Abstract

Polymers are one of the most important materials used in industry. No other material in the world can provide the properties of polymers. The main properties of polymers are influenced by their molecular weight. Various methods have been proposed to evaluate the molecular weight of polymers. Most of these methods require a lot of equipment and cost. One of the simplest and cheapest ways to evaluate the molecular weight of polymers is to measure their intrinsic viscosity. In fact, the amount of the intrinsic viscosity is a criterion for the amount of molecular weight. The intrinsic viscosity is obtained by the drainage time of the polymer solution in a capillary tube in compared to pure solvent. So far, many formulas have been proposed for obtaining the intrinsic viscosity of polymeric materials by drainage time data. In this article, some of the most important of these formulas are presented.

Keywords: intrinsic viscosity, capillary viscometer, relative viscosity, specific viscosity, single-data, multi-data

 Introduction

Molecular weight is the most important parameter of polymers. The properties of polymer materials are related to its molecular weight, thus one of the indirect methods for evaluating of polymer properties is remarking to its molecular weight.
There are different methods for achieving of polymer molecular weight. The viscometric method based on the study of interactions in dilute solutions of two polymers in a common solvent is one of the indirect methods to evaluating of polymer molecular weight. This method is conceptually and experimentally very simple.
The technique is based on the fact that dissolving a polymer in a solvent increases the viscosity of the final polymer solution. Then a parameter that is called intrinsic viscosity of that polymer and solution is calculated.

Various types of glass capillary viscometers, especially Ubbelohde-type glass capillary viscometers, are used for the determination of the intrinsic viscosity and other polymer parameters.

The intrinsic viscosity is related to the polymer’s molar mass and therefore reflects the material’s melting point, crystallinity and other properties. The Intrinsic Viscosity is dependent upon the length of the polymer chains. The longer the polymer chains are, the more entanglements between chains occur and therefore the viscosity value is higher.
intrinsic viscosity is the main indicator for the quality and the most important characteristic of polymers. calculating of intrinsic viscosity is a simple method for evaluating and classifying of properties of a polymer. For quality control by dilute solution viscometery, we can compare properties of different samples of one kind of a polymer material by comparing of their intrinsic viscosity.
The viscosity of the pure solvent and the viscosity of the polymer solution (polymer dissolved in solvent) are set in relation to each other, which leads to a relative viscosity value (ηr):

Where η is viscosity (poise) and t is drainage time (s) of liquid into the capillary viscometer. the sub-index “s” indicates “solution” and “0” indicates “pure solvent” viscosity.
The “specific viscosity” is calculated from:

The value of ηspc/C at the limiting concentration C →0 is the limiting viscosity number [η], more usually, called the intrinsic viscosity [η].

Several mathematical equations by different researchers and scientists is developed for calculating of intrinsic viscosity of polymer solutions. Generally, two methods for calculating of intrinsic viscosity is developed single-data and multi-data methods. In multi-point methods we need to more than one concentrations of the polymer in a Solvent for calculating of specific viscosity or relative viscosity while by using of Single-point method we can reach to intrinsic viscosity only by one capillary viscometery test.

Multi-point methods

The relationship between dilute solution viscosity and polymer concentration has been described by various functions, all of which have been used to obtain intrinsic viscosity by extrapolation to limiting zero concentration C. Here we mention some of the most famous of these equation that we use them in our software (MeasSoft Capillary viscometery).
These equations are found to be valid at low concentrations.

Huggins equation

The most extensively used equation is Huggins:

Where, KH is Huggins constant and is said to be a constant for a given polymer-solvent pair. Its value usually lies in between 0.3 (in a good solvent) and 0.5 (in a poor solvent). Thus, it is also a measure of solvent power for a polymer.

Kraemer equation

Other ordinary equation for calculating of intrinsic viscosity is Kraemer equation:

Where KK is Kraemer’s constant
In many polymer–solvent systems it has been proved that:
KH+KK = 0.5
(KH and KK are Huggins and kraemer constants, respectively.)

Schulz–Blaschke equation

The other equation is called Schulz–Blaschke equation:

where, ηsp is the specific viscosity and kSB is Schulz–Blaschke viscosity slope constant. The value of KSB was found to range between 0.3 and 0.4 and is almost independent on the molecular weight.

Arrhenius-Rother-Hoffmann

The other equation is called Arrhenius-Rother-Hoffmann:

Where KA is Arrhenius-Rother-Hoffmann constant.

Staudinger & Heuer

Staudinger & Heuer propose the following equation:

Where KS-H is Staudinger & Heuer constant

Martin

Martin proposed the following equation:

where KM is Martin constant.

Kreisa

Kreisa proposed the following equation:
where KKr is Kreisa constant.

Fuoss

Fuoss proposed the following equation:

where kFs is Fuoss constant.

Heller

Heller proposed the following equation:

where KHe is Heller constant.

Maron & Reznik

Maron & Reznik proposed the following equation:

where KH is Heller constant.

Maron-Reznik Modified equation

Maron-Reznik Modified equation is:

Single-point methods

The value resulting from the measurement for a single concentration may provide a good approximation to [η]. This gives rise to the so-called single-point procedures that avoid multiple measurements and extrapolation. In addition to saving work and reagents, such methods are the only choice when multiple dilutions are not feasible or practical.
if we have many data of capillary viscometery test. We can represent average of intrinsic viscosities plus standard deviation of them:

Solomon & Ciuta

Solomon & Ciuta equation is:

Deb and Chatterjee

Deb and Chatterjee equation is:

Palit and Kar

Palit and Kar have proposed equation:

Ram and Yaseen

Ram and Yaseen have developed this equation:

Billmeyer

Billmeyer have proposed this:

Heller

Heller equation is:

MeasSoft Capillary viscometery

MeasSoft provides a simple and user-friend program that calculate intrinsic viscosity of polymer solution by single and multi data methods. You can simply insert your drainage time of solutions and it simply give you intrinsic viscosities. You can access our prodoct from here and the video of this product from here.