Abstract
The multivariable power dependence of polymer properties on molecular characteristics (Dobkowski, 1981) has been applied to molecular weight dependence of tensile strength, and the known equation of Flory (1945) has been extended taking polydispersity of polymers into account. Constant parameters of the relevant regression equations have been calculated using experimental data on tensile strength and molecular weight averagesM n andM w of polystyrene (PS) and polycarbonate (PC). Then, the critical molecular weight for entanglementsM c has been obtained from the following relationship:A=Kσ∞ M cwhereA and σ∞ are parameters of the extended Flory equation for the tensile strength, and the constantK = 2 is assumed for linear polymers. It has been found thatM c of injection and compression moulded PS is equal to 34000 and 37350g/mole, respectively, whileM c of injection moulded PC equals to 5000 g/mole. The values ofM c calculated from the polymer tensile strength are consistent with published data obtained by other methods and with the computer modeling calculations. Branched polymers have only qualitatively been discussed. Dimensionless equations have been proposed for tensile strength characteristics for polymer materials.
The described procedure can be suggested as applicable to various polymers for the determination of theirM c values. However, more experimental data on another polymer materials will be necessary to support hitherto obtained results.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Bersted BH, Anderson TG (1990) Influence of molecular weight and molecular weight distribution on the tensile properties of amorphous polymers. J Appl Polym Sci 39:499–514
Bicerano J (1993) Prediction of polymer properties. Marcel Dekker, New York
Cassagnau P, Monfort JP, Marin G, Monge P (1993) Rheology of polydisperse polymers: relationship between intermolecular interactions and molecular weight distribution. Rheol Acta 32:156–167
Dettenmayer M (1983) Intrinsic crazes in polycarbonate: phenomenology and molecular interpretation of a new phenomenon. Adv Polym Sci 52/53:57–104
Dobkowski Z (1981) General approach to polymer properties dependent on molecular characteristics. Eur Polym J 17:1131–1144
Dobkowski Z, Brzeziński J (1981) Application of gel permeation chromatography and viscometry for characterization of branched polydisperse polycarbonate. Eur Polym J 17:537–540
Dobkowski Z (1982a) Influence of molecular weight distribution and long chain branching on the glass transition temperature of polycarbonate. Eur Polym J 18:563–567
Dobkowski Z (1982b) Influence of polydispersity and long chain branching on the melt viscosity of polycarbonate. Eur Polym J 18:1051–1059
Dobkowski Z (1983) Application of multimethod procedure for characterization of branched polydisperse polymers. J Appl Polym Sci 28:3105–3121
Dobkowski Z (1984) Dependence of polymer specific volume on molecular characteristics. Eur Polym J 20:399–403
Dobkowski Z (1986) Application of melt flow index for theological characterization of branched and linear polymers. Rheol Acta 25:195–198
Dobkowski Z (1988a) The linear master dependence for polymer melts in the non-Newtonian range. Polymer Bull 19:165–169
Dobkowski Z (1988b) General dependence of polymer properties on their molecular characteristics (in Polish). Prace Naukowe, Ser Chemia, z 43, Warsaw Univ Technol Publ, Warszawa
Dobkowski Z (1990) Application of multivariable power function for characterization of polymer properties dependent on molecular weight. ISPAC, Brno, p 44–48
Dobkowski Z (1994) Application of the general dependence of polymer properties on molecular characteristics to the tensile strength. In: Annual Report '93, ICRI, Warszawa, p 99–102
Eichinger BE (1994) Polymer. Biosym Technologies software, presented at the workshop on “Computer Aided Design and Characterization of Technologically Important Materials”, March 10–11, Warsaw
Ferry JD (1980) Viscoelastic properties of polymers, 3rd ed. Wiley, New York
Fetters LJ, Lohse DJ, Richter D, Witten TA, Zirkel A (1994) Connection between polymer molecular weight, density, chain dimensions, and melt viscoelastic properties. Macromol 27:4639–4647
Flory PJ (1945) Tensile strength in relation to molecular weight of high polymers. J Am Chem Soc 67:2048–2050
Graessley WW, Edwards SF (1981) Entanglement interactions in polymers and the chain contour concentration. Polymer 22:1329–1334
He T, Porter RS (1992) Molecular geometry and chain entanglement: parameters for the tube model. Makromol Chem Theory Simul 1:119–128
Kinloch AJ, Young RJ (1983) Fracture behavior of polymers. Applied Science, New York
Kramer EJ (1983) Microscopic and molecular fundamentals of crazing. Adv Polym Sci 52/53:1–56
Kramer EJ, Berger LL (1990) Fundamental processes of craze growth and fracture. Adv Polym Sci 91/92:1–68
Martin JR, Johnson JF, Cooper AR (1972) J Macromol Sci, Rev Macromol Chem C8:57; quoated after Bersted and Anderson (1990)
Nielsen LE, Landel RF (1994) Mechanical properties of polymers and composites, 2nd ed. Marcel Dekker, New York
Nunez RW, Martin JR, Johnson JF (1982) Influence of molecular weight and molecular weight distribution on mechanical properties of polymers. Polym Eng Sci 22:193–216
Plummer CJG, Cudre-Mauroux N, Kausch HH (1994) Deformation and entanglement in semicrystalline polymers. Polym Eng Sci 34:318–329
Sauer JA (1978) Static and dynamic properties of monodisperse polystyrenes: influence on molecular weight. Polymer 19:859–860
Sauer JA, Hara M (1990) Effect of molecular variables on crazing and fatigue of polymers. Adv Polym Sci 91/92:69–118
Schurz J (1974) Physikalische Chemie der Hochpolymeren. Springer, Berlin
Seitz JT (1979) Unpublished data, quoted by Dettenmayer (1983)
User guide (1993) Polymer, Pt. 2. Biosym Technologies, San Diego
Van Krevelen DW (1990) Properties of polymers, 3rd ed. Elsevier, Amsterdam
Van Krevelen DW (1992) Group contribution techniques for correlating polymer properties and chemical structure. In: Bicerano J (ed) Computational modeling of polymers. Marcel Dekker, New York, p 55–123
Ward IM (1971) Mechanical properties of solid polymers. Wiley, New York
Wasserman SH, Graessley WW (1992) Effect of polydispersity on linear viscoelasticity in entangled polymer melts. J Rheol 36:543–572
Wu S (1990) Chain structure, phase morphology, and toughness relationships in polymers and blends. Polym Eng Sci 30:753–761
Wyman DP, Elyash LJ, Frazer WJ (1965) Comparison of some mechanical and flow properties of linear and tetrachain branched “monodisperse” polystyrenes. J Polym Sci A3:681–696
Zang YH, Carreau PJ (1991) A correlation between critical end-to-end distance for entanglements and molecular chain diameter of polymers. J Appl Polym Sci 42:1965–1968
Author information
Authors and Affiliations
Additional information
The essential part of a lecture presented during the NATO Advanced Study Institute “Rheological Fundamentals of Polymer Processing”, Alvor, Portugal, 26 September–7 October 1994
Rights and permissions
About this article
Cite this article
Dobkowski, Z. Determination of critical molecular weight for entangled macromolecules using the tensile strength data. Rheola Acta 34, 578–585 (1995). https://doi.org/10.1007/BF00712317
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00712317