Polymer Engineering: Lecture Notes 2 or Polymer Characteristics PDF

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TOPIC 2: Polymer CharacteristicsPhysical Characteristics of Polymers-Polymer molar mass (physical)-Polymer structural arrangement (physical)The size and shape of a polymer chain are of considerable interest to the polymer engineer. An absolute measurement of polymer chain size can be obtained from l...

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TOPIC 2: Polymer Characteristics Physical Characteristics of Polymers -Polymer molar mass (physical) -Polymer structural arrangement (physical) The size and shape of a polymer chain are of considerable interest to the polymer engineer. An absolute measurement of polymer chain size can be obtained from light scattering, when the polymer is large compared with the wavelength of incident beam. Sometimes the absolute measurement cannot be used, but the size can be deduced indirectly from viscosity measurements, which are related to the volume occupied by the chain in solution. Models such as rods, discs, spheroids and random coils are used for polymers.

POLYMER MOLECULAR WEIGHT •

Molecular weight is a fundamental property of a material.

What is special about Polymer Molar Mass An important feature which distinguishes a synthetic high polymer from a simple molecule is the inability to assign an exact molar mass to a polymer. This is a consequence of the fact that in a polymerization reaction the length of the chain formed is determined entirely by random events. In a condensation reaction, it depends on the availability of a suitable reactive group; and in an addition reaction, on the 1

lifetime of the chain carrier. Because of the random nature of the growth process, the product is a mixture of chains of differing lengths - giving a distribution of chain lengths - which in many cases can be calculated statistically. The polymer is best characterised by a molar mass distribution and the associated molar mass averages, rather than by a single molar mass. As the methods used for estimating molar mass of polymers employ different averaging procedures, therefore more than one technique is normally employed to obtain two or more averages.

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Size: Polymer Chain Dimension A polymer chain in dilute solution is often pictured as a coil, continuously changing its shape under the action of random thermal motions. Thus at any time, the volume occupied by a chain in solution could differ from that occupied by its neighbours, and each sample contains a variety of chain lengths. These lead us to conclude that meaningful chain dimensions could be averaged values: (a) the average root mean square distance between the chain ends [r2]½ (b) the average root mean square radius of gyration, [s2]½ which is a measure of the average distance of a chain element from the centre of gravity of the coil. The brackets denote averaging due to chain polydispersity in the sample and the bar denotes averaging for the many conformotional sizes available to chains of the same molar mass. In the absence of extended volume effects, the 2 quantities are related for simple chains: [r2]½ = [6s2]½ but as the actual dimensions obtained can depend on the conditions of the measurement, other factors must also be considered. Freely-jointed Chain Model

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Initial attempts to arrive at theoretical dimensions of a linear chain, treated the molecule as a number of chain elements, n, jointed by bonds of length  . By assuming the bonds behave as universal joints, complete freedom of rotation about the bonds can be postulated. This model allows the chain to resemble the path of a diffusing gas molecule and random flight statistics (as in gases) is used. In 2 dimensions such motion is termed the “drunkard’s walk” and the end-to-end distance, rf, is estimated by considering the n links:

r f 2  n 2  Distance between chain ends is proportional to the square root of the number of bonds (n), and is considerably shorter than a fully extended chain. This model is however incomplete, as polymer chains occupy a volume in space, and the dimensions of any macromolecule are influenced by the bond angles and by interactions between the chain elements. These interaction can be classified into 2 groups: (a) Short range interactions which occur between neighbouring atoms or groups (forces of steric repulsion due to overlapping electron clouds. (b) Long range interactions which are comprised of attractive and repulsive forces between segments, widely separated in a chain, that occasionally approach one another during molecular flexing, and between segments and solvent molecules. These are often termed excluded volume effects. 4

How to Determine Polymer Molar Mass (MW)? •

The techniques commonly used for measuring molecular weight are: – Colligative Properties – Membrane Osmometry – Capillary Viscometry – Light Scattering – Gel Permeation Chromatography

How to Determine Polymer Chemical Structure? •

Chemical structures are often probed using: – Nuclear magnetic resonance – Raman spectroscopy – etc

Prior to the 1920’s it was difficult to believe or accept that molar masses of the order of 106 – 109 g mol-1 (now routinely accepted) were real and not just caused by the physical aggregation of much smaller molecules. However, MW measurement accuracy is lower compared to simple molecules. This is not surprising, especially when polymer samples exhibit polydispersity, and molar mass is at best an average dependent on the particular method of measurement used. Estimation of polymer molar mass is of considerable importance, as the chain length can be a controlling factor in determining solubility, elasticity, fibre forming capacity, tear strength, and impact strength in many polymers.

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The methods used to determine the molar mass (M) are either relative or absolute. Relative methods require calibration with samples of known M and include viscosity and vapour pressure osmometry. The absolute methods are often classified by the type of average they yield, ie, colligative techniques yield number averages, light scattering and the ultracentrifuge yield weight and z-average. Example: Consider a hypothetical polymer sample composed of chains of four distinct molar masses, 100 000, 200 000, 500 000 and 1 000 000 g mol-1 in the ratio 1:5:3:1, then: Mn = (1 x 105 + 5 x 2 x 105 + 3 x 5 x 105 + 1 x 106) / (1 + 5 + 3 + 1) = 3.6 x 105 g mol-1 (number average) Mw = [ 1 x (105)2 + {5 x (2 x 105)2} + {3 x (5 x 105)2} + {1 x (106)2 ] ÷ { (1 x 105) + (5 x 2 x 105) + (3 x 5 x 105) + (1 x 106)} = 5.45 x 105 g mol-1 (weight average) Mz = 7.22 x 105 g mol-1 (z-average)

The breadth of the distribution can often be gauged by establishing the polydispersity index = Mw/Mn or Mz/Mn For many polymerisations the most probable value is about 2.0, but both larger and smaller values can be obtained.

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Schematic diagram of averages

Measured averages of a poly(ethylene) sample

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An alternative method of describing the chain length of a polymer is to measure the average degree of polymerisation (DP), or the number of monomer units or residues in the chain, x = M/Mo where Mo = molar mass of monomer or residue, and M = appropriate average molar mass of polymer. x n  number average DP x w  weight average DP

A colligative method, eg, osmotic pressure, effectively counts the number of molecules present and provides a number average molar mass: Mn 

N M N i

i

i



W

 (W

i

i

/ Mi )

where Ni is the number of molecules of species, i of molar mass Mi mass Wi = Ni Mi / NA, where NA = Avogadro’s constant 8

From light scattering measurements, a method based on size rather than the number of molecules, a weight average molar mass is obtained: Mw 

N M N M i

2

i

i

 i

W M W i

i

i

Statistically, Mn is simply the first moment, and Mw is the ratio of the second to the first moment, of the number distribution. Viscometers measure viscosity and provides “viscosity average molecular weight:   Ni M i 1 M v    N i M i

  

1 /

where α is the viscosity index. Mark-Houwink-Sakurada equation relates viscosity (η) to MW:

  k.M v where Mv is viscosity-based MW. k and α are fitted constants (from Polymer Engg Handbook) A higher average, the Z-average, is given by: Mz

N  N

i

M i3

i

Mi 2

W M  W M i

2 i

i

i

can be measured using the ultracentrifuge. Mn determination involves counting the total number of molecules, regardless of shape or size, present in a unit mass of 9

polymer by (a) end group assay, (b) thermodynamic method, and (c) transport method. (a) End group assay by titration is of limited utility, since it can be used only when a polymer end group is amenable to analysis. It is used to detect amino end groups in nylons dissolved in m-cresol, by titration with methanolic perchloric acid solution. The sensitivity of the method increases rapidly as the chain length increases and the number of end groups drops. A practical upper limit reach an Mn  15000 g mol-1. (b) Thermodynamic methods are based on the colligative properties of dilute solutions. A colligative property is a function only of the number and not the nature of the solute molecules contained in a given volume. Thus colligative properties such as osmotic pressure, elevation of boiling temperature, depression of freezing temperature and lowering of vapour pressure, are suitable methods. Each technique requires that an equilibrium is established, between the solvent in solution and the pure solvent. Consequently these properties are determined by the solvent activity, a, and Raoult’s law can be used, for dilute solutions: a1 = x1 = (W1/M1) / {W1/M1 + W2/M2} = n1 / (n1 + n2) where n1 and n2 are the moles and w1 and w2 are masses of solvent and polymer, respectively. When the solution is sufficiently dilute: 1 - a1  {W2/M2} / {W1/M1} 10

and any of the colligative methods can be used to calculate M2.

Colligative Properties •

•

Properties of a solution that depend on the moles of solute present but not on the chemical properties of the solute, eg, freezing point, boiling point, osmotic pressure, vapor pressure. Measure these properties, compare them with the corresponding properties of the pure solvent, determine the moles of solute present in the solution. The number-average molecular weight can be calculated by dividing the mass of solute by the moles present.

Boiling and Freezing Temperature From the Clausius-Clapeyron equation: Mn = (RT2 V1 / H) (C / T)c o For boiling T, H and T are the boiling temperature of solvent, enthalpy of solvent vaporization and elevation of boiling temperature, respectively. For freezing T, H and T are the freezing temperature of solvent, enthalpy of fusion of solvent and depression of freezing temperature, respectively. The equation represents the limiting case at infinite dilution and it is necessary to extrapolate (T/C) for a series of concentrations to C = 0 to calculate Mn.

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The measurements are limited by the sensitivity of the thermometer. Currently T is measured within a precision of 10-3 K and the limit of accurate measurement of Mn is in the region of 30 000 g mol-1.

Membrane Osmometry • Determines the number average molecular weight (10,000 to >1,000,000 Daltons) of compounds soluble in organic and aqueous solutions, within 30°C130°C. • The unit has a stainless steel cell separated into two parts by a semi-permeable membrane. The upper cell is filled with the solution and the lower half filled with the solvent. This gives a negative osmotic pressure differential across the membrane corresponding to the concentration of the solution.

Osmotic Pressure Measurement of osmotic pressure, , of a polymer solution is carried out in a cell with the polymer solution separated from the pure solvent by a membrane, permeable only to solvent molecules. Initially, the chemical potential 1 of the solvent in the solution, is lower than that of the pure solvent 1o, and solvent molecules tend to pass through the membrane into the solution in order to attain equilibrium. This causes a build up of pressure in the solution compartment until, at equilibrium, the pressure exactly counteracts the tendency for further solvent flow. This pressure is the osmotic pressure. For a dilute polymer solution: V = nRT on substituting: c = (Ni Mi) / NAV 12

and n =  Ni /NA

(NA = Avogadro’s number)

(/c)  Ni Mi = ( Ni) RT  (/c)c o = RT/Mn Experimentally, a series of concentrations is studied and the results are treated according to virial expansions of /c, for example: /c = RT/Mn + B2c + B3c2 + ----(Plot /c) The static method of measuring osmotic pressure using 3 20 cc solution and a semi-permeable membrane is a slow process requiring 24 h to equilibrate at each concentration. The membranes, prepared from cellulose or its derivative, require careful preparation and equilibration. New high-speed automatic osmometers eliminate some of the problems with the static method by optical tracking of a bubble or strain gauge measuring diaphragm motion due to osmotic pressure. In the new osmometers, equilibration is rapid (5 - 30 min) and permeation is readily detected. The osmotic pressure measurements are sensitive to temperature and must be carried out under rigorously controlled temperature conditions using chemically stable solvents having low vapour pressure. The membrane permeability places a lower limit of Mn = 15000 g mol-1.

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Membrane osmometry • Determines the number average molecular weight (10,000 to >1,000,000 Daltons) of compounds soluble in organic and aqueous solutions, within 30°C-130°C.

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• The unit has a stainless steel cell separated into two parts by a semi-permeable membrane. The upper cell is filled with the solution and the lower half filled with the solvent. This gives a negative osmotic pressure differential across the membrane corresponding to the concentration of the solution.

Vapour pressure osmometry A technique, based on the lowering of the vapour pressure, called vapour pressure osmometry is useful for measuring Mn = 50 - 20 000 g mol-1. The apparatus consists of a thermostatted chamber, saturated with solvent vapour at the measurement temperature, and containing 2 differential matched thermistors capable of detecting temperature differentials of 10-4 K. A drop of solvent and a drop of solution are applied to each thermistor. Due to the vapour pressure difference between the solvent and the solution, solvent from the vapour phase will condense on the solution drop causing its temperature to rise. Because of the large excess of solvent present, evaporation and hence cooling of the solvent drop is negligible. When equilibrium is attained, the T between the 2 drops is a measure of the extent of the vapour pressure lowering by the solute.

Viscosity & Viscometric measurements

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Ubbelohde Glass Capillary Viscometer • Solution viscosity measurements using Ubbelohde Glass Capillary

Viscometers. • Viscosities of transparent liquids of up to 100,000 cSt can be

measured. • Dilute polymer solution viscosity measurements are made to

determine relative, inherent and intrinsic viscosities. • They require sample volumes of about 20 ml.

When a polymer dissolves in a liquid, the interaction of the 2 components stimulates an increase in polymer dimensions over that in the unsolvated state. Because of the vast difference in size between solvent and solute, an increase in viscosity occurs even in dilute solutions. A simple way of examining this effect is by capillary viscometry. It has been shown that the ratio of the flow time of a polymer 16

solution to that of the pure solvent to is equal to the ratio of their viscosity:

Relative Viscosity =

r   / o 

t to

As this has a limiting value of unity, a more useful quantity is specific viscosity:

 sp   r  1  t  t o  / t o Molecular interference is likely even in dilute solutions, thus sp is extrapolated to zero concentration:



sp



/c

   k c 2

c o

and the intercept is the limiting viscosity number []o, k is a shape independent factor called the Huggins constant = 0.3 - 0.9 for randomly coiling vinyl polymers.

Light Scattering 17

Light scattering is one of the popular methods for measuring the weight average molecular wt, Mw. The phenomenon of light scattering by small particles is familiar to us: the blue sky, varied colours at sunset, poor visibility while driving in foggy conditions, etc. Light is an electromagnetic wave, produced by the interaction of a magnetic and electric field, both oscillating at right angles to each other in the direction of propagation. When a beam of light strikes the atoms/molecules, the electrons are perturbed and oscillate with the same frequency as the exciting beam. This induces transient dipoles in the atoms/molecules, which act as secondary scattering centres by re-emitting the absorbed energy, ie, scattering takes place. For gases, Rayleigh showed that the reduced intensity of the scattered light Ro at any angle  to the incident beam, of wavelength  could be related to the molar mass of gas M, its lambda concentration C, and the refractive index increment, d n/ dc , by: 

R    2 / N A  2

4



 d n / dc  

2

1  cos  M 2

c

When a solute is dissolved in a liquid, scattering from the solute for molecules which are small compared with the wavelength of light is given by:

R (solute )  R (solution )  R (solvent ) and this is related to the change in Gibbs free energy, which in turn is related to the osmotic pressure, . 18

Light is usually obtained from a water-cooled mercury vapour lamp and one of wavelengths,  = 365,436 or 546 nm is selected by a filter. Scattering is detected by a photomultiplier, capable of revolving around the cell and the intensity is recorded on a galvanometer.

Gel Permeation Chromatography (GPC)

•

GPC is a high performance liquid chromatography technique for the separation of components based on their molecular size in solution.

•

GPC separates the sample and determines the molar mass distribution of sample. Coupled with a light scattering detector, the GPC provides for the on-line determination of absolute molar mass, size and conformation.

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The molecular weight range is 103 to 109 Daltons and molecular size range 10 to 500 nm.

The determination of the molar mass distribution by conventional fractionation techniques is time consuming, while GPC is a rapid, efficient and reliable method by which polymer samples are separated into fractions according to their molecular size, by means of sieving action.

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The polymer separation is achieved with a packed column of beads (often crosslinked polystyrene) having controlled pore size distribution. The larger molecules dissolved in the solvent carrier, cannot diffuse into the pores, and are rapidly eluted, while the smaller ones penetrate further with decreasing size and are retarded correspondingly. Thus the large molecules leave the column first and the small ones last because they travel a much longer path.

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Tetrahydrofuran is a commonly used solvent having similar polarity as the column packing to prevent partitioning, with a high boiling point and low viscosity. Columns are initially calibrated by measuring elution times of samples of known M. Usually []M is plotted against elution volume V. The product []M is proportional to the hydrodynamic volume of the polymer solution,...