Chem 664, Fall 2002 Handout #3, 09/11/01 #3-1

Definitions of symbols in “Polymer Physics” by Rubinstein & Colby symbol name defined as equal to proviso M molecular weight mass of one mole of polymerr end groups’ contribution neglected M = MoN monomer molecular weight mass of one mole of repeating units in primary structure specified Mo a polymer chain N degree of polymerization number of repeating units in a polymer end groups not counted chain @ numerical approximation » proportional with dimensionless const ~ proportional with dimensional const r linear dimension a measure of size of an object m mass a mass of an object D D fractal dimension exponent of linear dimension’s m ~ r , proportionality to mass m1 = Cmm2 r1 = Cr r2 D = logCm/logCr c polymer concentration mass of polymers of all sizes per unit ¥ volume of solution c = å cN N=1 concentration of N-mer mass of N-mer per unit volume of cN solution f volume fraction fraction of occupied volume of f = c /r polymer density in bulk is the same polymers per unit volume of solution as in solution r polymer density density of polymer in bulk state molar volume of monomer volume of one mole of repeating unit vm vm = Mo/r monomer molecular volume volume of a repeating unit vo vo = vm / NAV V pervaded volume volume of solution spanned by a polymer chain in solution Chem 664, Fall 2002 Handout #3, 09/11/02 #3-2

overlap volume fraction volume fraction of occupied volume of f* f* = N vo / V a polymer chain in a pervaded volume

P overlap parameter ratio of volume fraction to overlap P = fV / N vo volume fraction n mole fraction of polymer number of moles of N-mer relative to c N / MN N n N = with dp equals N, or mole number of moles of polymers of all å(cN / MN ) fraction of N-mer sizes. weight fraction of N-mer mass of N-mer relative to the total mass c wN w = N of polymers of all sizes N å cN z z-fraction of N-mer cNM N N zN = åcNM N “C” molar concentration of total number of moles of polymers of æ cN ö polymer all sizes per unit volume of solution C = å ç ÷ è M N ø molar concentration of N- number of moles of N-mer per unit c “CN”* C = N mer volume of solution N M N number density of polymer total number of molecules of all sizes æ “rn” ç cN ö rn = NAV ×å ÷ è M N ø

number average molecular M = åM ×n Mn n N N weight weight average molecular M = å M × w Mw w N N weight z-average molecular weight M = å M ×z Mz z N N p extent of reaction of p £ 1 polycondensation n (p, N) mole fraction of N-mer at p n(p,N) for polycondensation N -1 = p ×(1- p)