Instruction for practical work No 2 The Determination of Viscosity-Average Molecular Weight of Polymers THEORETICAL PART Molecular weight of polymers Molecular weight is one of the most fundamental parameters in characterizing a polymer. Measurements of the viscosity of dilute polymer solution provide the simplest and most widely used technique for routinely determining molecular weights of polymer samples. 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. The molecular weight of the polymer solution is very high so the viscosity of polymer solution is very high compared to that of pure solvent. The dilute solution viscosity measurement is applicable to all polymers, which dissolve to give solutions at a temperature between ambient to about 150 0 C. Viscosities are measured at concentrations of about 0.5 g/100 ml of solvent by determining the flow time of a certain volume of solution through a capillary of fixed length. Flow time in seconds is recorded as the time for the meniscus to pass between two designated marks on the viscometer. Viscosities of the polymer solutions are measured at constant temperature; usually at 25-30.0 ± 0.1 C. The intrinsic viscosity, η, as the function of average molecular weight, M, is represented by Mark-Houwink equations [η] = KM α (1) where K and α are constants for a given polymer solvent temperature system. These constants can be determined experimentally by evaluating a plot of log [η] versus log molecular weight which the molecular weight has been determined by an absolute method such as light scattering method or these constants can be found from Hand-books of polymers. 1
The Ubbelohde Capillary Viscometer Flow marks Capillary Picture 1. The Ubbelohde type of viscometer The Ubbelohde viscometer (Picture 1) is the most common type of viscometer used for the determination of the intrinsic viscosity. It was originally introduced in 1937. For the operation of the viscometer, a polymer solution of known concentration is put in the reservoir and aspirated to the upper bulb, usually by creating some vacuum in that chamber; then air is admitted so the solution flows down the capillary by gravity. The time for the liquid to flow between the two marks is recorded. This operation is repeated for increasingly dilute solutions of the same polymer/solvent. A duct parallel to the capillary allows pressure equilibration, so the flow of the fluid is only due to the hydrostatic head. The Ubbelohde type of viscometer is the most convenient to use as it is not necessary to have exact volumes of solution to obtain reproducible results. Furthermore, additional solvent can be added (as long as the total volume can be accommodated by the reservoir); thus concentration can be reduced without having to empty and refill the viscometer. CAUTION: It is necessary to ensure that the polymer solution is free from solid particles, either due to dust or incompletely dissolved polymer, as any particle that got stuck at the capillary tube would affect the flow time. 2
Measurement of the Intrinsic Viscosity Sevearl important viscosity functions are used in viscosity method for the determination of polymer molecular weight: - The relative viscosity is the dimensionless ratio of solution viscosity to solvent viscosity. - The specific viscosity is related to the fluid viscosity increase due to all polymer solute molecules. - The reduced viscosity is the fluid viscosity increase per unit of polymer solution concentration. - The intrinsic viscosity is the limit of the reduced viscosity as the polymer solute concentration approaches zero. The intrinsic viscosity is also the limit of the inherent viscosity as the solution polymer concentration approaches zero. The principle behind capillary viscometry is the Poiseuille s law, which states that the time of flow of a polymer solution (ps) through a thin capillary is proportional to the viscosity of the solution. The latter increases with increasing solution concentration. From Equation (2), the time of flow of the solvent (solv) or of the polymer solution will be proportional to the viscosity, and inversely proportional to the density: t solv = μ solv ρ solv (2) t ps= μps μps (3). It is convenient to define some terms related to the viscosity of polymer solutions: µ r is the relative viscosity (or viscosity ratio according to the IUPAC), defined as the ratio μ r= μps μ solv (4). µ sp is the specific viscosity, which is defined as the ratio μ sp= μps μ solv μ solv µ sp = µ r 1 (5). 3
µ red is the reduced viscosity (or viscosity numberaccording to the IUPAC), which is defined as μ red = μ sp c (6) where c is the polymer solution concentration. At the low polymer concentrations used in viscometry, ρ ps ρ solv, therefore, from Equations (2) (6), the relative viscosity becomes μ r = t ps t solv (7) By similar arguments, the specific viscosity can be expressed by the following equation: μ sp = μ r 1 = t ps t solv t solv (8). Both µ r and µ sp depend on the polymer concentration. Not uncommonly, viscosities are determined at a single concentration and the inherent viscosity (η inh ) as defined below is used as an approximate indication of molecular weight. η inh = ln η r / C (9) where concentration C is commonly expressed as g per 100 ml. The change in solution viscosity with increasing concentration can be expressed as a series in concentration C as given by the Huggins Equation and the Kraemer equation as shown below. η sp / C = [η] + k 1 [η] 2 C (10) ln η r / C = [η] k 1 [η] 2 C (11) Both the inherent and reduced viscosities extrapolate to give the intrinsic viscosity, [η], at zero concentration. [η] = (η sp / C) C=0 = (ln η r / C) C=0 (12). 4
For measuring intrinsic viscosity of polymer sample, solutions of known concentrations are prepared, the flow times of solvent (s) and the solutions (s) are measured using viscometer. Double extrapolation plots of reduced viscosity against concentration and inherent viscosity against concentration is plotted by calculating the corresponding reduced viscosity and inherent viscosity. The intrinsic viscosity is given by the common ordinate intercept of these graphs. From the Mark-Houwink equation the relationship among the molecular weight and viscosity are given below [η] = KM α (13) Where [η] is the intrinsic viscosity, M is Molecular weight, K and α are constants for a particular polymer solvent system. K and α can be found from literature. EXPERIMENTAL PART NOTE: Perform this laboratory work in a hood (if the polymer solution is prepared in toxic solvent) or by using local hood and wear coat, gloves and safety goggles. Reactive substances used in this practical work 1. Caprolactam (CPL) solution (with initial concentration 0.8%) in water 2. Distilled water The polymer investigated Caprolactam (CPL) is a widely used synthetic polymer that is the precursor to Nylon 6. 5
Tools needed in the work 1. 25 ml volumetric flasks, stoppered 2. Pippetes as required 3. Ubbelohde viscometer 4. Timer Procedure (a) Solution Preparation 1. Prepare solutions of CPL in water of different concentrations 0.8, 0.4, 0.2, 0.1, 0.05% from the initial solution made. (b) Determination of t solv 1. Measure 25-35 ml (depending on viscometer used) of proper solvent into an Ubbelohde viscometer. 2. Allow the solution to flow under gravity. Start timing with a stop-watch when the upper meniscus reaches X, and stop the stop-watch when the meniscus reaches Y. Repeat 4 to 5 times, and take the average of the three most consistent readings to be the solvent flow time t solv. 3. Pour out all the solvent, and hang the viscometer upside down. (c) Determination of solution flow time t ps 1. Pipette 25-35 ml of polymer solution into the viscometer. Follow the same procedure as in (b) to measure the solution flow time. 6
2. Reduce the concentration of the initial solution preparing the solution with a new concentration needed in the procedure. 3. Repeat the dilution 4 to 5 times. For each concentration repeat the measurement of flow time at least 4 times and the average value is computed. NOTE: At the end of the experiment, pour the content of the viscometer into a waste bottle. Analysis of Experimental Data 1. Tabulate your results as follow: Table1. Measurement of solvent flow time t 0 No. Solvent flow time t solv, s 1 2 3 4 5 Average of three most consistent measurements = Table 2. Measuerement of solution flow time t and calculated viscosities C Solution flow time, s Average η r= t ps /t solv η sp η sp /C Ln η r /C g/ml 1 2 3 4 t ps, s 2. Calculate reduced viscosity (η r ), specific viscosity (η sp ) and inherent viscosity (η inh ) by using the equations described above. 3. Plot (η sp /c) and (ln η r /c ) versus C in the same graph paper, and determine the intrinsic viscosity [η ]. Read [η] as the common intercept at C = 0 of the best straight lines through the two sets of points. 7
4. Determine the viscosity average molecular weight of your polymer sample. The intrinsic viscosity of a polymer is related to the viscosity average molecular weight by the Mark-Houwink Equation. Mark-Houwink parameters for caprolactam water solution at 25 0 C K = 0.0105 α = 0.69 5. Make the conclusion. 8