Physical Properties of Polymers

Muhammad Zafar Iqbal

Date: 24-04-2008

Today

The Development of High Elasticity

• Introduction• Creep Function and its relation to High Elasticity• Orientation time: Predictions without much validity• The effect of Frequency and Temperature on

Elasticity

Introduction• High elasticity is caused by uncoiling of chains• Rate of Uncoiling: Big Issue todayIn general, there are always two things to find:

1- Prediction of position of Equilibrium2- Rate of Approach to that equilibrium

• Equilibrium position can easily be identified through some definite constant values of physical property changes

• Rate is difficult to predict

• Today: Focus on uncoiling of chains per unit time on molecular basis.

The Creep FunctionSince we know that,

Here f(t) is called the creep function.It describes the development of creep quantitatively and

approaches to unity as creep is fully developed. Theoretically, you can also derive

Creep function from deformation-timeCurve by just subtracting the Proportions of ordinary and viscousDeformations.

Creep function’s molecular basisIs not thoroughly admitted butConsistent with some of experimental work.

Orientation Time• Recent works have shown that one can treat development of

high elasticity as a unimolecular reaction with rate constant 1/T (tow).

• Each chain uncoils independently and randomly.• On the basis of this orientation time, creep function will be

• Quantitatively, T is the time taken by the deformation to reach 1-1/e of its final equilibrium value.

• Qualitatively, T is called the orientation time and is a measure of response of chains to the orienting influence of stretching forces.

• For the above equation to be true, ln (1-f(t)) Vs t should be a straight line with slope (-1/T) but it does not come so.

• For this purpose, alternative approach was being defined.

• A no. of different uncoiling mechanisms operate in the system and each mechanism has a characteristic T value, Ti. As each chain is not likely to be surrounded by the same set of hindering forces, a set of orientation times about a mean value is quite feasible and we may write deformation as:

Where Di(infinity) is the equilibrium deformation and Ti is the orientation time of ith chain.

• But in the same way, the above equation has lost its simplicity because no. of variables involves in increase tremendously. Because Ti for each effect should be calculated independently and Ti for each uncoiling factor is very difficult to calculate.

• For this purpose, we assume that there are two or three mechanisms operating there.

• Where A1 and A2 are the fractional contributions of each factor and their sum must be equal to unity in any case.

For most of the cases, we observe the following D-log t curve

In most of the cases, we can measure this linear portion only. This typeof D-log t behavior can only be seen byassuming 2 to 3 T values but it is very difficult to see the actual molecular picture ofthis process by calculating all the T values

Due to these reasons, it is often more convenient to define creep function in terms of Tm which is the average orientation time due to all contributing factors.

The values of Tm and t quantify whether or not a polymer will show high elasticity.

If (Tm >> t ): Highly elastic deformation may be negligibly small and the total deformation measured will be ordinary elastic.

If (Tm<< t): (1- e –t/Tm) will tend to be zero, it means that high elastic deformation has reached its equilibrium value in a time less than the experimental time scale. The material will behave like a rubber.

Same is true for overall elastic modulus:And also,

Effect of Frequency and TemperatureThe transitions from a rubber to hard, brittle behavior can be

achieved by:1- Decreasing the time of stressing2- Increasing the effective orientation time

Tm if decreased can lead to rubbery behavior and this can be done by increasing temperature or by adding a plasticizer.

The variation of Tm with temperature is found to be:Where E is activation energy = 30-100 KcalThe D-t relationship will be now,If the activation energy of a chemical reaction is 30 Kcal,

temperature is increased by 10 0C, then rate of reaction is increased to 5 time the previous one.

Higher the E-value, more sensitive is the reaction to temperature.

For a polymer:E = 60 KcalTm = 100 Sect = 100 SecTemperature = 27 0C = 300 K

It means the transformation from rubbery to brittle behavior is very sharp ifthe polymer has high E-value.i.e. below this temperature, the material will break sharply under applied stress and its extensions at rupture is very little.Above this brittle point, the polymer stretches lazily and shows larger deformation.

A brittle point is the temperature at which the material has a definite but unknown Tvalue and most of times this is called Iso-elastic temperature.

Some aspects of brittle point• The material becomes brittle when t/Tm falls below a critical value.

This occurs when Tm exceeds a critical value.• Ideally the full Tm-Temperature relationship is needed to specify a

polymer but most of time, the only thing that we know is “SINGLE BRITTLE POINT”.

• Although exact Tm values are unknown, the brittle points of a series are quite useful in comparing the elastic properties of those polymers.

• Following is the data of experimentations conducted on single plasticized PVC in which effect of experimental conditions on brittle point was observed.

• In this experiment, a strip of definite thickness is bent round a mandrel at a definite speed. Here the brittle point is the minimum temperature at which this strip does not break under the test conditions.