade tolerance. A “suppressed” Douglas-fir tree is likely of low vigor and will probably die out. It typically would not be able to respond to an increase in sunlight if a neighboring tree fell over. A shade tolerant “suppressed” western hemlock on the other hand, may survive very nicely and be able to take advantage of increased sunlight if a neighboring tree were to fall over.

Crown class can also tell us something of the overall vigor of an evenaged stand. If most trees are in the intermediate crown class, then the stand is likely too crowded and the trees are stagnated. A stand with nearly every tree in the dominant category is either very young, and all of the trees are receiving plenty of sun, or very sparse and may be considered “understocked.” A typical evenaged stand has the majority of trees in the codominant class, and the fewest trees in the suppressed class. The relative ratios of dominant and intermediate classes are generally a function of species composition. Examine the data in Figure 5.5 and Table 5.1 below.

Figure 5.5. Diameter and crown class data for an evenaged stand near Larch Mountain. Data collected by MHCC Forest Measurements I class on January 26, 2005.

This 60-yr old stand of primarily Douglas-fir and western hemlock, displays a bell-shaped diameter distribution, typical of an evenaged stand. Most of the trees are clustered around the average DBH, with some smaller and some larger than the center range.

Table 5.1. Percent of each Species by Crown Class. Data collected in evenaged stand near Larch Mt. by MHCC Forest Measurements I class on January 26, 2005.

29% of all trees measured


35% of all trees measured


24% of all trees measured


13% of all trees measured

Western hemlock33366088

Note that the majority of trees are in the codominant crown class (35%), which most likely makes up the bulk of the 16’’-22” trees. It is interesting to examine the species composition data. The majority of dominant and codominant trees are Douglas-fir, while the intermediate and suppressed trees are primarily shade tolerant western hemlock. Therefore, many of the trees in the small diameter classes (6’-10”) may survive over time, even though they are surrounded by large trees. So there is another element to examine besides position in the crown.

5.2: Crown Classes - Biology

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A lattice system is a class of lattices with the same set of lattice point groups, which are subgroups of the arithmetic crystal classes. The 14 Bravais lattices are grouped into seven lattice systems: triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic.

In a crystal system, a set of point groups and their corresponding space groups are assigned to a lattice system. Of the 32 point groups that exist in three dimensions, most are assigned to only one lattice system, in which case both the crystal and lattice systems have the same name. However, five point groups are assigned to two lattice systems, rhombohedral and hexagonal, because both exhibit threefold rotational symmetry. These point groups are assigned to the trigonal crystal system. In total there are seven crystal systems: triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic.

A crystal family is determined by lattices and point groups. It is formed by combining crystal systems which have space groups assigned to a common lattice system. In three dimensions, the crystal families and systems are identical, except the hexagonal and trigonal crystal systems, which are combined into one hexagonal crystal family. In total there are six crystal families: triclinic, monoclinic, orthorhombic, tetragonal, hexagonal, and cubic.

Spaces with less than three dimensions have the same number of crystal systems, crystal families, and lattice systems. In one-dimensional space, there is one crystal system. In 2D space, there are four crystal systems: oblique, rectangular, square, and hexagonal.

The relation between three-dimensional crystal families, crystal systems and lattice systems is shown in the following table:

Crystal family Crystal system Required symmetries of the point group Point groups Space groups Bravais lattices Lattice system
Triclinic Triclinic None 2 2 1 Triclinic
Monoclinic Monoclinic 1 twofold axis of rotation or 1 mirror plane 3 13 2 Monoclinic
Orthorhombic Orthorhombic 3 twofold axes of rotation or 1 twofold axis of rotation and 2 mirror planes 3 59 4 Orthorhombic
Tetragonal Tetragonal 1 fourfold axis of rotation 7 68 2 Tetragonal
Hexagonal Trigonal 1 threefold axis of rotation 5 7 1 Rhombohedral
18 1 Hexagonal
Hexagonal 1 sixfold axis of rotation 7 27
Cubic Cubic 4 threefold axes of rotation 5 36 3 Cubic
6 7 Total 32 230 14 7
Note: there is no "trigonal" lattice system. To avoid confusion of terminology, the term "trigonal lattice" is not used.

The 7 crystal systems consist of 32 crystal classes (corresponding to the 32 crystallographic point groups) as shown in the following table below:

Crystal family Crystal system Point group / Crystal class Schönflies Hermann–Mauguin Orbifold Coxeter Point symmetry Order Abstract group
triclinic pedial C1 1 11 [ ] + enantiomorphic polar 1 trivial Z 1 _<1>>
pinacoidal Ci (S2) 1 1x [2,1 + ] centrosymmetric 2 cyclic Z 2 _<2>>
monoclinic sphenoidal C2 2 22 [2,2] + enantiomorphic polar 2 cyclic Z 2 _<2>>
domatic Cs (C1h) m *11 [ ] polar 2 cyclic Z 2 _<2>>
prismatic C2h 2/m 2* [2,2 + ] centrosymmetric 4 Klein four V = Z 2 × Z 2 =mathbb _<2> imes mathbb _<2>>
orthorhombic rhombic-disphenoidal D2 (V) 222 222 [2,2] + enantiomorphic 4 Klein four V = Z 2 × Z 2 =mathbb _<2> imes mathbb _<2>>
rhombic-pyramidal C2v mm2 *22 [2] polar 4 Klein four V = Z 2 × Z 2 =mathbb _<2> imes mathbb _<2>>
rhombic-dipyramidal D2h (Vh) mmm *222 [2,2] centrosymmetric 8 V × Z 2 imes mathbb _<2>>
tetragonal tetragonal-pyramidal C4 4 44 [4] + enantiomorphic polar 4 cyclic Z 4 _<4>>
tetragonal-disphenoidal S4 4 2x [2 + ,2] non-centrosymmetric 4 cyclic Z 4 _<4>>
tetragonal-dipyramidal C4h 4/m 4* [2,4 + ] centrosymmetric 8 Z 4 × Z 2 _<4> imes mathbb _<2>>
tetragonal-trapezohedral D4 422 422 [2,4] + enantiomorphic 8 dihedral D 8 = Z 4 ⋊ Z 2 _<8>=mathbb _<4> times mathbb _<2>>
ditetragonal-pyramidal C4v 4mm *44 [4] polar 8 dihedral D 8 = Z 4 ⋊ Z 2 _<8>=mathbb _<4> times mathbb _<2>>
tetragonal-scalenohedral D2d (Vd) 4 2m or 4 m2 2*2 [2 + ,4] non-centrosymmetric 8 dihedral D 8 = Z 4 ⋊ Z 2 _<8>=mathbb _<4> times mathbb _<2>>
ditetragonal-dipyramidal D4h 4/mmm *422 [2,4] centrosymmetric 16 D 8 × Z 2 _<8> imes mathbb _<2>>
hexagonal trigonal trigonal-pyramidal C3 3 33 [3] + enantiomorphic polar 3 cyclic Z 3 _<3>>
rhombohedral C3i (S6) 3 3x [2 + ,3 + ] centrosymmetric 6 cyclic Z 6 = Z 3 × Z 2 _<6>=mathbb _<3> imes mathbb _<2>>
trigonal-trapezohedral D3 32 or 321 or 312 322 [3,2] + enantiomorphic 6 dihedral D 6 = Z 3 ⋊ Z 2 _<6>=mathbb _<3> times mathbb _<2>>
ditrigonal-pyramidal C3v 3m or 3m1 or 31m *33 [3] polar 6 dihedral D 6 = Z 3 ⋊ Z 2 _<6>=mathbb _<3> times mathbb _<2>>
ditrigonal-scalenohedral D3d 3 m or 3 m1 or 3 1m 2*3 [2 + ,6] centrosymmetric 12 dihedral D 12 = Z 6 ⋊ Z 2 _<12>=mathbb _<6> times mathbb _<2>>
hexagonal hexagonal-pyramidal C6 6 66 [6] + enantiomorphic polar 6 cyclic Z 6 = Z 3 × Z 2 _<6>=mathbb _<3> imes mathbb _<2>>
trigonal-dipyramidal C3h 6 3* [2,3 + ] non-centrosymmetric 6 cyclic Z 6 = Z 3 × Z 2 _<6>=mathbb _<3> imes mathbb _<2>>
hexagonal-dipyramidal C6h 6/m 6* [2,6 + ] centrosymmetric 12 Z 6 × Z 2 _<6> imes mathbb _<2>>
hexagonal-trapezohedral D6 622 622 [2,6] + enantiomorphic 12 dihedral D 12 = Z 6 ⋊ Z 2 _<12>=mathbb _<6> times mathbb _<2>>
dihexagonal-pyramidal C6v 6mm *66 [6] polar 12 dihedral D 12 = Z 6 ⋊ Z 2 _<12>=mathbb _<6> times mathbb _<2>>
ditrigonal-dipyramidal D3h 6 m2 or 6 2m *322 [2,3] non-centrosymmetric 12 dihedral D 12 = Z 6 ⋊ Z 2 _<12>=mathbb _<6> times mathbb _<2>>
dihexagonal-dipyramidal D6h 6/mmm *622 [2,6] centrosymmetric 24 D 12 × Z 2 _<12> imes mathbb _<2>>
cubic tetartoidal T 23 332 [3,3] + enantiomorphic 12 alternating A 4 >
diploidal Th m 3 3*2 [3 + ,4] centrosymmetric 24 A 4 × Z 2 imes mathbb _<2>>
gyroidal O 432 432 [4,3] + enantiomorphic 24 symmetric S 4 _<4>>
hextetrahedral Td 4 3m *332 [3,3] non-centrosymmetric 24 symmetric S 4 _<4>>
hexoctahedral Oh m 3 m *432 [4,3] centrosymmetric 48 S 4 × Z 2 _<4> imes mathbb _<2>>

The point symmetry of a structure can be further described as follows. Consider the points that make up the structure, and reflect them all through a single point, so that (x,y,z) becomes (−x,−y,−z). This is the 'inverted structure'. If the original structure and inverted structure are identical, then the structure is centrosymmetric. Otherwise it is non-centrosymmetric. Still, even in the non-centrosymmetric case, the inverted structure can in some cases be rotated to align with the original structure. This is a non-centrosymmetric achiral structure. If the inverted structure cannot be rotated to align with the original structure, then the structure is chiral or enantiomorphic and its symmetry group is enantiomorphic. [1]

A direction (meaning a line without an arrow) is called polar if its two-directional senses are geometrically or physically different. A symmetry direction of a crystal that is polar is called a polar axis. [2] Groups containing a polar axis are called polar. A polar crystal possesses a unique polar axis (more precisely, all polar axes are parallel). Some geometrical or physical property is different at the two ends of this axis: for example, there might develop a dielectric polarization as in pyroelectric crystals. A polar axis can occur only in non-centrosymmetric structures. There cannot be a mirror plane or twofold axis perpendicular to the polar axis, because they would make the two directions of the axis equivalent.

The crystal structures of chiral biological molecules (such as protein structures) can only occur in the 65 enantiomorphic space groups (biological molecules are usually chiral).

There are seven different kinds of crystal systems, and each kind of crystal system has four different kinds of centerings (primitive, base-centered, body-centered, face-centered). However, not all of the combinations are unique some of the combinations are equivalent while other combinations are not possible due to symmetry reasons. This reduces the number of unique lattices to the 14 Bravais lattices.

The distribution of the 14 Bravais lattices into lattice systems and crystal families is given in the following table.

In geometry and crystallography, a Bravais lattice is a category of translative symmetry groups (also known as lattices) in three directions.

Such symmetry groups consist of translations by vectors of the form

where n1, n2, and n3 are integers and a1, a2, and a3 are three non-coplanar vectors, called primitive vectors.

These lattices are classified by the space group of the lattice itself, viewed as a collection of points there are 14 Bravais lattices in three dimensions each belongs to one lattice system only. They [ clarification needed ] represent the maximum symmetry a structure with the given translational symmetry can have.

All crystalline materials (not including quasicrystals) must, by definition, fit into one of these arrangements.

For convenience a Bravais lattice is depicted by a unit cell which is a factor 1, 2, 3, or 4 larger than the primitive cell. Depending on the symmetry of a crystal or other pattern, the fundamental domain is again smaller, up to a factor 48.

The Bravais lattices were studied by Moritz Ludwig Frankenheim in 1842, who found that there were 15 Bravais lattices. This was corrected to 14 by A. Bravais in 1848.

‌The four-dimensional unit cell is defined by four edge lengths (a, b, c, d) and six interaxial angles (α, β, γ, δ, ε, ζ). The following conditions for the lattice parameters define 23 crystal families

The names here are given according to Whittaker. [3] They are almost the same as in Brown et al, [4] with exception for names of the crystal families 9, 13, and 22. The names for these three families according to Brown et al are given in parenthesis.

The relation between four-dimensional crystal families, crystal systems, and lattice systems is shown in the following table. [3] [4] Enantiomorphic systems are marked with an asterisk. The number of enantiomorphic pairs is given in parentheses. Here the term "enantiomorphic" has a different meaning than in the table for three-dimensional crystal classes. The latter means, that enantiomorphic point groups describe chiral (enantiomorphic) structures. In the current table, "enantiomorphic" means that a group itself (considered as a geometric object) is enantiomorphic, like enantiomorphic pairs of three-dimensional space groups P31 and P32, P4122 and P4322. Starting from four-dimensional space, point groups also can be enantiomorphic in this sense.

AP Biology

This course can help prepare students who wish to continue their scientific education after high school, as well as students who wish to prepare for the SAT exam. The level of aptitude in this subject will assist students wishing to excel on the SAT and in college courses.

According to the College Board’s website, AP Biology courses are designed to be the equivalent of a college introductory course, usually taken during a biology major’s first year of college. Students who choose to take AP Biology may be allowed to skip over introductory biology courses and enroll in courses in which biology is a prerequisite. Because universities grant college credit for this course, they require that the textbooks, labs, and coursework used by AP courses be equivalent to those used in actual college courses.

This course is offered to highly motivated students who wish to pursue their interests in the biological sciences. Enrollment requirements for the AP Biology course depend on policies established by each high school offering the course, but AP Biology is usually preceded by a less rigorous entry level Biology course, and sometimes by Chemistry as well. While some schools may have selective acceptance into the course, determined by academic record in prerequisite courses, other schools adhere to a policy of open enrollment, encouraging its undertaking by students that demonstrate capability for the course, though they may have performed unsatisfactorily in previous science courses.

Topics covered by this course include, Anatomy & Physiology, Biochemistry, Biodiversity, Botany, The Cell, Developmental Biology, Ecology, Genetics, Molecular Biology, Origin of life, Population Biology, and Evolution.

Students taking AP Biology should first complete an introductory course in Biology, usually lasting one school year. An introductory course will prepare students to study higher levels of science and familiarize them with the scientific process. Students should also have experience with basic mathematical functions in order to complete experiments.

AP Biology is a serious course with a number course goals. According to the College Board’s website, by the time students take their AP Biology exam (or the SAT exam) they should:

  • Develop a conceptual framework of Biology as a science. Students should focus more on concepts and discoveries rather than simply memorizing terms and technical details and routinely repeating information on exams. Students should be able to appreciate science as a coherent body of information and seek to apply it both inside and outside of the classroom.
  • Gain an appreciation of the scientific process, its history, and its present day applications. Students should also be able to understand the importance of the scientific process while experimenting and be able to explain how they’ve used the scientific process in their own experiments both in writing and through the written word.
  • Develop a deeper understanding of different biological process, particularly as they apply to living beings and life cycles.
  • Use study notes and other study techniques in conjunction with various AP Biology textbooks.

The College Board also recently released a requirement for the AP Biology exam, underlining what portion of the test should be dedicated to what field of study. Accordingly, the following goals for the test were released:

  • 25% of the test should be dedicated to Molecules and Cells.
  • 25% of the test should be dedicated to Heredity and Evolution.
  • 50% of the test should be dedicated to Organisms and Populations.

Students studying for both the AP Biology exam as well as the SAT should keep these parameters in mind. These basic goals may determine how much time is spent covering these different areas of study over the course of the school year as well as how much time is allotted to complete each section of the AP Biology test.

Students interested in taking AP Biology or any other Advanced Placement course should keep in mind that taking college level courses in high school requires a commitment of time and energy. Students that commit themselves to their classes and treat them as college level courses will see a definite pay off in their grades as well as their confidence.

Students wishing to get into prestigious, well-respected colleges or universities should definitely consider taking Advanced Placement courses. These courses look excellent on high school transcripts and can give students an invaluable look at college courses before they even enroll in them. Students also have the opportunity to earn college credit before graduating, which can save valuable time and money once college begins. The more students work to prepare themselves for the high-pressure college atmosphere before beginning their college education, the more enjoyable and successful their college career will be in the end. So, for student wishing to get a jump start on their college education and their careers after college, the AP course program is the perfect choice!

Here you will find AP Biology outlines and slides. We are working to add more AP Biology resources such as vocabulary terms, unit notes, topic notes, study questions, practice quizzes and glossary terms.


Ethers feature bent C–O–C linkages. In dimethyl ether, the bond angle is 111° and C–O distances are 141 pm. [3] The barrier to rotation about the C–O bonds is low. The bonding of oxygen in ethers, alcohols, and water is similar. In the language of valence bond theory, the hybridization at oxygen is sp 3 .

Oxygen is more electronegative than carbon, thus the hydrogens alpha to ethers are more acidic than in simple hydrocarbons. They are far less acidic than hydrogens alpha to carbonyl groups (such as in ketones or aldehydes), however.

Ethers can be symmetrical of the type ROR or unsymmetrical of the type ROR'. Examples of the former are diethyl ether, dimethyl ether, dipropyl ether etc. Illustrative unsymmetrical ethers are anisole (methoxybenzene) and dimethoxyethane.

In the IUPAC Nomenclature system, ethers are named using the general formula "alkoxyalkane", for example CH3–CH2–O–CH3 is methoxyethane. If the ether is part of a more-complex molecule, it is described as an alkoxy substituent, so –OCH3 would be considered a "methoxy-" group. The simpler alkyl radical is written in front, so CH3–O–CH2CH3 would be given as methoxy(CH3O)ethane(CH2CH3).

Trivial name Edit

IUPAC rules are often not followed for simple ethers. The trivial names for simple ethers (i.e., those with none or few other functional groups) are a composite of the two substituents followed by "ether". For example, ethyl methyl ether (CH3OC2H5), diphenylether (C6H5OC6H5). As for other organic compounds, very common ethers acquired names before rules for nomenclature were formalized. Diethyl ether is simply called "ether", but was once called sweet oil of vitriol. Methyl phenyl ether is anisole, because it was originally found in aniseed. The aromatic ethers include furans. Acetals (α-alkoxy ethers R–CH(–OR)–O–R) are another class of ethers with characteristic properties.

Polyethers Edit

Polyethers are generally polymers containing ether linkages in their main chain. The term glycol generally refers to polyether polyols with one or more functional end-groups such as a hydroxyl group. The term "oxide" or other terms are used for high molar mass polymer when end-groups no longer affect polymer properties.

Crown ethers are cyclic polyethers. Some toxins produced by dinoflagellates such as brevetoxin and ciguatoxin are extremely large and are known as cyclic or ladder polyethers.

Aliphatic polyethers
Name of the polymers with low to medium molar mass Name of the polymers with high molar mass Preparation Repeating unit Examples of trade names
Paraformaldehyde Polyoxymethylene (POM) or polyacetal or polyformaldehyde Step-growth polymerisation of formaldehyde –CH2O– Delrin from DuPont
Polyethylene glycol (PEG) Polyethylene oxide (PEO) or polyoxyethylene (POE) Ring-opening polymerization of ethylene oxide –CH2CH2O– Carbowax from Dow
Polypropylene glycol (PPG) Polypropylene oxide (PPOX) or polyoxypropylene (POP) anionic ring-opening polymerization of propylene oxide –CH2CH(CH3)O– Arcol from Covestro
Polytetramethylene glycol (PTMG) or Polytetramethylene ether glycol (PTMEG) Polytetrahydrofuran (PTHF) Acid-catalyzed ring-opening polymerization of tetrahydrofuran –CH
2 CH
2 CH
2 CH
2 O–
Terathane from Invista and PolyTHF from BASF

The phenyl ether polymers are a class of aromatic polyethers containing aromatic cycles in their main chain: Polyphenyl ether (PPE) and Poly(p-phenylene oxide) (PPO).

Related compounds Edit

Many classes of compounds with C–O–C linkages are not considered ethers: Esters (R–C(=O)–O–R′), hemiacetals (R–CH(–OH)–O–R′), carboxylic acid anhydrides (RC(=O)–O–C(=O)R′).

Ethers have boiling points similar to those of the analogous alkanes. Simple ethers are generally colorless.

Selected data about some alkyl ethers
Ether Structure m.p. (°C) b.p. (°C) Solubility in 1 liter of H2O Dipole moment (D)
Dimethyl ether CH3–O–CH3 −138.5 −23.0 70 g 1.30
Diethyl ether CH3CH2–O–CH2CH3 −116.3 34.4 69 g 1.14
Tetrahydrofuran O(CH2)4 −108.4 66.0 Miscible 1.74
Dioxane O(C2H4)2O 11.8 101.3 Miscible 0.45

The C-O bonds that comprise simple ethers are strong. They are unreactive toward all but the strongest bases. Although generally of low chemical reactivity, they are more reactive than alkanes.

Specialized ethers such as epoxides, ketals, and acetals are unrepresentative classes of ethers and are discussed in separate articles. Important reactions are listed below. [4]

Cleavage Edit

Although ethers resist hydrolysis, they are cleaved by hydrobromic acid and hydroiodic acid. Hydrogen chloride cleaves ethers only slowly. Methyl ethers typically afford methyl halides:

These reactions proceed via onium intermediates, i.e. [RO(H)CH3] + Br − .

Some ethers undergo rapid cleavage with boron tribromide (even aluminium chloride is used in some cases) to give the alkyl bromide. [5] Depending on the substituents, some ethers can be cleaved with a variety of reagents, e.g. strong base.

Peroxide formation Edit

When stored in the presence of air or oxygen, ethers tend to form explosive peroxides, such as diethyl ether hydroperoxide. The reaction is accelerated by light, metal catalysts, and aldehydes. In addition to avoiding storage conditions likely to form peroxides, it is recommended, when an ether is used as a solvent, not to distill it to dryness, as any peroxides that may have formed, being less volatile than the original ether, will become concentrated in the last few drops of liquid. The presence of peroxide in old samples of ethers may be detected by shaking them with freshly prepared solution of a ferrous sulfate followed by addition of KSCN. Appearance of blood red color indicates presence of peroxides. The dangerous properties of ether peroxides are the reason that diethyl ether and other peroxide forming ethers like tetrahydrofuran (THF) or ethylene glycol dimethyl ether (1,2-dimethoxyethane) are avoided in industrial processes.

Lewis bases Edit

Ethers serve as Lewis bases. For instance, diethyl ether forms a complex with boron trifluoride, i.e. diethyl etherate (BF3·OEt2). Ethers also coordinate to the Mg center in Grignard reagents. The cyclic ether thf is more basic than acyclic ethers. It forms complexes with many metal halides.

Alpha-halogenation Edit

This reactivity is similar to the tendency of ethers with alpha hydrogen atoms to form peroxides. Reaction with chlorine produces alpha-chloroethers.

Ethers can be prepared by numerous routes. In general alkyl ethers form more readily than aryl ethers, with the later species often requiring metal catalysts. [7]

The synthesis of diethyl ether by a reaction between ethanol and sulfuric acid has been known since the 13th century. [8]

Dehydration of alcohols Edit

2 R–OH → R–O–R + H2O at high temperature

This direct nucleophilic substitution reaction requires elevated temperatures (about 125 °C). The reaction is catalyzed by acids, usually sulfuric acid. The method is effective for generating symmetrical ethers, but not unsymmetrical ethers, since either OH can be protonated, which would give a mixture of products. Diethyl ether is produced from ethanol by this method. Cyclic ethers are readily generated by this approach. Elimination reactions compete with dehydration of the alcohol:

The dehydration route often requires conditions incompatible with delicate molecules. Several milder methods exist to produce ethers.

Williamson ether synthesis Edit

This reaction is called the Williamson ether synthesis. It involves treatment of a parent alcohol with a strong base to form the alkoxide, followed by addition of an appropriate aliphatic compound bearing a suitable leaving group (R–X). Suitable leaving groups (X) include iodide, bromide, or sulfonates. This method usually does not work well for aryl halides (e.g. bromobenzene, see Ullmann condensation below). Likewise, this method only gives the best yields for primary halides. Secondary and tertiary halides are prone to undergo E2 elimination on exposure to the basic alkoxide anion used in the reaction due to steric hindrance from the large alkyl groups.

In a related reaction, alkyl halides undergo nucleophilic displacement by phenoxides. The R–X cannot be used to react with the alcohol. However phenols can be used to replace the alcohol while maintaining the alkyl halide. Since phenols are acidic, they readily react with a strong base like sodium hydroxide to form phenoxide ions. The phenoxide ion will then substitute the –X group in the alkyl halide, forming an ether with an aryl group attached to it in a reaction with an SN2 mechanism.

Ullmann condensation Edit

The Ullmann condensation is similar to the Williamson method except that the substrate is an aryl halide. Such reactions generally require a catalyst, such as copper.

Electrophilic addition of alcohols to alkenes Edit

Alcohols add to electrophilically activated alkenes.

Acid catalysis is required for this reaction. Often, mercury trifluoroacetate (Hg(OCOCF3)2) is used as a catalyst for the reaction generating an ether with Markovnikov regiochemistry. Using similar reactions, tetrahydropyranyl ethers are used as protective groups for alcohols.

Preparation of epoxides Edit

Epoxides are typically prepared by oxidation of alkenes. The most important epoxide in terms of industrial scale is ethylene oxide, which is produced by oxidation of ethylene with oxygen. Other epoxides are produced by one of two routes:

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Thoughtful and coordinated approaches to implementation will enable educators to inspire future generations of scientifically literate students. That is the vision of the NGSS. This website provides a range of high-quality resources that empower educators, administrators, parents, and the general public to help bring this vision to life.

6 Class 4: Driven Self-Assembly (Kr≠1)

6.1 Concept

(3) (4) (5)

Class 4: Driven self-assembly. a) Kinetic asymmetry arises from the presence of different energy barriers for the fuel and waste reactions with respect to the unassembled (M) and assembled (M2) states. b) Energy diagram illustrating how kinetic asymmetry creates the conditions required for the permanent population of the high-energy assembly M2 under stationary conditions. The green trajectory represents the counterclockwise (green) direction of the cycle depicted in Figure 11 a. The dark green arrow corresponds to the process during which waste molecules are generated. The size of the dark red circles indicate the relative population of the respective state reported in previous simulations. 62


This equilibrium illustrates that the self-assembly of M to form M2 is now coupled to fuel consumption, thus permitting a transfer of energy between the two processes. Kinetic asymmetry in the system creates a situation in which a chemical fuel drives the self-assembly of M into M2. In this case, the identification of the high-energy molecule as a “fuel” that drives the system to a non-equilibrium state leaves no room for ambiguity. 41

6.2 Biology—Microtubule Formation

Microtubules are noncovalent protein polymers that play an essential role in intracellular organization. Microtubule filaments give structure and shape to eukaryotic cells, serve as tracks for intracellular transport, and are involved in chromosome segregation during cell division. Microtubule networks are highly dynamic structures which are continuously being remodeled through stochastic length fluctuations at the ends of the individual microtubules, a property referred to as dynamic instability. 137, 138 Dynamic instability manifests itself through periods of persistent microtubule growth which are occasionally interrupted by moments of rapid shrinkage (called “catastrophe”), followed by a switch back to polymer growth (called “rescue”). We will illustrate here that dynamic instability is a property that originates from kinetic asymmetry in the energy consumption pathway of this chemically fueled self-assembly process.

Microtubules are stiff, nanotubular structures with an outer diameter of around 25 nm (Figure 12). 19, 139 The subunit of microtubules is a heterodimer of α- and β-tubulin proteins—each with a mass of around 50 kDa—which associate in a head-to-tail manner to form linear structures called protofilaments. Typically, 13 such protofilaments engage in lateral interactions to form a microtubule. In the microtubule lattice, lateral interactions between protofilaments are α to α and β to β, except at the seam, where α-tubulin binds β-tubulin. As a result of the longitudinal arrangement of αβ-tubulins in protofilaments, microtubules have one end (−) where the α-subunits are exposed, and one end (+) where the β-subunits are exposed. Frequently, the (−)-end of microtubules is anchored to microtubule organizing centers, such as the centrosome. Dynamic instability occurs predominantly at the (+)-end of microtubules.

a) GTP-fueled self-assembly of microtubules. b) Structural changes in the αβ-tubulin dimer as a function of the occupancy of the E-site with GDP or GTP. Conversion of GTP into GDP in assembled tubulin leads to strain in the microtubule lattice. Figure inspired by Ref. 144 .

Microtubule assembly and disassembly is regulated by guanosine triphosphate (GTP Figure 12 a). Both α- and β-tubulin have a binding site for GTP, but these sites have very different properties and functions. 140 The binding site in α-tubulin (N-site) is buried within the tubulin dimer at the interface between α- and β-tubulin. GTP bound to the N-site plays a structural role and is non-exchangeable and non-hydrolysable. On the other hand, the binding site in β-tubulin (E-site) is exposed on the surface of free tubulin and on the terminal tubulin subunits located at the (+)-end of microtubules. The properties of this binding site change dramatically upon the incorporation of free tubulin onto the microtubule. With free tubulin, nucleotide exchange at the E-site is possible and the bound GTP is chemically stable. However, upon inclusion in the microtubule, nucleotides bound to the E-site become non-exchangeable and GTP is rapidly converted into GDP+Pi. 141, 142 The difference in the properties of the E-site between free and polymerized tubulin constitutes the basis for kinetic asymmetry in this process and for that reason it is relevant to discuss what happens upon polymerization from a structural point of view.

Microtubule formation initiates with an exchange of GDP by GTP in free tubulin. GDP-tubulin does not polymerize, but the exchange of GDP with GTP causes a conformational change in the T5 loop of β-tubulin, which activates tubulin for polymerization (Figure 12 b). 143, 144 Polymerization of GTP-tubulin is a thermodynamically favored process, which is evidenced by the fact that the use of non-hydrolysable analogues of GTP results in the formation of thermodynamically stable microtubules that do not display dynamic instability. 145 Two important processes occur when GTP-activated tubulin attaches to the microtubule (+)-end. Firstly, lateral and longitudinal interactions with the microtubule lattice cause a straightening of the tubulin, which in the free form is curved with a 12° kink at the dimer interface. Secondly, binding to the polymer activates the E-site for the catalytic cleavage of GTP into GDP+Pi, which occurs rapidly after association of GTP-tubulin with the microtubule following first order kinetics . Consequently, microtubules are composed mostly of GDP-tubulin, even though that unit by itself does not polymerize under equilibrium conditions. Importantly, the conversion of GTP into GDP compacts the tubulin structure, leading to an increase in lattice strain in the microtubule. The presence of lattice strain implies that these are high-energy structures composed of “spring-loaded” GDP-tubulin. The reason why the structure does not collapse originates from the presence of a stabilizing GTP cap at the (+)-end of the microtubule. Although the precise nature of the GTP cap is still under debate, there is consensus that the microtubule end must be regarded as a dynamic structure, where the amount of GTP-tubulin depends on the availability of free GTP-tubulin. 146 A reduced influx lowers the amount of stabilizing GTP-tubulin in the cap and increases the possibility that the entire microtubule will collapse (“catastrophe”).

Within the context of this Review, it is of relevance to recognize the elements that install kinetic asymmetry in the cycle that describes GTP-fueled microtubule formation. The observation that GDP–GTP exchange can only occur in the E-site of free tubulin implies that fuel activation involves only the building block and not the assembly. In addition, only the E-site of assembled tubulin is catalytically active, which implies that energy dissipation leads to the formation of a high-energy assembly composed of GDP-tubulin. Consequently, a kinetic preference for counterclockwise directionality exists in the system, which shows that GTP–GDP conversion and microtubule self-assembly are coupled processes. The structural analysis illustrates that the energy released from GTP is stored as lattice strain in the GDP-rich assembly.

6.3 Chemistry—Self-Assembled Fibers with Dynamic Instability

The installation of kinetic asymmetry has so far rarely been considered in the design of synthetic dissipative self-assembly processes. As discussed above, the main focus has been on the formation of the self-assembled structure, which in nearly all cases regards the thermodynamically stable self-assembly corresponding to M*2 in our general scheme. In most cases, little attention has been paid to the potential presence of the high-energy assembly M2, although, as we have seen in this section, it is the fuel-driven formation of this species that leads to valuable properties, such as the dynamic instability of microtubules. However, although kinetic asymmetry has not been actively sought for, experimental observations strongly suggest that some systems behave in a similar manner as microtubules.

Van Esch and co-workers reported on the chemically fueled self-assembly of fibers which displayed properties that strongly resembled the dynamic instability of microtubules (Figure 13). 147, 148 This system relied on the activation of N,N′-dibenzoyl- l -cysteine (DBC) for self-assembly by means of an esterification reaction with dimethyl sulfate. DBC by itself did not assemble under the experimental conditions (basic pH) because of electrostatic repulsion between the carboxylate groups. The addition of dimethyl sulfate, which is a strong methylating agent, caused the formation of the monoester of DBC, which self-assembled into bundles of fibers with micrometer dimensions, thereby leading to gelation of the aqueous solution. However, at the high experimental pH values, gradual hydrolysis of the methyl ester took place, which caused re-formation of the starting compound DBC, and spontaneous dissolution of the gel was observed over time. Similar to the example discussed in the Section 5.3, it was observed that the lifetime of the gel could be regulated by tuning the rates of the forward (fuel concentration) and backward reactions (pH).

Chemically fueled driven self-assembly of fibers that show features reminiscent of the catastrophic collapse of microtubules.

Two observations strongly suggested that the properties of the system were not solely governed by the thermodynamically stable fibers (M*n) composed of the monoester of DBC, but that also the unactivated building block DBC played a role in the self-assembly process. Firstly, a delay was observed between changes in the concentration of the monoester and the rheological behavior of the gel in the decay phase. For example, at pH 11, a gel state was still observed after 10 hours, whereas the concentration of the monoester had already dropped to 0.6 m m after 5 hours. The second observation came from a confocal microscopy study, which provided insight into the behavior of single fibers during the dissipative cycle. The addition of dimethyl sulfate at pH 11 resulted in the rapid formation of fibers, which reached a maximum length in a time that corresponded with the time required for the gel to reach the maximum storage modulus. Next, the fibers entered a shrinking regime and decreased in length. However, rather than the expected gradual and simultaneous shrinking of all fibers, a stochastic abrupt collapse of the fibers was observed, reminiscent of the collapse of microtubules. The fibers shrunk only from their ends a fracturing or homogeneous dissolution of the fibers was not observed. A time regime existed in which the growing and shrinking of fibers occurred simultaneously. Altogether, these observations are coherent with the formation of high-energy fibers that are (partially) composed of the non-activated building block DBC, obtained through the hydrolysis of the methyl esters of the building blocks in the fibers. The strong similarity with the dynamic instability of microtubules suggests that the fuel-driven cycle is regulated by a similar kinetic scheme. A detailed kinetic analysis of the activation and deactivation reaction steps would serve to unequivocally demonstrate the presence of kinetic asymmetry in this system.

Eleven Free Courses To Learn Bitcoin, Blockchain And Cryptocurrencies

Prague, Czech Republic - June, 2019: Main crypto currency coins next to each other: Bitcoin, . [+] Litecoin, Ripple, Monero, Ethereum.

One of the best (and worst) things about bitcoin, blockchain and cryptocurrencies is just how new the technology and its practical implementations are. Even though there have been many early adapters, the ecosystem as a whole involves a lot of learning, especially for those looking to come up to speed.

This represents a massive opportunity as well as a pitfall for those who are on the outside looking in. I like to monitor different courses in the space for my own education as well as for resources to share with others to include them as part of the discussion and learning: I've compiled this list as a set of reliable resources to do just that.

This free online course is taught by Andreas Antonopoulos (author of Mastering Bitcoin) and Antonis Polemitis and it represents the first course in the MSc in Digital Currency offered by UNIC. The course places bitcoin and cryptocurrencies in the broader framework of the history of money, before talking about the practical implementation of bitcoin, other cryptocurrencies, and the evolving relationship between digital currencies and financial institutions, as well as the broader world.

It requires no prerequisite knowledge of cryptocurrencies to dive in. There is a final exam component at the end that tests your grasp of the concepts taught.

2- Coinbase Learn

This simple set of interactive flashcards is a great resource for those who want to cover the basics of cryptocurrencies, from buying and selling to mining in a short amount of time. Other than a slight advertisement of Coinbase as safe and regulated, the mini-course remains an objective resource that covers a lot of ground in a surprisingly intuitive and short fashion. A great resource to share with absolute beginners who have little time on their hands and want to get up to speed fast.

This free Coursera course introduces basic cryptography concepts and then links them to the basics of Bitcoin. Through videos, the course lecturer explains how decentralization is implemented in practice, how Bitcoin mining works, and how Bitcoins are stored. A short explanation is then given to altcoins and the future of the space.

The course is offered by Princeton University, and though no certificate is presented for completion, the knowledge and way it's presented serves as a useful introduction to cryptocurrencies and Bitcoin principles, with an emphasis on the security of Bitcoin. The instructor, Arvind Narayanan is an assistant professor of computer science at Princeton who focuses on the security and stability of Bitcoin -- so that's naturally where his Coursera course gravitates towards.

You'll want to get more information about the rest of the ecosystem outside of Bitcoin elsewhere, but otherwise, this is a solid resource.

This UC Berkeley EdX course differentiates itself by also offering a dedicated section to the Ethereum Virtual Machine, along with a specific section focused on the game theory of what it would take to attack the Bitcoin blockchain -- a fresh approach to enumerating the theoretical security pitfalls of the system.

In an interesting twist, the two instructors were undergraduates who are part of the Blockchain @ Berkeley group. The course, like other EdX courses, is free to audit and take but will cost money ($99 USD) if you want a verified certificate to prove your completion.

This Youtube series focuses on some specific technical elements within bitcoin, from the components of private keys, to confronting the scaling and centralization risks sometimes inherent in the way bitcoin and cryptocurrencies are implemented in practice.

The learning section of the website (the official website for ethereum) includes a series of free resources that are curated together in lots of detail about ethereum, the second largest cryptocurrency by market capitalization. It dives into the smart contracts side of ethereum, as well as the basics, and also focuses on knowledge for the latest updates and roadmap for ethereum. At the end, a section is dedicated to criticism and other perspectives on how ethereum could be doing better -- leaving it a fairly well-balanced selection of knowledge about the ecosystem that is packaged like a curated course.

A free course with about two hours worth of video on the basics of distributed systems and its placement in the history of money. Perhaps a good resource for people who want to take a slightly slower pace than the Coinbase flashcards, but don't want to be fully immersed in different elements of blockchain and different parts of the ecosystem as with the fully-fleshed out courses presented by EdX and Coursera.

It's a free offering on Udemy that has also been used by about 40,000 other students.

This EdX course, offered through the Linux Foundation (which is building the HyperLedger framework) offers an introductory course to blockchain and what role HyperLedger plays in the space, as well as the tools available. It's built for a non-technical business audience, and is an introductory course to blockchain principles outside of the discussion around Bitcoin, Ethereum and other cryptocurrencies. The course itself is free, but a verified certificate from EdX will cost $99 USD.

This video course, developed in partnership with IBM, and taught by two developers in IBM's blockchain enablement division, goes over the basics of blockchain then leads to a demo and lab component where you can actually work with the HyperLedger framework and practice with it. You'll be able to use the HyperLedger Composer after this course. While slightly more technical, the level is still marked for beginners, even non-technical ones.

What's better than free? Earning money for learning. Coinbase offers a selection of introductory courses and quizzes in cryptocurrencies that don't often have a dedicated course, such as Dai (a stablecoin), EOS and privacy focused ZCash. This will allow any learner to get a more holistic view of altcoins and different cryptocurrencies than the standard courses focused on bitcoin and ethereum. You'll earn small amounts of the cryptocurrency in question for answering quiz questions on the topic, so you'll have a small amount to work with in practice after.

This mini-textbook course, offered by Ivey Business School in Canada (associated with the University of Western Ontario), focuses on a crash course to bitcoin in the framework of the economic impact and aspects of bitcoin activities. Consider it a mini-crash course in bitcoin that also ties it to its broader economic impact.

Watch the video: Biology ञववजञन class -48 Khan Sir Biology classes. #KhansirBiologyclass. #khansirpatna (January 2022).