Category: Physics Notes PPT

What are Elastomers?

Every day we are dependent upon products and use them as have developed through experimentation and discovery.  Having knowledge that evolves regarding the chemical properties, we understand the benefits of developing new products, including products that are made of elastomers.

Countless things like the tires allow the smooth movement of the car over the road. Also, the rubber storage containers in our kitchen and many things with flexible molecular structures are all elastomers. What makes these objects flex and return to original shape? Why are some products rigid compared to others? What holds these structures together? Let us learn more about elastomers.

Elastomers Definition

In chemistry, material made of a long chain of molecules is known as polymer and elastomer. It is known as the polymer having both viscous and elastic properties. A substance which is thick, sticky, and consistent somewhere between the solid and gas stage are known as viscous. How fast or slow a liquid flow is determined by the viscosity of the liquid. When you pour oil from a container, you will see that it pours much slower compared to water, since it is more viscous.

Properties of Elastomers

In chemistry, the bonds that hold several compounds together are very strong compared to size. The flexibility of the object is determined by the bond force and the compound’s ability to manipulate into different shapes.

• Comparatively, elastomers intermolecular forces are weak. The forces of repulsion and attraction between molecules and other particles are known as intermolecular forces.

• As elastomers are not tightly bonded together by attraction to their nucleus, they can stretch apart and have higher failure strain than many other compounds.

• The material that will fail at a molecular level when stain is imparted on them, they are known as non-elastic compounds.

• The elements used to make elastomers are carbon, silicon, hydrogen, and oxygen, which hold together well in different conditions.

Categories of Elastomers

As a consensus, there are two categories of elastomers:

When heated, thermoset elastomers do not melt. When exposed to different types of environmental conditions, they retain their structure. This property of elastomers makes them very useful in different industries where heat and pressure are applied at various levels since they will not break down.

Whereas, thermoplastic elastomers can be melted and reformed into different shapes and configured as per requirement and their use. E.g., you can think of a stick of butter when picturing thermoplastic elastomers. The stick can be cooled and melted many times and molded into different shapes while retaining its original properties.

Elastomers Examples

In manufacturing processes like injection molding, thermoplastic elastomers are used. Thermoplastic polyurethanes are used in many applications, including production of foam seating, seals, gaskets, etc.

All types of saturated and unsaturated rubbers and polysulfide rubbers

•  Natural Rubber – This is used in the manufacture of gaskets, shoe heels…

• Polyurethanes – This material is used in the textile industry for manufacturing elastic clothing such as lycra is also used as foam, wheels, etc.

• Polybutadiene – This type of elastomer material is used on wheels or tires of vehicles, giving them extraordinary resistance to wear and tear.

• Neoprene – This material is primarily used in manufacturing of wetsuits and is also used as wire insulation, industrial belts, etc.

• Silicone – This material is used in a variety of materials and areas since they have excellent chemical and thermal resistance. Silicon is used in manufacture of medical prostheses, pacifiers, lubricants, mold, etc.

Types of Elastomers

Following are the two types of elastomers:

1. Saturated elastomers

2. Unsaturated elastomers

Unsaturated Elastomers:

By using sulfur vulcanization unsaturated elastomers can be cured, and non-sulfur vulcanization is desired, for examples:

• Synthetic polyisoprene

• Butadiene rubber

• Neoprene rubber

• Nitrile rubber

• Butyl rubber

Saturated Elastomers:

This type of elastomers cannot be cured by sulphur vulcanization process, for examples:

• Ethylene propylene rubber (EPR)

• Ethylene-vinyl acetate (EVA)

• Polyacrylic rubber

• Silicone rubber

• Fluoroelastomers

• Polyether block amides.

• Chlorosulfonated polyethylene rubber

Do you know?

Elastomers are used to manufacture duckbills and diaphragms of plastic diaphragm check valves; also, O-rings and gasket seals. This is because of its unique physical and chemical properties. Most designing processes can benefit from a better understanding of elastomeric materials. 

Electric polarization is a part of the study of classical electromagnetism. If one has to define electric polarisation, it can be said that electric polarization (or polarization density or just polarization) is a vector field that defines the density of permanent or induced electric dipole moments in a dielectric material. Polarization is said to be completed when the dielectric is placed in an external electric field and gains an electric dipole moment.

Thus dielectric and polarization definition can be stated as ‘the electric dipole moment induced per unit volume of the dielectric material.’ It also explains the response of material on the applied electric field and how the material changes the electric field. It can be thus used to calculate the forces that come out due to these interactions. 

It is also compared with magnetization which measures the relative response of a material to a magnetic field in magnetism. The unit for measurement is coulombs per square meter and polarization is represented by a vector P. 

Dielectric Polarization Significance

The displacement of bound charged elements of dielectric material occurs due to the external electric field application. These elements cannot freely move around the material because they are bound to the molecules. Elements with a negative charge are displaced opposite and those with a positive charge move towards the field. An electric dipole moment is formed though the molecules are neutral in charge. 

Let’s say that a volume element ∆V in the material with a dipole moment ∆p, the polarization density P can be described as

P =  [frac {Delta p}{Delta V}]

Usually, the dipole moment ∆p varies from point to point within the dielectric therefore the polarization density P inside an infinitesimal volume dV with an infinitesimal dipole moment do is

P = [frac {dp}{dV}]

Qb is indicated for the bound charge of the result of polarization. ‘Dipole moment per unit charge’ is the definition that is now widely accepted. 

How to Explain Dielectric Polarization?

In an insulator or dielectric, the slight change in position of negative and positive charge takes place in opposite directions that are caused by an external electric field. The electrical polarization occurs when, because of the electric field, the negative electrons are pushed towards the positive atom nuclei surrounding it. This distortion of charges results in one side of the atom becoming a little negative and the opposite side becoming a little positive. 

However, in some chemically bound molecules like water molecules, polarization partially takes place due to the rotation of molecules into the same line under the influence of the electric field. 

Electric Polarization in Dielectrics 

Now we will define electric polarization and the effects of the application of electric fields in molecules. There are polar and nonpolar molecules. Let’s consider that Pi Pi is the induced electric polarization and u_i is the induced dipole moment. Now, the induced dipole moment is directly proportional to the strength of the electric field applied (E) . Hence, ui α E. Hyperpolarization occurs within the molecules if the electric force is very low, so we have to say that u_i = α_i F. Here, αi is the proportionality constant. Thus, this is the induced polarizability constant of the polarizing molecules,

Thus, the induced polarization of dielectric material in chemistry means the amount of induced moment in the polarized molecule when the unit electric field of the current strength is applied. 

Unit and Dimension of Polarizability 

The electric polarization constant has the dimension of volume and is derived from the definition and polarizing formula. Unit of dipole moment obtained from Coulomb’s law can be stated as esu X cm and force unit as esu cm^-2.

As the atom size, ionization energy, and atomic number increase, the polarizability of the atom increases. 

Dielectric and Polarization 

Dipolar polarization can be achieved by inducing an electric field in the molecules which can exhibit uneven distortion of the nuclei (distortion polarization). The ‘orientation polarization’ happens because of a permanent dipole (arising from 104.45 deg angle), for eg, oxygen and hydrogen atom in water.  

Effect of Temperature on Polarization –

The orientation polarization is zero because of the fixed polarized chemical bond and inability to orient in a fixed direction. Strong intermolecular forces oppose the free rotation of the polarized molecules like in a condensed system. This is the reason why molecules in carbon dioxide, ethane, propane, methane, nitrogen, hydrogen do not vary with temperature. 

However, molecules in many substances like benzyl alcohol, methyl chloride, hydrochloric acid, nitrobenzene, etc, are temperature-dependent and vary with varying temperatures. 

Clausius Mossotti Equation –

A relation between the polarizability of substances and the dielectric constant of the non-polar medium between the two plates is derived from electromagnetic theory. The distortion of 1 mole of the polarizing substance by a unit electric field gives rise to induced polarizability constant. Hence, the electric polarization constant formula – 

Dielectric constant (D) =  [frac {C}{C_0}]

where 

C = capacitance of the condenser having the polarized substance and 

C₀ = vaccum.

 

Therefore the dielectric is a dimensionless quantity shown with the unit of vacuum.   

Dielectric loss 

When a dielectric material is put through an AC voltage, the insulating material absorbs and dissipates electrical energy in the form of heat. This dissipation of this energy is known as dielectric loss.

A capacitor, which makes proper uses of another electrolyte to achieve more capacitance than the other form of capacitor, is known as an electrolytic capacitor. It is a liquid substance with a highly influential mixture of anion subatomic particles. Usually, three various types of capacitors are termed as an electrolytic capacitor. They are as follows 

• Aluminium electrolytic capacitor

• Tantalum electrolytic capacitor

• Niobium electrolytic capacitor

A particular type of electrolytic capacitor with the capacity to store hundreds and thousands of farads more electric charge is called supercapacitors. They are often familiar as a double-layer electrolytic capacitor.

Electrolytic Capacitor Uses

• All the capacitors under the electrolytic capacitor are neutralized. That is, the voltage of anode is always higher than that of the cathode. Due to the capability of massive electric charge storage, they are mostly employed to deliver low-pass signals. In electrical supply, they are profoundly implemented for noise filtering or decoupling. 

• Sometimes they are used in input and output smoothing. They are employed as a low-frequency filter if the signal is a DC one with a feeble AC constituent.

• Electrolytic capacitors are mostly found working as filters in loud-speakers. It aims to decrease the amplifier’s vibration. The vibration of the prime one is a 50Hz 60 Hz electrical sound persuaded from the mains supply. It could be heard if expanded.

Features of Electrolytic Capacitor

Let’s discuss some features of the electrolytic capacitor:

Accumulation of Capacitance

The electrical features of it depend mostly on the involved electrolyte and the anode. The ability to store an electric charge of the electrolytic capacitors, have huge forbearances 20% and accumulates at the minimum rate as the time goes on. An aluminium capacitor is implemented for this. Whose very little capacitance is 47µF can be anticipated to have a value of something between 37.6µF to 56.4µF.

Tantalum capacitors are also able to tolerate high, but their maximum working voltage is at the bottom. So they can’t work as a substitute for aluminium capacitors.

Electric Charge Storage Capacity, Worth, and Forbearances

The electrolyte and anode are mostly defined as the electrical features of a device. The results and the capacity to store electric charges are dependent on temperature and frequency. The capacitor with non-solid electrolytes contents shows a tremendous capacity over temperature and frequency than the solid electrolytes content capacitor. The basic measuring unit of the electric storage ability of an electrolyte capacitor is microfarad. The value of capacitance, which is mentioned by the producers in the datasheets, is known as nominal capacitance or rated capacitance. If the value of a device’s electrical storage capacity is measured at 1kHz frequency, it will be a 10 per cent deduction of 100/110Hz. The temperature there will be 200 c.

The capacity tolerance can be defined as the percentage of the permitted digression of the measured capacitance from the rated value. Some capacitors are very easy to use following the series of their endurance. Their values are stated hereunder:

• From the E3 series, the capacitance and tolerance capacity measured is ±20%, letter code “M.”

• In the series E6, measured capacitance and tolerance is ±20%, letter code “M.”

• For the E12 series, the valued capacitance and tolerance is±10%, letter code “K.” 

Advantages and Disadvantages of Electrolytic Capacitors

• Most of the storage capacity levels that the electronic capacitors have been obtained from a layer of gas on one plate. It is possible only with the involvement of absolute polarity. The formula will be like: capacitance (C) is the magnitude of charge (Q) on every plate divided by the voltage (V) involved with the plates: C=Q/V. The presence of this gaseous layer and generous dielectric effect provides an electrolytic capacitor, comparatively more capacitance in volume, than the other forms of capacitors.

• There are disadvantages, too, regarding the use of electrolytic capacitors. The possibility of leakage currents is very high in these capacitors. Value tolerances, equivalent series resistance capacity, and short life-span are some other drawbacks of these electrolytic capacitors.

Applications of Electrolytic Capacitors

• It is used to prevent voltage fluctuations in different filtering devices.

• When DC signal is weaker than AC, it is used as an input-output smoothing filter

• These types of capacitors are primarily employed for filtering noise or decoupling in electric supply.

• To control the coupling of signals between amplifier stages and to store power in flash lamps is another function of these capacitors.

The electron volt is not a frequently used unit, but it plays a vital role in electricity and magnetism, nuclear physics, etc. Now the question that arises is what is an electron volt? Basically, the electron volt is a unit of energy and is abbreviated as eV. 

In physics, an electronvolt is the amount of kinetic energy required by a single electron accelerating from rest through an electric potential difference of one volt. It is abbreviated as eV. 

An electron volt is a small unit of energy. When we want to move the charge having a value of 1 electron from lower potential to higher potential, then the charge will accelerate with some kinetic energy of 1eV. The electron volt (eV) is defined as: an electron volt is the amount of energy required to move a charge equal to 1e⁻ across a potential difference of 1eV.

Value of 1eV

We know that in order to move an electron with a potential difference of 1V, then the amount of work done is,

[Rightarrow W = qDelta V = 1e^{-} C (1V)frac{J}{C}]

[Rightarrow W 1eV = 1.6 * 10^{-19} J ]

Relation Between 1eV and Joules

Both electron volt and the joules can be related by unit conversions. One should always keep in mind that unit conversion can be done if and only if both measuring units are of the same scale. Here, both electron volt and joules are the units of energy and hence they are interchangeable.

So, the electron volt and joules have a relation given by:

[Rightarrow 1eV = 1.6 * 10^{-19} J ]

Therefore the value of one electron volt is equal to [1.6 * 10^{-19} J ].

The eV-Joule Conversion is very helpful in solving physics problems. The eV to Joule conversion table is given below:

eV to Joule Conversion

The Joule-eV Conversion is very helpful in solving problems related to electric charge in physics. The table for Joule to eV conversion is given below:

Joule to eV Conversion

Solved Examples:

1: A Particle Carrying Charge of 4e Falls through a Potential Difference of 4V. Calculate the Energy Acquired by the Particle.

Sol: We know that whenever an object falls from a higher level to a lower level the potential energy stored will release in the form of kinetic energy. Thus the energy acquired by the particle will be kinetic energy.

Given,

Charge of the particle = q = 4e 

The potential difference between two levels = ΔV = 4V 

We need to calculate the kinetic energy, then:

[Rightarrow K.E = qDelta V]

[Rightarrow  K.E = (4e)(4)]

[Rightarrow  K.E = 16 e]

[Rightarrow  K.E = 16 * 1.6  * 10^{-13} eV]

[Rightarrow  K.E = 25.6 eV]

Therefore, the energy acquired by a charge of 4e when it falls through a potential difference of 4V is 25.6eV.

2: Define Electron Volt and Prove that 1eV = [10^{-19} J].

Sol:  Electron Volt definition: An electron volt is the amount of energy required to move a charge equal to 1e⁻ across a potential difference of 1eV. This is how we define one e
lectron volt.

Now, to prove that the value of 1eV is [10^{-19} J] we will use the unit conversions for a better understanding.

Now, we know that in order to move an electron with a potential difference of 1V, then the amount of work done is,

[Rightarrow W = qDelta V = 1e^{-} C(1V) frac{J}{C}]

[Rightarrow W = 1eV = 1.6 * 10^{-19} Joules ]

Therefore, 1 electron volt is equal to 1.6 x 10⁻¹⁹ Joules.

3: What is the Value of One Mega Electron Volt?

Sol: 1 mega unit = [10^{6} eV]

Then, 1 mega electron volt is given by,

[Rightarrow 1MeV = 10^{6} * 1.6 * 10^{-19}]

[Rightarrow 1MeV = 1.6 * 10^{-13} eV]

Therefore, the value of one mega electron volt is  [10^{-13} eV].

The article covers all the important concepts of electron volt such as its conversion from one unit to another. Solved examples are also given in the above article that will help students to understand the unit of electron-volt.

Energy Bands Description 

In gases, the arrangement of molecules is not at all close, that is, they are far away from each other, and are loosely packed. The molecular arrangement in liquids is moderate, that is, the molecules are a little far away from each other. When it comes to solids, the molecules are so tightly packed or arranged that the electrons (a sub-atomic particle with an electric charge of negative 1) tend to move towards the orbitals of the neighbouring atoms. Consequently, the electron orbitals overlap as and when the atoms come together. Because of the intermixing of atoms in the substances of the solid-state, there will be a formation of energy bands, instead of the single energy levels. The set of energy levels, which are closely or tightly packed, are what we call the Energy Bands.

 

Classification of Energy Bands 

Valence Band 

Although the electrons move in the atoms in certain energy levels, the energy of the electrons present in the innermost shell is higher than the energy of the electrons present in the outermost shell. Valence electrons are the electrons, which are present in the outermost shell. The valence electrons contain a series of energy levels and form an energy band known as the valence band. The valence band is the band, which has the highest occupied energy.

 

Conduction Band 

The valence electrons are not held tightly or firmly to the nucleus, due to which, even at room temperature, a few of the valence electrons leave the valence band to become free. They are referred to as the free electrons because of the fact that they tend to move towards the neighbouring atoms. The free electrons conduct the current in the conductors and are therefore known as the conduction electrons. The conduction band is the one that contains the conduction electrons and has the lowest occupied energy levels.

 

Forbidden Energy Gap

The forbidden energy gap refers to the gap between the valence band and the conduction band. As the name suggests, the forbidden energy gap has no energy as a result of which no electron stays in this energy band. While going to the conduction band, the valence electrons pass through the forbidden energy gap. If the forbidden energy gap is greater, then the valence band electrons are tightly bound or firmly attached to the nucleus. For pushing the electrons out of the valence band, we require some amount of external energy equal to the forbidden energy gap.

The figure given below shows the conduction band, valence band, and the forbidden energy gap. Based on the size of the forbidden energy gap, the conductors, semiconductors, and insulators are formed.

 

Conductors 

Conductors are the substances or materials that conduct electricity as they allow electricity to flow through them. The forbidden energy gap disappears in the conductors, as the conduction band and the valence band come close to each other and overlap. Copper, gold, and silver are a few examples of conductors. The figure given below shows the structure of energy bands in conductors.  

 

The Characteristics of Conductors are as Follows:

• There is no forbidden energy gap in a conductor.

• The valence band and the conduction band overlap in conductors.

• There are a high number of free electrons available for the conduction of electricity.

• With a slight increase in voltage, there is an increase in the conduction as well.

• No concept of hole formation is there because the continuous flow of electrons contributes to the current produced.

 

Insulators

Insulators are the substances or materials that don’t conduct electricity as they don’t allow electricity to flow through them. The forbidden energy gap in the insulators is large enough due to which the conduction of electricity can’t take place. Rubber and wood are a few examples of insulators. The figure given below shows the structure of energy bands in insulators.

 

The Characteristics of Insulators are as Follows:

• The forbidden energy gap is large enough in insulators with a value of 10eV.

• The electrons in the valence band are tightly bound or firmly attached to atoms.

• Some insulators might show conduction with an increase in the temperature.

 

Semiconductors 

Semiconductors are substances or materials having conductivity between the conductors and the insulators. In semiconductors, the forbidden energy gap is small, and the conduction of electricity will take place only if we apply some external energy. Germanium and silicon are a few examples of semiconductors. The figure given below shows the structure of energy bands in semiconductors.

 

The Characteristics of Semiconductors are as Follows:

• The forbidden energy gap is small in a semiconductor.

• For Germanium (Ge), the value of the forbidden energy gap is 0.7eV, and for Silicon (Si), it is 1.1eV.

• The conductivity of semiconductors increases with the rise in temperature.

• Semiconductors are neither a good conductor or an insulator.

What Are Significant Figures?

In Mathematics, we encounter questions where the solution comes out as 7.73. 

We have a practice of rounding off the figures; here, we may get confused that can 7.73 be written as such or 7.7 or 7.730 or 7.70?

Let’s take another example:

Suppose your friend’s salary got incremented to ₹55,000. Now, he tells his salary as ₹55,000, however close to the exact amount. 

Which means he told the rounded-off amount to you.

The above examples were to explain the significance of the figures or digits.

So, what is the definition of significant figures?

Significant figures in the measured value of a physical quantity which tells the number of digits in which we have a surety.

What Do You Understand by Significant Figures?

Let’s say you have a rod, and its length is measured 25.3 cm.

Here, the digit after the decimal point is called the ‘Doubtful digit’.

It’s because the measurement can be 25.2, or 25.28 or 25.345 cm as we are not confident about the value to be preferred, while the digits in the number ‘25’ are accurate because we have confidence upon these digits.

Significant Digits = Adding all the accurate digits + First doubtful digit.

There are common rules for counting significant figures that are discussed further.

What Are the Rules for Determining Significant Figures?

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Following are the common rules for counting significant figures in a given expression:

1. Rule 1: All non-zero digits are significant

For example, we have a number 7.744

It has four significant digits.

2. Rule 2: All zeroes occurring between two non-zero digits are significant

For example, 2007 has four significant digits, and 1.08079 has six significant digits.

3. Rule 3: Ending zeroes: The ending zero will be significant, if and only if, it is after the decimal.

For example, in a number, 3.400, the ending zero is after the decimal is significant. Now, according to rule 2, if the zeroes occur between the two significant digits, then they are also significant.

So, the number, 3.400, has four significant figures, i.e., 3, 4, 0, 0.

4. Rule 4 or Rule of Initial Zeroes: In a number less than one, all zeros to the right of the decimal point and the left of non-zero digits are NOT significant.

In simple words, the zeroes at the initial zeroes are not significant.

Let’s take a number, 0.00078

Here, we can see 0 at the initial (before the decimal point), which is not significant and the three non-ending zeroes. 

So, 0.00078 has two significant digits.

Let’s say, a number, 0.9080

Here initial zero is insignificant, and 9080 has four significant digits.

5. Rule 5: All zeroes on the right of the last non-zero digits in the decimal part are significant.

For example, a number, 0.00700, has three significant figures 7, 0, 0.

6. Rule 6: All zeroes on the right of non-zero digits are NOT significant.

Here, we have numbers like 420, 4300; the ending zero is not after the decimal.

So,  zero is not significant, and they have two significant digits only.

7. Rule 7: Power of 10 is insignificant

For example, 3.4 x 108 is the number, having 108 ending zeroes, but the power of 10 is always insignificant and having only two significant digits, i.e., 3 and 4.

Rules for Arithmetic Operation of Significant Figures

1. Addition 

Let’s say the sum of three measurements of length; 3.2 m, 1.88 m, and 1.056 m  is 6.136 m, rounded off to 6.1 m.

2. Subtraction

If we take x = 15.87 m, and y = 15.8 m, then,

x  – y = 15.87 – 15.8 = 0.07 m, which is rounded off to 0.1 m.

In the subtraction of quantities, the magnitude and accuracy are almost destroyed.

Here, 15.87 has four significant figures and 15.8 has three. So, on subtracting these two numbers, we get 0.01 m which has one significant digit.

3.  Multiplication

For example, x = 3.5 and y = 2.125, then xy = 7.4375

Here, out of 3.5 and 2.125, 3.5 has the least significant digits, i.e., 2. 

So, rounding off 7.4375 to two significant digits, which is 7.4.

4. Division

If x = 9600, y = 11.25, then

x/y = 9600/11.25 = 853.33..

Here, 9600 has the least significant digits, i.e., 2. So, the answer will also have two significant digits.

Therefore, 853.33 is rounded off to 830.

Error Arithmetic Operations of Significant Figures

Relative error or fractional error and percentage error

Relative error or fractional error is calculated by the formula:

 =  mean absolute error/ mean value = Δμ’/μ

Percentage error is calculated by the formula:

= Δμ’/μ x 100 %

The measurements of different rods have got these values 4.2, 3.5, 4.7, 4.4, and 5.4, respectively. Find the mean value, relative, and the percentage error.

Here, mean (μ) = (4.2 + 3.5 + 4.7+ 4.4 + 5.4)/5 = 4.44 ≈ 4.4

 Absolute errors in measurement are:

Δμ1 = 3.5 – 4.2 = – 0.7

           Δμ2 = 4.7 – 3.5 = 1.2

           Δμ3 = 4.4 – 4.7 = – 0.3

           Δμ4 = 5.4 – 4.4 = 1.0

So, mean absolute error, Δμ’ = (- 0.7 + 1.2 – 0.3 + 1.0)/4 = 0.3

Relative error: Δμ’/μ = 0.3 / 4.4 = +/- ≈ 0.068 ≈ 0.1

Percentage error: 0.1 x 100% = +/- 10 %