diff --git a/docs/lectures/organic-chemistry/lesson-4_24-09-2024.md b/docs/lectures/organic-chemistry/lesson-4_24-09-2024.md index 8137ed5..744ab3b 100644 --- a/docs/lectures/organic-chemistry/lesson-4_24-09-2024.md +++ b/docs/lectures/organic-chemistry/lesson-4_24-09-2024.md @@ -30,7 +30,7 @@ Heteratoms and bonds are responsible for the reactivity on a particular molecule

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- Lone pairs make $\ce{O}$ a base and a nucleophile @@ -39,7 +39,7 @@ Heteratoms and bonds are responsible for the reactivity on a particular molecule - This creates electron-deficient sites (partial positive charge, $\delta^+$) on those carbons, making them electrophilic (prone to be attacked by nucleophiles).

- +

- The $\pi$ bond is easily broken. @@ -62,7 +62,7 @@ Heteratoms and bonds are responsible for the reactivity on a particular molecule ### Parts of a functional group

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- **Ethane** @@ -96,7 +96,7 @@ Ethane consists of **nonpolar $\ce{C-C}$ and weakly polar $\ce{C-H}$ bonds**, re Hydrocarbons are compounds make up of only the elements carbon and hydrogen; they may be aliphatic or aromatic

- +

- Aliphatic hydrocarbons have three subgroups @@ -112,13 +112,13 @@ Hydrocarbons are compounds make up of only the elements carbon and hydrogen; the - The **phenyl group**

- +

### Functional groups with carbon heteroatom $\ce{C-Z}$ $\sigma$ bonds

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The structure on the right shows a 3D molecular model where carbon is bonded to the heteroatom $\ce{Z}$ with an arrow indicating the direction of the electron density being pulled toward the more electronegative atom $\ce{Z}$. @@ -128,7 +128,7 @@ The structure on the right shows a 3D molecular model where carbon is bonded to > **Halogens** are highly reactive elements from Group 17 of the periodic table, including fluorine $\ce{F}$, chlorine $\ce{Cl}$, bromine $\ce{Br}$, and iodine $\ce{I}$. When a halogen forms a bond with another element, particularly carbon, the resulting compound is called a **halide**. Halides (e.g., alkyl halides) have polar carbon-halogen bonds due to the high electronegativity of halogens, making them reactive in organic chemical reactions like substitution and elimination.

- +

### Functional groups with $\ce{C-O}$ group @@ -137,7 +137,7 @@ The structure on the right shows a 3D molecular model where carbon is bonded to - The polar $\ce{C=O}$ bond makes the carbonyl carbon an electrophile, while the lone pairs on $\ce{O}$ allow it to react as a nucleophile and base

- +

**NOTE**: the carbonyl group also contains a bond that is more easily broken than a $\ce{C-O}$ bond @@ -145,7 +145,7 @@ The structure on the right shows a 3D molecular model where carbon is bonded to #### Atoms classification

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| **1. Carbon atoms** | **2. Hydrogen atoms** | **3. Alcohols and alkyl halides** | **4. Amines and amides** | @@ -154,11 +154,11 @@ The structure on the right shows a 3D molecular model where carbon is bonded to | 6-acetylmorphine | 6-acetylmorphine | Cortisol | Motuporamine B | | **Carbon atoms** are classified by the number of carbon atoms bonded to them; a 1° carbon is bonded to one other carbon, and so forth. | **Hydrogen atoms** are classified by the type of carbon to which they are bonded; a 1° hydrogen is bonded to a 1° carbon, and so forth. | **Alcohols and alkyl halides** are classified by the type of carbon to which they are bonded; a 1° alcohol has an OH group bonded to a 1° carbon, and so forth. | **Amines and amides** are classified by the number of carbon atoms bonded to the nitrogen atom; a 1° amine has one C–N bond, and so forth. |

- +

- +

#### Why all this fuss? @@ -198,7 +198,7 @@ In an ionic compound, such as sodium chloride $\ce{NaCl}$, the positively charge > Ion-ion interactions are among the strongest types of attractive forces in chemistry because they involve full charges and lead to the stable, rigid structures seen in many ionic solids. This is what gives ionic compounds distinct physical properties, like hardness and high thermal stability.

- +

This image describes **ion-ion interactions**, which are the strong electrostatic attractions that occur between oppositely charged ions in ionic compounds. These interactions are a type of **intermolecular force** but are much stronger than the forces found between covalent molecules. @@ -231,7 +231,7 @@ The strength of van der Waals forces increases with the size and surface area of - This can induce a temporary dipole in another molecule.

- +

#### var der Waals forces in relation with surface area @@ -239,7 +239,7 @@ The strength of van der Waals forces increases with the size and surface area of All compunds exhibit van der Waals forces $\rightarrow$ The larger the surface area of a molcules, the larger the attractive forces between two molecules, and the stronger the intermolecular forces.

- +

#### var der Waals forces and polarizability @@ -258,7 +258,7 @@ Dipole-Dipole interactions are the attractive forces between the permanent dipol **NOTE**: These attractive forces caused by permanent dipoles are much stronger than weak van der Waals forces

- +

#### Intermolecular non-covalent bonding forces @@ -268,7 +268,7 @@ Dipole-dipole interactions can occur when both the drug and the binding site hav This orientation is **beneficial** if it allows other functional groups on the drug to interact with the corresponding regions of the binding site effectively, enhancing the binding strength.

- +

However, if the dipoles align but the other binding groups on the drug are **not positioned correctly**, this orientation can be **detrimental**, reducing the effectiveness of the interaction. @@ -281,7 +281,7 @@ The strength of dipole-dipole interactions decreases with distance between the d #### Hydrogen bonding

- +

Hydrogen bonding typically occurs when a hydrogen atom bonded to O, N, or F, is electrostatically attracted to a lone pair of electrons on an O, N, or F atom in another molecule. @@ -293,7 +293,7 @@ They vary in strength between $\text{5-25 kJ/mol}$ and are weaker than electrost The electron deficient hydrogen is called a ***hydrogen bond donor*** $\rightarrow$ **HBD**. The electron rich heteroatom on the other hand is called a ***hydrogen bond acceptor*** $\rightarrow$ **HBA**.

- +

- $\ce{X-H}$ is a hydrogen bond donor (HBD), with the hydrogen being $\delta^+$. @@ -306,7 +306,7 @@ In this mechanism, a drug molecule may contain such donor or acceptor groups to In hydrogen bonds the inteaction involves orbitals and is **directional**, optimum orientation is where the $\ce{X-H}$ bond points directly to the lone pair on $\ce{Y}$ such that the angle between X, H and Y is $\ce{180°}$

- +

#### Typical H-Bond donors and Acceptors in eeceptor-proteins @@ -341,7 +341,7 @@ where $\propto$ denotes inverse proportionality. **NOTE**: Ionic bonds are the most important initial interactions as a drug enters the binding site

- +

Ionic bonds are the strongest non-covalent interactions, typically ranging from $\text{20-40 kJ/mol}$, because they involve full charges. This makes them much stronger than hydrogen bonds or van der Waals forces, which rely on partial or temporary charges. Unlike other interactions, the strength of ionic bonds decreases less rapidly with distance, meaning they remain effective over larger distances. Additionally, in hydrophobic environments where water can't interfere, ionic bonds become even stronger, playing a crucial role in stabilizing interactions in biological systems. @@ -369,14 +369,14 @@ The boiling point of a compund is referred to as the temperature at which liquid - A good example is water: it's high boiling point is due to its extensive hydrogen **bonding network**, which requires a significant amount of energy to break. This is why water boils at a much higher temperature than many other small molecules.

- +

- The relative strength of the intermolecular forces increases from pentane to butanal to 1-butanol. - The boiling points of these compounds increase in the same order.

- +

**Other factors contributing to the boiling point value** @@ -386,7 +386,7 @@ The boiling point of a compund is referred to as the temperature at which liquid - For example, **pentan-3-one** has a larger surface area than **acetone**, which results in stronger intermolecular forces and a higher boiling point (102°C for pentan-3-one vs. 56°C for acetone).

- +

- **Polarizability**: @@ -415,11 +415,11 @@ For covalent molecules of approximately the same molecular weight, the melting p - The stronger the intermolecular attraction, the higher the melting points.

- +

- +

#### The effect of symmetry on melting pointso @@ -427,7 +427,7 @@ For covalent molecules of approximately the same molecular weight, the melting p - For compunds having the same functional group and similar molecular weights, **the more compact and symmetrical the shape, the higher the melting point**.

- +

- A compact symmetrical molecule like neopentane packs well into a crystalline lattice whereas isopentane does not. It has a much higher melting point than isopentane. @@ -439,7 +439,7 @@ For covalent molecules of approximately the same molecular weight, the melting p Solubility is defined as the extend to which a compound, called a solute, dissolves in a liquid, called a solvent. The energy needed to break up the interactions between the molecules or ions of the solute comes from new interactions between the solute and the solvent.

- +

#### Solubility trends @@ -460,7 +460,7 @@ hexane). Most ionic compounds are soluble in water, but insoluble in organic solvents. To dissolve an ionic compund, the strong ion-ion interactions must be replaced by many weaker ion-dipole interactions.

- +

> 💡 What is an ion-dipole interaction? @@ -473,7 +473,7 @@ Most ionic compounds are soluble in water, but insoluble in organic solvents. To An organic molecule is water soluble only if it contains one polar functional group capable of hydrogen bonding with the solvent for every five $\ce{C}$ atoms in contains. Compare the solubility of butane and acetone in $\ce{H2O}$ and $\ce{CCl4}$

- +

#### Butane and acetone solubility @@ -481,7 +481,7 @@ An organic molecule is water soluble only if it contains one polar functional gr Since butane and acetone are both organic compounds, they are both soluble in the organic solvent $\ce{CCl4}$. Butane, which is nonpolar, is insoluble in $\ce{H2O}$. Acetone is soluble in $\ce{H2O}$ because it contains only three $\ce{C}$ atoms and its $\ce{O}$ atom can hydrogen bond with an $\ce{H}$ atom of $\ce{H2O}$.

- +

@@ -517,7 +517,7 @@ There are several different B vitamins, so a subscript is added just to distingu - Vitamin A is water insoluble because it contains only one OH group and 20 carbon atoms.

- +

#### Vitamin C @@ -527,7 +527,7 @@ There are several different B vitamins, so a subscript is added just to distingu - Each carbon atom is bonded to an oxygen which makes it capable of hydrogen bonding, and thus, water soluble.

- +

### Functional groups and electrophiles @@ -538,7 +538,7 @@ There are several different B vitamins, so a subscript is added just to distingu - An electronegative heteroatom like $\ce{N}$, $\ce{O}$, or $\ce{X}$ makes a carbon atom electrophilic, as shown below.

- +

- In the examples, a partially positive carbon atom ($\delta^+$) is attached to an electronegative atom (like $\ce{Cl} or $\ce{OH}$), making the carbon **electrophilic** (electron-poor), which is susceptible to attack by nucleophiles. @@ -548,25 +548,25 @@ There are several different B vitamins, so a subscript is added just to distingu A lone pair on a heteroatom makes it basic and nucleophilic

- +

$\pi$ bonds create nucleophilic sites and are more easily broken than $\sigma$ bonds.

- +

An electron-rich carbon reacts with an electrophile, symbolized as $\text{E}^+$. For example, alkenes contain an electron-rich double bond, and so they react with electrophiles $\text{E}^+$.

- +

Alkyl halides possess an electrophilic carbon atom, so they react with electron-rich nucleophiles.

- +

#### Biomolecules @@ -584,5 +584,5 @@ Alkyl halides possess an electrophilic carbon atom, so they react with electron- - **Lipids**: commonly form from fatty acids and alcohols

- +

\ No newline at end of file diff --git a/docs/lectures/organic-chemistry/lesson-5_27-09-2024.md b/docs/lectures/organic-chemistry/lesson-5_27-09-2024.md index 5dd03c3..33e005c 100644 --- a/docs/lectures/organic-chemistry/lesson-5_27-09-2024.md +++ b/docs/lectures/organic-chemistry/lesson-5_27-09-2024.md @@ -9,7 +9,7 @@ All C atoms in an alkane are surrounded by four groups, making them $\ce{sp^3}$ hybridized and tetrahedral, with all bond angles of $\text{109.5°}$. The 3D representation and ball-stick models for these alkanes indicate the tetrahedral geometry around each $\ce{C}$ atom.

- +

In contrast, the Lewis structures are not meant to imply any 3D arrangement. @@ -19,7 +19,7 @@ In contrast, the Lewis structures are not meant to imply any 3D arrangement. The three-carbon alkane $\ce{CH3CH2CH3}$ aka propane has a moleculer formula $\ce{C3H8}$. In the 3D representation, each $\ce{C}$ atom has two bonds in the plane, one in bond front and one bond behind.

- +

The five-carbon alkane $\ce{CH3CH2CH2CH2CH3}$ called pentane, has mol formula $\ce{C5H12}$. @@ -27,7 +27,7 @@ The five-carbon alkane $\ce{CH3CH2CH2CH2CH3}$ called pentane, has mol formula $\ The carbon skeleton for pentane can be drawn in a variety of ways really, each of the following representations has five carbons in a row and represents pentane (not an isomer of pentane).

- +

## Constitutional isomers @@ -35,7 +35,7 @@ The carbon skeleton for pentane can be drawn in a variety of ways really, each o There are two different ways to arrange four carbons, giving two compounds with molecular formula $\ce{C4H10}$, named butane and isobutane. Butane and isobutane are constitutional isomers—two different compounds with the same molecular formula. Constitutional isomers (also called structural isomers) differ in the way the atoms are connected to each other

- +

Butane is an example of a straight-chain alkane, while isobutane is a branched-chain alkane. This difference in structure influences their boiling points, melting points, and how they interact in chemical reactions. @@ -66,7 +66,7 @@ Butane is an example of a straight-chain alkane, while isobutane is a branched-c Cycloalkanes have a molecular formula of $\rightarrow$ $\ce{C_nH_2_n}$ and contain carbon atoms arranged in a ring. Simple cycloalkanes are named by adding the prefix _cyclo-_ to the name of the acyclic alkane having the same number of carbons.

- +

**NOTE**: these all have two fewer $\ce{H}$ atoms than an acyclic alkane with the same number of carbons @@ -104,7 +104,7 @@ Naming three or four alkyl groups is more complicated because the parent _hydroc An **alkyl group** is derived from an alkane (a hydrocarbon with only single bonds) by removing one hydrogen atom. This allows the group to bond to another molecule (such as another carbon chain). When you remove a hydrogen atom from different positions on a molecule, you can create different alkyl groups.

- +

#### Explanation using propane @@ -129,7 +129,7 @@ Would you like to go into more details about primary and secondary carbons, or h There are two different butane isomers which yield four possible alkyl groups containing four carbons.

- +

The prefixes like **"iso-"**, **"sec-"**, and **"tert-"** are used in the **naming of alkyl groups** to describe their **branching** patterns. These prefixes help specify how the alkyl group is attached and how the carbon atoms are arranged. Here's an explanation of each: @@ -164,7 +164,7 @@ The prefixes like **"iso-"**, **"sec-"**, and **"tert-"** are used in the **nami - **tert-Butyl** ($\ce{(CH3)3C-}$): A highly branched structure with the attachment at a **tertiary carbon**.

- +

### How to name an alkane using the IUPAC System @@ -172,31 +172,31 @@ The prefixes like **"iso-"**, **"sec-"**, and **"tert-"** are used in the **nami - **Step 1**: find the parent carbon chain and add the suffix

- +

If there are two chains of equal length, pick the chain with more substituents. In the following example, two different chains in the same alkane have seven $\ce{C}$ atoms. The left one identifies our main chain, as it contains a higher number of substituents.

- +

- **Step 2**: Numbering the atoms in the carbon chain to give the first substituent the lowest number.

- +

If the first substituent is the same distance from both ends, number the chain to give the second substituent the lower number

- +

When numbering a carbon chain results in the same numbers from either end of the chain, assign the lower number alphabetically to the first substituent

- +

- **Step 3**: Name and number the substituents. @@ -209,7 +209,7 @@ When numbering a carbon chain results in the same numbers from either end of the - and so forth.

- +

- **Step 4**: Combine substituents names and number + parent + suffixo @@ -218,7 +218,7 @@ When numbering a carbon chain results in the same numbers from either end of the - Precede the name of each substituent by the number that indicates its location

- +

**NOTE**: Separate numbers by commas and separate numbers from letters by hyphens. The name of an alkane is a single word, with no spaces after hyphens and commas. @@ -288,25 +288,25 @@ $$ - **Step 1**: find the parent cycloalkane

- +

- **Step 2**: name and number the substituents. No number is needed to indicate the location of a single substituent.

- +

For rings with more than one substituent, begin numbering at one substituent and proceed around the ring to give the second substituent the lowest number

- +

**Then, just as in alkanes**: with two different substituents, number the ring to assign the lower number to the substituents alphabetically.

- +

#### Naming alkanes vs. cycloalkanes @@ -314,7 +314,7 @@ For rings with more than one substituent, begin numbering at one substituent and If the number of carbons in the ring is greater than or equal to the number of carbons in the longest chain, the compound is named as a cycloalkane. If there are more carbons in the chain, the compound is named as an alkane.

- +

> **_Sidenote_** @@ -326,7 +326,7 @@ If the number of carbons in the ring is greater than or equal to the number of c A few examples more

- +

### Common Names for some Polycyclic Alkanes @@ -335,7 +335,7 @@ A few examples more - Many of these names were given long ago before the IUPAC system was adopted, and are still widely used. Additionally, some names are descriptive of shape and structure, like those below

- +

#### Fossil Fuels @@ -366,13 +366,13 @@ A few examples more Alkanes have low bp’s and mp’s compared to more polar compounds of comparable size. Bp and mp increase as the number of carbons increases due to increased surface area.

- +

The bp of isomers decreases with branching due to decreased surface area, while Mp increases with increased symmetry.

- +

### Conformation of acyclic alkanes @@ -380,7 +380,7 @@ The bp of isomers decreases with branching due to decreased surface area, while Conformations are different arrangements of atoms that are interconverted by rotation about single bonds

- +

Names are given to two different conformations: @@ -393,7 +393,7 @@ The angle that separates a bond on one atom from a bond on an adjacent atom is c For ethane in the staggered conformation, the dihedral angle for the $\ce{C—H}$ bonds is 60 degrees; for eclipsed ethane, it is 0 degrees.

- +

### Newman projections, drawing and understanding @@ -403,7 +403,7 @@ For ethane in the staggered conformation, the dihedral angle for the $\ce{C—H} - **Step 1:** Look directly down the C—C bond (end-on), and draw a circle with a dot in the center to represent the carbons of the C—C bond.

- +

- **Step 2:** Draw in the bonds. @@ -411,19 +411,19 @@ For ethane in the staggered conformation, the dihedral angle for the $\ce{C—H} - Draw the bonds on the back carbon $\ce{C}$ as three lines coming out of the edge of the circle.

- +

- **Step 3:** Add the atoms on each bond.

- +

### Newman Projections, Ethane

- +

- The **staggered** and **eclipsed** conformations of ethane interconvert at room temperature. @@ -438,19 +438,19 @@ The difference in energy between staggered and eclipsed conformers is $\text{~3 **NOTE**: ***Torsional strain*** is an increase in energy caused by eclipsing interactions.

- +

Another example of conformations is **propane**

- +

Energy minimums and maximums occur every 60° as the conformation swaps: staggered $\rightarrow$ eclipsed. Conformations that are in neither one of the two states are said to be intermediate in energy.

- +

Butane, like many other high mol weight alkanes have several $\ce{C-C}$ bonds, capable of rotation. @@ -460,11 +460,11 @@ Butane, like many other high mol weight alkanes have several $\ce{C-C}$ bonds, c A staggered conformation with two larger groups 180° from each other is called **anti** whereas a staggered conformation with two larger groups 60° from each other is called **gauche**.

- +

- +

The relative energies of the individual staggered conformations depend on their steric strain. **Steric strain** is an increase in energy resulting when non-bonded atoms are forced too close to each other. @@ -476,13 +476,13 @@ $$ $$

- +

#### Energy and dihedral angle values in buthane

- +

- Staggered conformations 1, 3, and 5 are at energy minima. @@ -508,7 +508,7 @@ The barrier to rotation determines how easily or freely a molecule can rotate ar Since the lowest energy conformations has all bonds staggered and all larger groups in an anti conformation, alkanes are drawn using zigzag skeletal structures to reflect this.

- +

### Angle strain in cycloalkanes @@ -518,32 +518,32 @@ Besides torsional and steric strain, the conformations of cycloalkanes are also **NOTE**: Cycloalkanes with more than three $\ce{C}$ atoms in the ring are not flat molecules. They are puckered to reduce strain.

- +

Cycloalkanes distort their shape in to alleviate angle and torsional strain

- +

The image below illustrates that if cyclohexane were flat, it would experience **angle strain** due to the bond angles being 120°, larger than the ideal 109.5°. Additionally, all hydrogens would be aligned in an **eclipsed conformation**, causing **torsional strain**.

- +

A flat cyclohexane structure would suffer from **angle strain**, as the bond angles (120°) deviate from the ideal tetrahedral angle (109.5°), and **torsional strain**, due to eclipsed hydrogens. Cyclohexane adopts a chair conformation to minimize these strains, creating a more stable, lower-energy structure.

- +

The chair conformation is so stable because it eliminates angle strain (all $\ce{C—C—C}$ angles are 109.5 degrees), and torsional strain (all hydrogens on adjacent $\ce{C}$ atoms are staggered).

- +

- In cyclohexane, three C atoms pucker up and three C atoms pucker down, alternating around the ring. @@ -564,14 +564,14 @@ The chair conformation is so stable because it eliminates angle strain (all $\ce - The bottom $\ce{C}$'s come out of the page, bonds to them are sometimes in bold

- +

- **Step 2**: label the up $\ce{C}$'s and the down $\ce{C}$'s on the ring - There are 3 up and 3 down, they alternate around the ring

- +

- **Step 3**: draw in the axial H atoms @@ -579,7 +579,7 @@ The chair conformation is so stable because it eliminates angle strain (all $\ce - On a down $\ce{C}$ the axial $\ce{H}$ is down

- +

- **Step 4**: Draw in the equatorial $\ce{H}$ atoms @@ -589,7 +589,7 @@ The chair conformation is so stable because it eliminates angle strain (all $\ce - *On an "up" carbon, the axial hydrogen points straight up, and the equatorial hydrogen points slightly downward*

- +

@@ -600,7 +600,7 @@ Cyclohexanes undergo a conformational change called **ring-flipping** As a result of a ring flip, the up carbons become down carbons and the down carbons become up carbons. Axial and equatorial $\ce{H}$ atoms are also interconverted during a **ring-flip**; axial $\ce{H}$ atoms become equatorial $\ce{H}$ atoms and equatorial $\ce{H}$ atoms become axial.

- +

[YT: visualize ring flipping](https://www.youtube.com/watch?v=DuX32urvZvQ) @@ -611,7 +611,7 @@ As a result of a ring flip, the up carbons become down carbons and the down carb There are two possible chair conformations, the equatorial position has more room than the axial position $\Rightarrow$ larger substituents are more stable in the equatorial positions.

- +

- Cyclohexane also can exist in a boat conformation. @@ -620,7 +620,7 @@ There are two possible chair conformations, the equatorial position has more roo The boat conformation is destabilized by torsional strain because the hydrogens on the four carbon atoms in the plane are eclipsed. Additionally, there is steric strain because two hydrogens at either end of the boat, the "flag pole" hydrogens, are forced close to each other.

- +

While less stable, the boat conformation is not a fixed state. Cyclohexane molecules are constantly undergoing a conformational change called "ring-flipping," which interconverts between different conformations, including the boat conformation. However, due to its higher energy, the boat conformation is less populated compared to the chair conformations at equilibrium. @@ -635,14 +635,14 @@ While less stable, the boat conformation is not a fixed state. Cyclohexane molec - This forms conformation $\ce{A}$

- +

- **Step 2**: Ring flip the cyclohexane ring - Convert the up $\ce{C}$'s to down $\ce{C}$'s and vice versa. The chosen $\ce{C}$ now puckers down.

- +

- **Step 3**: Add the substituents to the second conformation @@ -651,7 +651,7 @@ While less stable, the boat conformation is not a fixed state. Cyclohexane molec - This forms Conformation B.

- +

The two chair conformations of cyclohexane are different, so they are not equally stable. Larger axial substituents create destabilizing $\text{1,3-diaxial interactions}$. In methylcyclohexane, each unfavorable $\ce{H}$,$\ce{CH3}$ interaction destabilizes the conformation by $\text{0.9 kcal/mol}$, so Conformation $\ce{B}$ $\text{is 1.8 kcal/mol}$ less stable than Conformation $\text{A}$. @@ -667,9 +667,9 @@ Since there are two such interactions in Conformation B, the total increase in e > When a bulky group, such as a methyl group $\ce{CH3}$, is placed in an axial position on the cyclohexane ring, it can come into close contact with the axial hydrogens on the same side of the ring. These are called diaxial interactions because they involve two axial substituents (the methyl group and the hydrogen atoms).

- +

- +