Fluid resistance to flow is referred to as viscosity. It is quantitatively characterized by the visc — Physical Chemistry — Kinetics Chemistry Question
Determination of molecular mass parameters (characteristics) by viscometry
Fluid resistance to flow is referred to as viscosity. It is quantitatively characterized by the viscosity coefficient (fluids with high viscosity coefficients reveal enhanced resistance to flow). Experimentally, the viscosity coefficient can be determined by following the rate at which a liquid flows out from a thin capillary.
The viscosity of solutions of low-molecular weight compounds only slightly depends on their concentration. By contrast, solutions of polymers are characterized by a pronounced dependence of their viscosity on the polymer concentration, which allows determining the latter from viscometry data analysis.
For dilute polymer solutions, it was found that the reduced viscosity ηred and polymer concentration c (in g/mL) are related as follows:
ηred = (t - t0) / (t0 * c)
where t and t0 are flow times of the solution and pure solvent, respectively.
The intrinsic viscosity [η] can be further determined from extrapolation of the reduced viscosity to zero polymer concentration:
ηred = [η] + k * c
The intrinsic viscosity is a function of the polymer and solvent nature. In general, it is related to the molar mass of the polymer according to the Mark-Kuhn-Houwink equation:
[η] = K * M^a
Increasing of the solvent-polymer affinity results in more expanded polymer coils, which, in turn, provides for higher resistance to the solution flow. Thus, the index of power (a) is growing with increasing of the solvent affinity towards the polymer.
Usually a polymer sample is polymolecular (polydisperse), i. e. it contains macromolecules of different molecular weights. Accordingly, polymer samples are characterized by average molar masses (depends on the way of averaging). Thus, a viscosity-average molar mass Mv can be found from the Mark-Kuhn-Houwink equation using experimentally determined [η] and reference data for K and a.
Polydispersity (or heterogeneity) index of a polymer sample can be determined as the ratio of its viscosity-average molar masses found in solvents significantly differing in their affinity towards the polymer.
In this task you will find the polydispersity index of a polystyrene sample by capillary viscometry using toluene (K = 0.017 cm3/g, a = 0.69) and methyl ethyl ketone (K = 0.039 cm3/g, a = 0.57). All constants are given for 25 °С.
Chemicals and reagents
* Polystyrene (number-average molar mass of about 100 000) solution in toluene, 10 g dm-3, 25 cm3
* Polystyrene (number-average molar mass of about 100 000) solution in methyl ethyl ketone, 10 g dm-3, 25 cm3
* Toluene, 50 cm3
* Methyl ethyl ketone, 50 cm3
Apparatus and glassware
* Ubbelohde or other capillary viscometer
* Graduated cylinder, 10 cm3
* 10 glass vials, 20 cm3
* Volumetric pipette, 5 cm3
* Stopwatch
Procedure
a) For both polymer solutions, prepare a number of dilutions (in the concentrations range of 1 to 10 g/dm3).
b) Measure flow time for the solvent (toluene) using the Ubbelohde viscometer (repeat three times).
c) Measure flow times for all polystyrene solutions in toluene (repeat each three times)
d) Fill in the table below.
[VISUAL]
e) Repeat ii. b) – d) for polystyrene solutions in methyl ethyl ketone.
Calculate the relative, specific and reduced viscosities for each solution studied
Model Answer
The viscosity values calculated from the flow times of polystyrene solutions (2 to 10 g/L) determined with the Ubbelohde viscometer at 25 °C are given in the tables below. Each flow time value is an average of three measurements.
Polystyrene/toluene, the solvent flow time t0 = 24.4 s
* Concentration c of the polymer (g dm-3): 10 | 5 | 3.3 | 2
* Flow time t (s): 72.8 | 41.0 | 34.0 | 29.8
* η_rel = t/t0: 2.98 | 1.68 | 1.39 | 1.22
* η_sp = (t - t0)/t0: 1.98 | 0.68 | 0.39 | 0.22
* η_sp/c (dm3 g-1): 0.198 | 0.136 | 0.119 | 0.111
Polystyrene/methyl ethyl ketone, the solvent flow time t0 = 26.0 s
* Concentration c of the polymer (g dm-3): 10 | 5 | 3.3 | 2
* Flow time t (s): 36.0 | 30.8 | 28.8 | 27.7
* η_rel = t/t0: 1.38 | 1.18 | 1.11 | 1.07
* η_sp = (t - t0)/t0: 0.38 | 0.18 | 0.11 | 0.07
* η_sp/c (dm3 g-1): 0.038 | 0.036 | 0.033 | 0.035
Plot the reduced viscosity against polystyrene concentration for each solvent.
Model Answer
[VISUAL]
Reduced viscosity η_sp/c is plotted against polystyrene concentration c (g/l) for both solvents. The data points from part 34.1 are used to construct the plots.
Approximate the dependences from i. 2 with appropriate straight lines.
Model Answer
The linear approximations for the plots of reduced viscosity vs concentration are:
* Toluene: y = 0.0113x + 0.084
* Methyl ethyl ketone: y = 0.0008x + 0.0313
Determine the intrinsic viscosity of the polystyrene solutions in toluene and methyl ethyl ketone as Y-intercept.
Model Answer
Analysis of the data leads to the intrinsic viscosity [η] (as the Y-intercept of the linear fit):
* Toluene: [η] = 0.0840 dm3 g-1
* Methyl ethyl ketone: [η] = 0.0313 dm3 g-1
Using the Mark-Kuhn-Houwink equation, determine the corresponding values of viscosity-average molar masses of the polystyrene sample.
Model Answer
Using the Mark-Kuhn-Houwink equation ([η] = K * M_v^a):
* For toluene:
M_v = 226000 g mol-1
* For methyl ethyl ketone:
M_v = 125000 g mol-1
Evaluate the polydispersity index of the polystyrene sample.
Model Answer
The polydispersity index equals the ratio of the viscosity-average molar masses in the two solvents:
Polydispersity index = 226000 / 125000 = 1.81