It is very much important to determine the average molecular weight of a polymer as their properties depend on it. Not all polymer molecules of a particular grade have the exact same molecular weight. The number average molar mass is a way of determining the molecular mass of a polymer. It can be shown that the weight average molecular weight is a good measure for the expected statistical size of the polymer, whereas the number average molecular weight is a measure for the chain length. According to these methods, m n and m w are determined from the diffusion constant vs. Typical polymers consist of mixtures of many molecular species and molecular weight methods always provide average values. Polymers contain a wide range of chains with different molecular weight, unlike many other substances. The number average molecular weight is the statistical average molecular weight of all the polymer. A polymer is a molecule made up of repeating structural monomer units. The weightaverage molecular weight is larger than or equal to the number average molecular weight. Made by faculty at the university of colorado boulder department of chemical and biological engineering.
Therefore, the number average molecular weight may be determined experimentally by measuring the total number of moles of polymer in a known weight of sample. Number average molecular weight number average molecular weight can be evaluated using dilute solution of a polymer. The molecular weight of a polymer differs from typical molecules, in that polymerization reactions produce a distribution of molecular weights and shapes. The number average molecular weight m n measuring system requires counting the total number of molecules in a unit mass of polymer irrespective of their shape or size. Where, pdi polydispersity index m w weight average mol. The more units that are connected, the higher the molecular weight. Sep 09, 2014 weight average molecular weight mw 40 the probability factor in a weightaverage considers the mass of the molecules so that the heavier molecules of the polymer segment are more important. Because of this, polymer molecular weights are usually given as averages. Absolute methods include colligative methods membrane osmometry, ebulliometry, cryoscopy, and vaporphase osmometry, light scattering, and equilibrium sedimentation. Some of the most common methods for determining these parameters are colligative property measurements, light scattering techniques, viscometry, and size exclusion. Flory, principles of polymer chemistry, 1st edition 1953 cornell university the intrinsic viscosity is defined by. In the numerator each contributing molecular weight in the sample, called m i, is multiplied by the corresponding number of moles, n i. Number average molecular weight molecular weight is determined by calculating the total molecular weight of.
Consider of polymer property which depends not just on the number of polymer molecules but on the size or weight of each polymer molecule. Chain entanglement small molecules, even relatively large hydrocarbons such as the paraffins, do not have long enough chains to become entangled and do not exhibit polymer properties. Chain entanglement small molecules, even relatively large hydrocarbons such as the paraffins, do not have long enough chains to become entangled and do not exhibit polymer. Oct 03, 2017 molecular weight the number average molecular weight is the total weight of the polymer molecules divided by the total number of polymer molecules. It is a way of determining the molecular mass of a polymer. Mn can be predicted by polymerization mechanisms and is mea. Polymer sample usually contains molecules of various polymerization degree experimental methods give us only some average of the molecular weight a c km c y 0. Weight average molecular weight m w and number average molecular weight m n are two ways we can characterize the polymer molecular weight. There are a number of different techniques that come under the general heading of light scattering and a range of parameters that can be measured. Thus, we cannot calculate the exact molecular weight of a polymer.
Our laboratories work with organisations of all sizes from the largest oems to the smaller niche polymer material developers, we provide the number average molecular weight mn, mass average molecular weight mw, z average molecular weight mz and polydispersity molecular weight distribution mwd for a broad range of polymers and plastic. The e1 exemption concerns polymers with a number average molecular weight navg mw in a range that is greater than or equal to 1,000. Determination of viscosity average molecular weight of polymer. An indication of the dispersion of the molecular weight distribution in a given polymer sample may be obtained from values of ratios between the different types of average molecular weight. The molecular weight of a polymer is determined by analyzing osmotic pressure data. Mw if monomer is methylmethacrylate 5c, 2o, and 8h. Hence, a polymer with a molecular weight of 10,000. If the polymer is pmma, calculate number and weight average molecular weights.
Consider a polymer, which contains four molecular weight polymers in different numbers and weight 8. The weight average molecular weight is larger than or equal to the number average molecular weight. Jan 26, 2017 the average molecular weight of a polymer can be determined by the following equation. Polymer molecular weight analysis by 1 h nmr spectroscopy.
Osmotic pressure and polymer molecular weight determination. What is the molecular weight of a given sample of polymer, for example, of polystyrene. Polymer molecular weight determination semantic scholar. Sec explained static light scattering technologies for gpc. A polymers molecular weight is related to that of the monomer, and the number of monomers present in the polymer molecule.
Hence, the molecular weight of polystyrene is 104n, where n is the styrene molecule number in the polymer chain. Light scattering, for example, only yields the weight average molecular mass. The molar mass distribution or molecular weight distribution describes the relationship between the number of moles of each polymer species n i and the molar mass m i of that species. Difference between number average and weight average. The two repeat units in this copolymer are acrylonitrile and butadiene. Molecular weight polymers an overview sciencedirect topics. Polymer molecular weight an overview sciencedirect topics. Download hires imagedownload to mspowerpointcite this. Degree of polymerization dp total number of repeat units mers or n. The sum of all molecular species of the number of moles n i of each species.
The ratio of the weight average and number average molecular weights, is a measure of the polydispersity of a polymer mixture how widely distributed the range of molecular. Ppt polymers molecular weight powerpoint presentation. Polymer degradation is a change in the propertiestensile strength, color, shape, or molecular weightof a polymer or polymerbased product under the influence of one or more environmental factors, such as heat, light, chemicals and, in some cases, galvanic action. If so, share your ppt presentation slides online with. Molecular weight and dimensions of polymers and their assemblies. Polymer molecular weight could be expressed as number average molecular weight, weight average molecular weight, and polydispersity. Mass spectrometry for polymers benefits and analytical considerations for ms analysis of polymers the benefit of mass spectrometry is the ability to make absolute mass measurements at a molecular level rather than an average across a whole sample, making mixtures easier to deal with. Molecular weight there are different ways that molecular weights of a polymer can be expressed. Introduction to materials science, chapter 15, polymers. Modified polymers have gone through a chemical modification.
Polymer science fundamentals of polymer science molecular weights of polymers prof. Premamoy ghosh polymer study centre arghya 3, kabi mohitlal road p. Within static light scattering, there are a number of different technologies with acronyms such as sls, mals, lals and rals and others. The molecular weight of the polymer is measured by using viscometer and the molecular weight obtained by this technique is called viscosity average molecular weight. Since the molecularweight distribution of commercial polymers is normally a continuous function, molecularweight averages can be determined by integration if the appropriate mathematical form of the molecular. In linear polymers the individual polymer chains rarely have exactly the same degree of polymerization and molar mass, and there is always a distribution around an average value. The molecular weight of the polymer solution is very high so the viscosity of polymer solution is. Molecular weight and polymer properties is the property of its rightful owner. A polymer must have a high molecular weight before it has useful properties, especially mechanical properties. Characterization of molecular weight distributions by a. Jan 10, 2020 number average of molecular weight is measured to determine number of particles. The distribution of molecular weight can be summarized by the number average molecular. There is a range or distribution of molecular weights. Colligative methods indicate the number of molecules, thus leading to a number average molecular weight.
How to calculate molecular weight of polymer determining. Chemistry notes for class 12 chapter 15 polymers the word polymer has a greek origin. The determination of numberaverage molecular weight. Polymer molecules, even ones of the same type, come in different sizes chain lengths, for linear polymers, so the average molecular mass will depend on the method of averaging. Number average of molecular weight is the total weight of polymer, \ref5, divided by the number of polymer molecules, \ref6. The stress relaxation gt for two polymers homologues with different molecular weights.
Number average molecular weight is the mole fraction of molecules in a polymer sample. But since a solution is the basis for analysis using gpc, the technique is limited to thermoplastic, uncrosslinked polymers. Based on the end group analysis using an 82 mhz picospin nmr spectrometer, the number average molecular weight of the peg acetyl triarm is 1142 gmol. Some methods yield simple, others mixed, averages of the molecular weight. Weightaverage molecular weight total weight of each poly present in the polymer 1450g weight of poly1 present in polymer 20g weight fraction of poly1 201450, weight fraction of poly2 801450, weight fraction of poly3 6001450, weight fraction of poly4 7501450 contribution made by each poly towards average weight of polymer weight fraction of poly1x weight of each unit for poly1 201450 x 10 0.
Mn the number average molecular weight is the statistical average molecular weight of all the polymer chains in the sample, and is defined by. Both the distribution shape and the average mw influence. The osmotic pressure of the solvent across the semipermeable membrane is measured by the membrane osmometer. Molecular weights of polymers chemistry libretexts. These repetitive units were originally the monomer molecules. Page 2 by where n i is the number of moles of polymer with molecular weight m i. Unescoiupac postgraduatecoursein polymer science molecular weight and dimensions of polymers and their assemblies jiri horsky institute of macromolecular chemistry ascr, heyrovsky sq. The number of monomers, or sometimes the number of repeat units, in a polymer. Molecular weights that are important in determining polymer properties are the number average.
A polymer s molecular weight is the sum of the atomic weights of individual atoms that comprise a molecule. Polymer molecular weight analysis by 1h nmr spectroscopy. Measuring molecular weight, size and branching of polymers. Polymer molecular weight distribution and definitions of. Molecular weight polymers an overview sciencedirect. Because colligative properties depend on the number of molecules, we expect, and will show, that colligative property experiments give a number average molecular weight. The molecular weight of standards are measured originally by membrane osmometry for number average molecular weight, and by light scattering for weight average molecular weight as described above. Polymer molecular weight could be expressed as number average molecular.
When polymer chains form their lengths and thus their weights differ. The number average molecular weight m n is given by \ref7, where m i is molecular weight of a molecule of oligomer n, and n i is. Polymer molecular weight distribution and definitions of mw agilent. In the case of highmolecularweight polymers, the number average molecular weight is directly determined by membrane osmometry, while the weightaverage molecular weight is determined by lightscattering and other scattering techniques as described in chapter 3.
Static light scattering, also called classical light scattering, is a technique used to measure molecular weight and molecular radius of gyration. For ease of notation, the weight average molecular weight mw will henceforth be written simply as m. Polymers molecular weight 1 polymers molecular weight. Molecular weight 1 to create a solid with useful mechanical properties the chain must be long one may describe chain length in terms of polymer average molecular weight, which can be defined in several ways. The number average molecular weight is the statistical average molecular weight of all the polymer chains in the sample, and is defined by. Calculates the number average and the weight average molecular weight from a polymer molecular weight distribution. Determination of molecular weight and molecularweight. Mn snimi sni where miis the molecular weight of a chain and niis the number of chains of that molecular weight.
The retention volume at the peak maximum of each standard is equated with its stated molecular weight. Polymer molecular weight distributions 11 samples of synthetic polymers always contain polymer chains with a range of chain lengths one way to describe the length of the polymer chains is in terms of an average molecular weight, i. Average molecular weights determination of molecular weights is very important because as the chain length is the controlling factor in determining solubility, elasticity, processability and mechanical properties 1 molecular weight properties 2. Polymerization reactions produce a distribution of molecular weights and shapes.
M s r t 1 s d m is the molecular weight of the sample, r is the universal gas constant, t is the temperature. The two averages can lead to very different molecular weight averages. Plasticizers the most widely used primary plasticizers have a low molecular weight known as monomeric plasticizers. Weightaverage molecular weight total weight of each poly present in the polymer 1450g weight of poly1 present in polymer 20g weight fraction of poly1 201450, weight fraction of poly2 801450, weight fraction of poly3 6001450, weight fraction of poly4 7501450 contribution made by each poly towards average weight of polymer weight fraction of poly1x weight of each unit for poly. Polymers consist of repeat units monomers chemically bonded into long. Determining number of moles to determine the number of moles of polymer the analysis method must respond equally to each molecule without regard to its chain length. In other words, it is the total weight of the sample divided by the number of molecules in the sample. Determination of molecular weights by light scattering. The number average molecular weight mn of the pmma prepared by the living polymerization with ch3cd32cmgbr was determined by the absolute method using deuterium nmr.
When the complete mmd is available from gpc, any average molecular mass can be computed simply and easily. In this chapter we discuss using colligative properties to measure the molecular weight of polymers. Polymer molecular weight is defined as a distribution rather than a specific number because polymerization occurs in such a way to produce different chain lengths. Polymer molecular weight distribution and definitions of mw. Molecular weight some initial observations but for most polymers there is a distribution of chain lengths we must therefore define an average degree of polymerization dp the average number of structural units in the polymer chain and an average molecular weight m the average degree of polymerization times the molecular. Mar 30, 2016 calculates average molecular weight using a mass basis and a molar basis. It can be obtained by multiplying the mass of each repeating unit m 0 by the degree of polymerisation and then adding the mass of end groups. An introductory knowledge of ideal versus nonideal solution behavior and colligative properties.
Our laboratories work with organisations of all sizes from the largest oems to the smaller niche polymer material developers, we provide the number average molecular weight mn, massaverage molecular weight mw, zaverage molecular weight mz and polydispersity molecular weight distribution mwd for a broad range of polymers and plastic. In this experiment the number average molecular weight, mn, of a sample of polyethylene glycol. Since m eg is usually small 18 for the polyester reaction, it is neglected and r7. One chamber contains pure solvent and the other chamber contains a solution in which the solute is a polymer with an unknown. It indicates the average length of the bulk resins polymer chains. The number average molecular weight is the statistical average. Molecular weight the physical properties of polymers.
Relative molar mass of a substance is defined 19 as the ratio of the average mass per molecule of specified isotopic composition of the substance to one twelfth of the mass. Polymer molecular weight characterization is important because it determines many physical properties. Molecular weight and dimensions of polymers and their. Procedure to determine the numberaverage molecular weight of a. Polymers atactic polymers will generally be amorphous, soft, flexible materials. Synthetic polymer chains within a given sample are of varying lengths i. Polymer is defined as a chemical substance of a high molecular mass formed by the combination of a large number of simple molecules, called monomers. A question of molecular weight american polymer standards. A membrane osmometer is a device used to indirectly measure the number average molecular weight of a polymer sample. It gives the average of the molecular masses of the individual macromolecules. For long chain molecules, all molecules are not necessarily characterized by a chemical formula of the same weight. Molecular weight determination chemistry libretexts. Mn number average molecular weight mw weightaverage molecular weight mz zaverage molecular weight a2 second virial coefficient b22 introduction light scattering can be a confusing topic. Polymer solutions an introduction to physical properties iwao teraoka polytechnic university brooklyn, new york.
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