One of the ways to measure the average molecular weight of polymers is viscosity of solution. Viscosity of a polymer depend on concentration and molecular weight of polymers. Viscosity techniques is common since it is experimentally simple. Molecular weight distribution is one of the important characteristic of polymer because it affects polymer properties.
There are various molecular weights in the range of curve. The distribution of sizes in a polymer sample isn't totally defined by its central tendency. The width and shape of distribution must be known.
The equality is occurring when all polymer in the sample have the same molecular weight. Gel permeation chromatography is also called size exclusion chromatography. It is widely used method to determine high molecular weight distribution. In this technique, substances separate according to their molecule size.
The sample is injected into the mobile phase then the mobile phase enters into the columns. Retention time is the length of time that a particular fraction remains in the column. GPC gives a full molecular distribution, but its cost is high. K is a distribution coefficient related to the size and types of the molecules.
Solvent leaves the solvent supply, then solvent is pumped through a filter. The desired amount of flow through the sample column is adjusted by sample control valves and the reference flow is adjusted that the flow through the reference and flow through the sample column reach the detector in common front.
The reference column is used to remove any slight impurities in the solvent. In order to determine the amount of sample, a detector is located at the end of the column. Also, detectors may be used to continuously verify the molecular weight of species eluting from the column. The flow of solvent volume is as well monitored to provide a means of characterizing the molecular size of the eluting species. After polymerization, the molecular weight increased because of the progress of lactide polymerization initiated from end of PEG chain.
One of the most used methods to characterize the molecular weight is light scattering method. When polarizable particles are placed in the oscillating electric field of a beam of light, the light scattering occurs. Light scattering method depends on the light, when the light is passing through polymer solution, it is measure by loses energy because of absorption, conversion to heat and scattering.
The intensity of scattered light relies on the concentration, size and polarizability that is proportionality constant which depends on the molecular weight. A major problem of light scattering is to prepare perfectly clear solutions.
This problem is usually accomplished by ultra-centrifugation. A solution should be as possible as clear and dust free to determine absolute molecular weight of polymer. Also, it can be performed rapidly with less amount of sample and absolute determinations of the molecular weight can be measured. The weaknesses of the method is high price and most times it requires difficult clarification of the solutions.
Experiments are performed at several angles and at least at 4 different concentrations. The straight line extrapolations provides M w. X-rays are a form of electromagnetic wave with wavelengths between 0. X-ray scattering is particularly used for semicrystalline polymers which includes thermoplastics, thermoplastic elastomers, and liquid crystalline polymers.
Two types of X-ray scattering are used for polymer studies:. At least two SAXS curves are required to determine the molecular weight of a polymer. The SAXS procedure to determine the molecular weight of polymer sample in monomeric or multimeric state solution requires the following conditions. The solution should be dilute enough to avoid spatial correlation effects. Osmometry is applied to determine number average of molecular weight M n.
There are two types of osmometer:. When molecular weight is more than that limit, the quantity being measured becomes very small to detect. Vapor pressure is very sensitive because of this reason it is measured indirectly by using thermistors to measure voltage changes caused by changes in temperature. The solvent is separated from the polymer solution with semipermeable membrane that is strongly held between the two chambers.
One chamber is sealed by a valve with a transducer attached to a thin stainless steel diaphragm which permits the measurement of pressure in the chamber continuously. In this technique, there are problems with membrane leakage and symmetry.
Properties of polymers depend on their molecular weight. There are different kind of molecular weight and each can be measured by different techniques. Size exclusion chromatography SEC is a useful technique that is specifically applicable to high-molecular-weight species, such as polymer.
It is a method to sort molecules according to their sizes in solution. The sample solution is injected into the column, which is filled with rigid, porous, materials, and is carried by the solvent through the packed column. The sizes of molecules are determined by the pore size of the packing particle in the column within which the separation occurs. For polymeric materials, the molecular weight M w or molecular size plays a key role in determining the mechanical, bulk, and solution properties of materials.
It is known that the sizes of polymeric molecules depend on their molecular weights, side chain configurations, molecular interaction, and so on. For example, the exclusion volume of polymers with rigid side group is larger than those with soft long side chains.
Therefore, in order to determine the molecular weight and molecular weight distribution of a polymer, one of the most widely applied methods is gel-permeation chromatography. Gel permeation chromatography GPC is a term used for when the separation technique size exclusion chromatography SEC is applied to polymers. The primary purpose and use of the SEC technique is to provide molecular weight distribution information about a particular polymeric material.
Typically, in about 30 minutes using standard SEC, the complete molecular weight distribution of a polymer as well as all the statistical information of the distribution can be determined. Thus, SEC has been considered as a technique essentially supplanting classical molecular weight techniques. To apply this powerful technique, there is some basic work that needs to be done before its use. The selection of an appropriate solvent and the column, as well as the experimental conditions, are important for proper separation of a sample.
It is well known that both the majority of natural and synthetic polymers are polydispersed with respect to molar mass.
For synthetic polymers, the more mono-dispersed a polymer can be made, the better the understanding of its inherent properties will be obtained. A polymer is a large molecule macromolecule composed of repeating structural units typically connected by covalent chemical bonds. Polymers are common materials that are widely used in our lives. One of the most important features which distinguishes most synthetic polymers from simple molecular compounds is the inability to assign an exact molar mass to a polymer.
This is a consequence of the fact that during the polymerization reaction the length of the chain formed is determined by several different events, each of which have different reaction rates. Hence, the product is a mixture of chains of different length due to the random nature of growth. In addition, some polymers are also branched rather than linear as a consequence of alternative reaction steps.
The molecular weight M w and molecular weight distribution influences many of the properties of polymers:. Consequently, it is important to understand how to determine the molecular weight and molecular weight distribution. Simpler pure compounds contain the same molecular composition for the same species. For example, the molecular weight of any sample of styrene will be the same In contrast, most polymers are not composed of identical molecules.
The molecular weight of a polymer is determined by the chemical structure of the monomer units, the lengths of the chains and the extent to which the chains are interconnected to form branched molecules. Because virtually all polymers are mixtures of many large molecules, we have to resort to averages to describe polymer molecular weight. The polymers produced in polymerization reactions have lengths which are distributed according to a probability function which is governed by the polymerization reaction.
There are several possible ways of reporting polymer molecular weight. Three commonly used molecular weight descriptions are: the number average M n , weight average M w , and z-average molecular weight M z. Bulk properties weight average molecular weight, M w is the most useful one, because it fairly accounts for the contributions of different sized chains to the overall behavior of the polymer, and correlates best with most of the physical properties of interest. There are various methods published to detect these three different primary average molecular weights respectively.
For instance, a colligative method, such as osmotic pressure, effectively calculates the number of molecules present and provides a number average molecular weight regardless of their shape or size of polymers. The weight average molecular weight of a polymer in solution can be determined by either measuring the intensity of light scattered by the solution or studying the sedimentation of the solute in an ultracentrifuge.
From light scattering method which is depending on the size rather than the number of molecules, weight average molecular weight is obtained. This work requires concentration fluctuations which are the main source of the light scattered by a polymer solution.
The intensity scattered by molecules N i of molecular weight M i is proportional to N i M i 2. The polydispersity index PDI , is a measure of the distribution of molecular mass in a given polymer sample. The equality of M w and M n would correspond with a perfectly uniform monodisperse sample.
The ratio of these average molecular weights is often used as a guide to the dispersity of the chain lengths in a polymer sample. The properties of a polymer sample are strongly dependent on the way in which the weights of the individual molecules are distributed about the average.
For example, polystyrene and its block copolymer polystyrene-b-polyisoprene have quite narrow distribution. Every hexane molecule has a molecular weight of Now if we add another carbon to our chain, and the appropriate amount of hydrogen atoms, we've increased our molecular weight to That's fine, but the molecule is no longer hexane.
It's heptane! If we have a mixture of some molecules of hexane and some of heptane, the mixture won't act like pure heptane, nor will it act like pure hexane. The properties of the mixture, say, its boiling point, vapor pressure, etc. But polymers are different. Imagine polyethylene. If we have a sample of polyethylene, and some of the chains have fifty thousand carbon atoms in them, and others have fifty thousand and two carbon atoms in them, this little difference isn't going to amount to anything.
If you really want to know the truth, one almost never finds a sample of a synthetic polymer in which all the chains have the same molecular weight. Instead, we usually have a bell curve, a distribution of molecular weights. Some of the polymer chains will be much larger than all the others, at the high end of the curve. Some will be much smaller, and at the low end of the curve. The largest number will usually be clumped around a central point, the highest point on the curve.
So we have to talk about average molecular weights when we talk about polymers. And we're not going to stop there. The average can be calculated in different ways, and each way has its own value.
So let's talk about some of these averages, why don't we? It is just the total weight of all the polymer molecules in a sample, divided by the total number of polymer molecules in a sample. It's based on the fact that a bigger molecule contains more of the total mass of the polymer sample than the smaller molecules do. Demographics A good way to understand the difference between the number average molecular weight and the weight average molecular weight is to compare some American cities.
Now we'll take a look at their populations. Now let's calculate the simple average population of the four cities: Now we see that of these four cities, that average population is , It has a value greater than or equal to one: it is equal to one only if all the molecules have the same weight i.
The molecular weight distribution can be shown graphically by plotting the number of molecules against the molecular weight. It is worth noting that these plots are sometimes shown with molecular weight decreasing along the x -axis. In many cases, it is important to know not only the average molecular weight, but also the distribution of molecular weights. This is illustrated in the example below, in which no molecules would actually have a weight equal to the number average molecular weight, since this would lie between the two peaks.
Number average molecular weight, M N The number average molecular weight is defined as the total weight of polymer divided by the total number of molecules.
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