CHAPTER
3.4 Size Exclusion Chromatography
3.4.7 MALDI-MS [27]
MALDI-MS refers to matrix-assisted laser desorptionionization mass spectros- copy. It is also called MALFI-TOF, because the mass spectrometer is a time- of-flight version. In this technique, the polymer is mixed with a molar excess of a 140 CHAPTER 3 Practical Aspects of Molecular Weight Measurements
salt, for cationization, and deposited on a probe surface. A UV laser is pulsed at the mixture, vaporizing a layer of the target area. Collisions between cations and polymer in the cloud of debris form charged polymer molecules. These are extracted and accelerated to a fixed kinetic energy by application of a high poten- tial. They are diverted into a field-free chamber, where they separate during flight into groups of ions according to their mass/charge ratios. The output of a detector at the end of the drift region is converted to a mass spectrum on the basis of the time elapsed between the initiation of the laser pulse and the arrival of the charged species at the detector. Lighter ions travel faster and reach the detector earlier. Responses from a multiplicity of laser shots are combined to improve the signal/noise character of the mass spectrum.
MALDI-TOF is a useful technique at present for low-molecular-weight poly- mers. Application to most commercially important polymers is problematic at the time of writing, however, because these materials have high mean molecular weights and broad molecular weight distributions[28].
Appendix 3A: Multigrade Motor Oils [29]
Certain polymers act to improve theviscosity index (VI) in crankcase lubricants.
The principles involved are those described inSection 3.3. Most internal combus- tion engines are designed to function most efficiently by maintaining approxi- mately constant engine torque over the wide temperature range that the lubricating oil may experience. If the crankcase oil is too viscous at low tempera- tures, the starting motor will have difficulty in cranking the engine and access of the lubricant may be impeded to all the components it is designed to protect. On the other hand, if the oil is too fluid at the engine’s operating temperature, which can exceed 200C, it may fail to prevent wear of metal parts and may be con- sumed too fast during running of the vehicle. Oil-soluble polymers are used as VI improvers to counteract the tendency for the lubricant’s viscosity to drop with increasing crankcase temperature.
VI improvers require oxidation resistance without generation of corrosive by- products, thermal stability, compatibility with the other additives in the lubricant package, shear stability and solubility, or, rather, absence of separation over the operating range of the engine. This balance of properties is achieved by use of certain polymers at the 0.53.0% level. The commercially important VI impro- vers are polymethacrylates, ethylene-propylene copolymers, and hydrogenated styrenediene copolymers. At low temperatures the oil is a relatively poor solvent for the polymer and the macromolecules tend to shrink into small coils which add very little to the viscosity of the mixture. At high temperatures, however, the oil is a better solvent and swells the polymer coils. The result is a greater hydrody- namic volume of the macromolecular solute, higher viscosity of the solution (cf.Eq. 3-63), and compensation for the increased fluidity of the base oil.
PROBLEMS
3-1 Two “monodisperse” polystyrenes are mixed in equal quantities by weight.
One polymer has a molecular weight of 39,000 and the other has a molec- ular weight of 292,000. What is the intrinsic viscosity of the blend in ben- zene at 25C? The MarkHouwinkSakurada constants for polystyrene/
benzene areK59.1831025dL/g anda50.74.
3-2 The following are data from osmotic pressure measurements on a solution of a polyester in chloroform at 20C. The results are in terms of centi- meters of solvent. The density of HCCl3is 1.48 g cm23. FindMn:
Concentration (g/dL) h(cm HCCl3)
0.57 2.829
0.28 1.008
0.17 0.521
0.10 0.275
3-3 Consider the following data obtained from a series of osmotic pressure (π) experiments at 310 K. The solutions consist of poly(vinyl acetate) and tol- uene. Note thatR58.314 J/mol K and that the molar volume of toluene at 310 K is 106 cm3/mol.
Concentrationc, kg/m3 π/c, J/kg
2.3 16.9
4.3 17.4
6.3 18.3
10.1 21.5
(a) Obtain a plot ofπ/cagainstcusing the above data.
(b) Estimate the concentration range over which the truncated osmotic vir- ial equation (i.e., ignorec2and all higher order concentration terms) is valid.
(c) Determine the number average molecular weight (kg/mol) of the poly (vinyl acetate) sample and the second virial osmotic coefficient (m3 mol/kg2).
(d) Calculate the difference between the chemical potential of toluene in the solution with the polymer concentration of 10.1 kg/m3and that of pure toluene under the same atmospheric pressure.
3-4 One major factor that determines the osmotic pressure of a polymer solution (π) is the intermolecular interaction between the solvent and polymer molecules. Such interaction leads to the observed difference in the chemical potentials of the solvent in the solution and in its pure form 142 CHAPTER 3 Practical Aspects of Molecular Weight Measurements
(i.e., μ12μ01) at the same temperature and pressure. And it is shown that μ12μ015 2V10πwhereV10 is the molar volume of the solvent.
(a) Since the intermolecular interaction between solvent and polymer molecules can be quantified by the Flory-Huggins interaction parame- terχ, derive an expression relatingπandχ.
(b) Given that the Taylor’s series expansion of ln(1x2)5x21/2x22
1/3x23 . . . , show that at very low concentrations (i.e., ignoring
second-order and higher terms), π5 RTcM22 where c2 and M2 are the concentration of the polymer expressed as mass of polymer per unit volume of the solution and its number average molecular weight, respectively.
(c) Ignoring third-order and higher terms in the expression obtained in part (b), show that solvent-polymer pairs exhibiting χ values greater than 0.5 would yield negative osmotic pressure.
3-5 The relative flow times (t/t0) of a poly(methyl methacrylate) polymer in chloroform are given below.
(a) Determine [η] by plottingηsp/candηinhagainstc.
(b) FindMvfor this polymer. [η]53.431025M0v:80(dL/g).
Concentration (g/dL) t/t0
0.20 1.290
0.40 1.632
0.60 2.026
3-6 The MarkHouwinkSakurada constants for polystyrene in tetrahydrofu- ran at 25C are K56.8231023cm3/g and a50.766. The intrinsic vis- cosity of poly(methyl methacrylate) in the same solvent is given by
½η51:2831022M0v:69cm3=g
Show how this information can be used to construct a calibration curve for poly(methyl methacrylate) in gel permeation chromatography, using anionic polystyrenes as calibration standards.
3-7 A polymer with true molecular weight averages Mn5430;000 and Mw51000000 is contaminated with 3% by weight of an impurity with molecular weight 30,000. What effects does this contamination have on the average molecular weights determined by light scattering and by mem- brane osmometry?
3-8 Polyisobutene A has a molecular weight around 3000 and polyisobutene B has a molecular weight around 700,000. Which techniques would be best for direct measurement ofMnandMwof each sample?
3-9 The MarkHouwink relation for polypropylene in o-dichlorobenzene at 130C was calibrated as follows. A series of sharp fractions of the poly- mer was obtained by fractionation, and the molecular weight of each frac- tion was determined by membrane osmometry in toluene at 90C. The samples were then dissolved in o-dichlorobenzene at 130C and their intrinsic viscosities ([η]) were measured. The resulting data fitted an expression of the form
ln½η5lnK1alnMn
whereKandaare the desired MarkHouwink constants. It was concluded from this that intrinsic viscosities of all polypropylene polymers in the appropriate molecular weight range could be represented by
½η5KMan
Is this conclusion correct? Justify your answer very briefly.
3-10 What molecular weight measurement methods could be used practically to determine the following?
(a) Mn of a soluble polymer from reaction of glycol, phthalic anhydride, and acetic acid. The approximate molecular weight of this sample is known to be about 1200.
(b) Mwof a polystyrene with molecular weight about 500,000.
(c) Mn of high-molecular-weight styrene-methyl methacrylate copolymer with uncertain styrene content.
3-11 In an ideal membrane osmometry experiment a plot of π/cRTagainst cis a straight line with intercept 1/M. Similarly, an ideal light-scattering experiment at zero viewing angle yields a straight line plot of Hc/τ against c with intercept 1/M. For a given polymer sample, solvent, and temperature,
(a) Are theMvalues the same from osmometry and light scattering?
(b) Are the slopes of the straight-line plots the same?
Explain your answers briefly.
3-12 A sample of poly(hexamethylene adipamide) weighs 4.26 g and is found to contain 431023mol COOH groups by titration with alcoholic KOH.
From this information Mn of the polymer is calculated to be 2100. What assumption(s) is (are) made in this calculation?
3-13 A dilute polymer solution has a turbidity of 0.0100 cm21. Assuming that the solute molecules are small compared to the wavelength of the incident light, calculate the ratio of the scattered to incident light intensities at a 90 angle to the incident beam and 20 cm from 2 mL of solution. Assume that all the solution is irradiated.
144 CHAPTER 3 Practical Aspects of Molecular Weight Measurements
3-14 Solution viscosities for a particular polymer and solvent are plotted in the form (η2η0)/(cη0) againstcwhereηis the viscosity of a solution of poly- mer with concentration cg cm23andη0is the solvent viscosity. The plot is a straight line with an intercept of 1.50 cm3g21 and a slope of 0.9 cm6g22. Give the magnitude and units of Huggins’s constant for this polymersolvent pair.
3-15 The following average molecular weights were measured by gel perme- ation chromatography of a poly(methyl methacrylate) sample:
Mn2:153105; Mv4:643105; Mw4:973105 Mz9:393105; Mz111:553106; Mz122:223106
Provide quantitative estimates of the breadth and skewness of the weight distribution of molecular weights.
3-16 Einstein’s equation for the viscosity of a dilute suspension of spherical particles is
η=η05112:5φ (3-61)
whereφis the volume fraction of suspended material. Express the intrinsic viscosity (in deciliters per gram) as a function of the apparent specific vol- ume (reciprocal density) of the solute.
3-17 This multipart question illustrates material balance calculations used, for example, in formulating polyurethanes. Refer to Section 1.5.4 for some of the reactions of isocyanate groups. This problem is an extension of the concepts mentioned in Section 3.1.9 on end-group determinations. Some useful definitions follow:
Equivalent weight, E5weight of compound per active group for a given reaction. (total weight)/(equivalent weight)5no. of equivalents.
E5Mn
f (3-17-i)
wherefis the functionality, i.e., the number of chemically effective groups per molecule for the reaction of interest (Section 1.3.2). In hydroxyl- terminated polymers, which are often called polyols, E follows from the definition of the term hydroxyl number, OH, inSection 3.1.9, as: Then
E556:1ð1000Þ
OH (3-17-ii)
Then:
Mn556:1ð1000Þf
OH 5Ef (3-17-iii)
For a mixture of polyols A and B,
ðOHÞmix5ðOHÞAwA1ðOHÞBwB (3-17-iv) wherewis the weight fraction.
ðMnÞmix556;100 fAfB
ðOHÞAfBwA1ðOHÞBfAð12wAÞ (3-17-v) Percent isocyanate5the percent by weight of isocyanate (NCO) groups present. The amine equivalent,AE, is the weight of the sample which reacts with 1 gram equivalent weight of dibutyl amine (reaction 1-13).
AE5Mn=ðno:of reactive groupsÞ (3-17-vi) AE5 4200
%NCO5 ðformula wt:of NCOÞð100 g compoundÞ
g NCO (3-17-vii)
for isocyanates: E5 4200
%NCO5AE (3-17-viii)
For toluene diisocyanate (TDI, often 80 parts 2,4 isomer and 20 parts 2,6 isomer): %NCO5(42)2(100)/174548, since 425the formula weight of the isocyanate NCO group.
Isocyanate index (index number)5100(actual amount of isocyanate used)/(equivalent amount of isocyanate required). An excess of isocyanate groups is used in some applications like flexible foam. The analytical values required for isocyanate formulas are the isocyanate value, hydroxyl number, residual acid value (acid number), and water content. The last two parameters reflect the following reactions:
~NCO +−COOH → ~N C O H
O (3-17-ix)
(a) TDI is used to make a foam expanded with the carbon dioxide pro- duced by reaction with 3 parts of water per 100 parts of a polyester having hydroxyl and acid functionalities (a polyester polyol) with an OH number562 mg KOH/g and an acid number (acid value)5 2.1 mg KOH/g. Calculate the amount of TDI required to provide iso- cyanate indexes of 100 and 105.
2 −NCO + H2O → −NH−C−NH− + CO2 O
(3-17-x) (b) Design an isocyanate-ended prepolymer (low-molecular-weight poly- mer intended for subsequent reaction, as in Eq. 1-13, for example), 146 CHAPTER 3 Practical Aspects of Molecular Weight Measurements
consisting of equal weights of a triol with molecular weight 3200 and a diol with molecular weight 1750. Use TDI as the diisocyanate monomer to provide 3% free isocyanate, by weight, in the final prepolymer.
(c) MDI is the acronym for 4,40-diisocyanato-diphenylmethane. Its struc- ture is shown in Eq. (1-12). A prepolymer is made from an MDI (572 parts) and a polyol (512 parts). The equivalent weight of the MDI is 143 and that of the polyol is 512. Calculate the available NCO, in %, in the prepolymer.
(d) How much MDI, at 98 isocyanate index, is required to react with 100 parts of a polyether polyol with hydroxyl number of 28 mg KOH/g, an acid value of 0.01 mg KOH/g, and a water content of 0.01% (by weight), blended with 4.0 parts of ethylene glycol and 2 parts of m- phenylene diamine?[30]
References
[1] S.I. Sandler, Chemical, Biochemical, and Engineering Thermodynamics, fourth ed., Wiley, New York, 2006.
[2] H. Benoit, D. Froelich, in: M.B. Huglin (Ed.), Light Scattering from Polymer Solutions, Academic Press, New York, 1972.
[3] T.C. Chau, A. Rudin, Polymer (London)15 (1974) 593.
[4] C. Tanford, Physical Chemistry of Macromolecules, Wiley, New York, 1961.
[5] P.J. Flory, T.G. Fox, J. Am. Chem. Soc. 73 (1951) 1904.
[6] C.M. Kok, A. Rudin, Makromol. Chem. Rapid Commun. 2 (1981) 655.
[7] P.J. Flory, W.R. Krigbaum, J. Chem. Phys. 18 (1956) 1806.
[8] D.K. Carpenter, L. Westerman, (Part II.) in: P.E. Slade Jr. (Ed.), Polymer Molecular Weights, Dekker, New York, 1975.
[9] M.L. Huggins, J. Am. Chem. Soc. 64 (1942) 2716.
[10] E.O. Kraemer, Ind. Eng. Chem. 30 (1938) 1200.
[11] A. Rudin, G.B. Strathdee, W.B. Edey, J. Appl. Polym. Sci. 17 (1973) 3085.
[12] O.F. Solomon, I.Z. Ciuta, J. Appl. Polym. Sci. 6 (1962) 683. O.F. Solomon, B.S. Gotesman, Makromol. Chem. 104 (1967) 177.
[13] A. Rudin, R.A. Wagner, J. Appl. Polym. Sci. 19 (1975) 3361.
[14] M.L. Higgins, J.J. Hermans, J. Polym. Sci. 8 (1952) 257.
[15] J.C. Moore, J. Polym. Sci. Part A 2 (1964) 835.
[16] L.H. Tung, J. Appl. Polym. Sci. 10 (1966) 375.
[17] J.H. Duerksen, Sep. Sci. 5 (1970) 317.
[18] N. Friis, A.E. Hamielec, Adv. Chromatogr. 13 (1975) 41.
[19] Z. Grubisic, P. Rempp, H. Benoit, J. Polym. Sci. Part B 5 (1967) 753.
[20] H.K. Mahabadi, A. Rudin, Polym. J. 11 (1979) 123. A. Rudin, H.L.W. Hoegy, J. Polym. Sci. Part A-1 10 (1972) 217.
[21] A.R. Weiss, E. Cohn-Ginsberg, J. Polym. Sci. Part B 7 (1969) 379.
[22] C.J.B. Dobbin, A. Rudin, M.F. Tchir, J. Appl. Polym. Sci. 25 (1980) 2985 (ibid.27, 1081 (1982)).
[23] A. Rudin, G.W. Bennett, J.R. McLaren, J. Appl. Polym. Sci. 13 (1969) 2371.
[24] M.G. Pigeon, A. Rudin, J. Appl. Polym. Sci. 46 (1992) 763.
[25] R. Amin Senayei, K. Suddaby, A. Rudin, Makromol. Chem. (1993).
[26] M.G. Pigeon, A. Rudin, J. Appl. Polym. Sci. 51 (1994) 303.
[27] H.S. Creel, Trends Polym. Sci. 1 (1993) 336.
[28] B. Thomson, K. Suddaby, A. Rudin, G. Lajoie, Eur. Polym. J. 32 (1996) 239.
[29] M.K. Mishra, R.G. Saxton, Chemtech 35 (1995).
[30] G. Woods, The ICI Polyurethanes Book, second ed., Wiley, New York, 1990.
148 CHAPTER 3 Practical Aspects of Molecular Weight Measurements
4
Mechanical Properties of Polymer Solids and Liquids
With a name like yours, you might be any shape, almost.
—Lewis Carroll,Through the Looking Glass