ABBREVIATIONS AND SYMBOLS

Transcription

1 ABBREVIATIONS AND SYMBOLS AA ACA or P 1 6-ACA Actis 12-ADA 11-AUA BHET BPA-PC CAPEX CD CHDM CL COOH [COOH] CSD CSTR CVD DEG DHI DLC acetaldehyde aminocaproic acid 6-amino-n-caproic acid amorphous carbon treatment on an internal surface 12-amino-n-dodecanoic acid 11-amino-n-undecanoic acid bishydroxyethyl terephthalate poly(bisphenol A carbonate) capital expenses cyclic dimer cyclohexanedimethanol caprolactam carboxyl groups concentration of carboxyl end groups carbonated soft drink continuous-stirred-tank reactor chemical vapor deposition diethylene glycol direct high intrinsic viscosity diamond-like carbon Solid State Polymerization, Edited by Constantine D. Papaspyrides and Stamatina N. Vouyiouka Copyright 2009 John Wiley & Sons, Inc. 281

2 282 ABBREVIATIONS AND SYMBOLS DMT dimethyl terephthalate DSC differential scanning calorimetry DP degree of polymerization E&E electrical and electronic EG ethylene glycol EVOH ethylene vinyl alcohol HMD hexamethylenediamine HPPA high-performance polyamides HP-SSP high-pressure solid state polymerization HT hydrotalcite IPA isophthalic acid ISBM injection stretch blow molding IV solution intrinsic viscosity M monomer M&EB material and energy balances MHET monohydroxyethyl terephthalate MW molecular weight MXD6 amide compound NaSIPA sodium 5-sulfoisopthalic acid [NH 2 ] concentration of amine end groups NPG neopentyl glycol NPU nitrogen purification unit OH hydroxyl groups OPEX operation expenses PA homopolymer PA 66; parallel arrangement PAs polyamides PA1 copolyamide 66 with 1 wt% NaSIPA PA2 copolyamide 66 with 2 wt% NaSIPA PA3 copolyamide 66 with 3 wt% NaSIPA PA 6 polycaproamide; polyamide 6 PA 11 polyundecanamide PA 12 polydodecanamide PA 42 poly(tetramethylene oxamide) PA 46 poly(tetramethylene adipamide); polyamide 46 PA 66 poly(hexamethylene adipamide); polyamide 66 PA 610 poly(hexamethylene sebacamide) PA 612 poly(hexamethylene dodecanamide) PBT poly(butylene terephthalate) PC polycarbonate PCR post-consumer recycling PCT poly(dimethylene cyclohexane terephthalate) PE polyethylene PEs polyesters

3 ABBREVIATIONS AND SYMBOLS 283 PEI poly(ethylene isophthalate) PEN poly(ethylene naphthalate) PEPA 2-(2 -pyridyl)ethylphosphonic acid P-EPQ tetrakis(2,4-di-tert-butylphenyl)[1,1-biphenyl]-4,4 - diylbisphosphonite PET poly(ethylene terephthalate) PFR plug flow reactor PMDA pyromellitic dianhydride PMMA poly(methyl methacrylate) POM poyoxymethylene PP polypropylene PS polystyrene PTA purified terephthalic acid PTN poly(trimethylene naphthalate) PTT poly(trimethylene terephthalate) PVA poly(vinyl acetate) PVD physical vapor deposition PVOH poly(vinyl alcohol) R radicals RHB reheat blow molding RV solution relative viscosity SA staggered arrangement SDM standard deviation of the mean S-HIP solid high-iv polycondensation SHP sodium hypophospite SMT solid melt transition SSP solid state polymerization SwSP swollen-state polymerization TA terephthalic acid TGA thermogravimetric analysis THF tetrahydrofuran TMA trimellitic anhydride UHMW-PET ultrahigh-molecular-weight PET English Letters a a c b c bulk c byp c byp,gas-phase c byp,s specific area for diffusion cross-sectional area of a solid state polymerization reactor concentration of reactive end groups in bulk concentration of a generic low-molecular-weight by-product concentration of a by-product in the gas phase concentration of a by-product at the gas solid interface

4 284 ABBREVIATIONS AND SYMBOLS c cat(i) c DE c eff c E c Gly c OH c OH,i c COOH c P c TA c W C C i C r C s C w d d D 0 D byp D EG D Gly D i D TA D tube D W D wp E E a E a,1 E a,2 E a,eg E a,w G G h 0 h v i IV u j H/D concentration of an i-metal catalyst concentration of diester groups effective concentration; concentration of reactive end groups in the amorphous domains concentration of ester groups concentration of glycol concentration of hydroxyl end groups concentration of inactive hydroxyl groups concentration of carboxyl end groups -pressure heat capacity concentration of terephthalic acid concentration of water concentration; condensate molecule; concentration of end groups in an amorphous region concentration of inactive end groups; concentration of species i concentration of end groups in an amorphous region after IV levels off sulfonate group concentration water concentration in the polymer phase average distance between neighboring end groups mean diameter of particles initial carboxyl or amine end group excess diffusion coefficient of a by-product diffusion coefficient of ethylene glycol diffusion coefficient of glycol axial or molecular diffusion coefficient of species i diffusion coefficient of terephthalic acid diffusion coefficient that describes Brownian motion in a tube diffusion coefficient of water diffusivity of water in the polymer phase activation energy activation energy of polymerization activation energy of a transesterification reaction activation energy of an esterification reaction activation energy of ethylene glycol diffusion activation energy of water diffusion growth rate of crystals gas phase (subscript) heat transfer coefficient between the polymer and gas phases heat of vaporization of species i ultimate IV after a long SSP time Colburn factor

5 ABBREVIATIONS AND SYMBOLS 285 1/J deactivation factor k Boltzmann ; apparent or intrinsic rate of polymerization k o,i rate of an uncatalyzed i-reaction k 2 reaction rate for second-order kinetics k 3 reaction rate for third-order kinetics k byp gas-phase mass-transfer coefficient for the ith by-product k cop reaction rate for copolyamide SSP k cat reaction rate for catalyzed SSP k cat(i) rate of an i-metal-catalyzed reaction k f rate for forward reaction (polymerization) k G,i gas-side mass-transfer coefficient k H +,i rate of a proton-catalyzed i-reaction k hom reaction rate for homopolymer SSP k i reaction rate for reaction i k i reverse rate of i-reaction k plot rate derived from the slopes of a rate expression k P,i polymer-side mass-transfer coefficient k r reaction kinetic ; rate for a reverse reaction (depolymerization) K eq equilibrium for polymerization K G,i overall mass-transfer coefficient in the gas phase K i equilibrium for reaction i l c thickness of lamellae l r length of repeat unit of PET L 0 average of chain-end length L t length of tie chain; chain-end length ṁ mass flow rate of a fluid M 0 molecular weight of a repeating unit of PET M c critical entanglement molecular weight M n number-average molecular weight M n0 initial number-average molecular weight MW n number-average molecular weight M ν viscosity-average molecular weight n total number of end groups at the initial stage of SSP; number of carbon in a repeating unit; power of time n total number of end groups after IV levels off n 1 number of end groups for R = R 0 at the initial stage of SSP n 1 number of end groups for R = R 0 after IV levels off n 2 number of end groups for R = L/2 at the initial stage of SSP n 2 number of end groups for R = L/2 after IV levels off n a number of end groups available for a reaction n g number of end groups in 1.0 g of PET molar flow rate of gas ṅ G

6 286 ABBREVIATIONS AND SYMBOLS n 1 number of lamellae in a polymer molecule n t number of tie chains on a polymer molecule N length of a polymer molecule N P-G,i diffusion flux of species i between the polymer and gas phases N Re Reynolds number p ratio of overlapping volume to sphere volume; polymerization conversion p G,i bulk partial pressure of species i in the vapor phase pi partial pressure species i in equilibrium with bulk liquid p N2 G partial pressure of nitrogen in the gas phase p N2 m log mean of the partial pressures of nitrogen at the sphere surface and in the bulk gas phase p t polymerization conversion P system pressure P polymer phase (subscript) P i polymer molecule of degree of polymerization i Pi sat vapor pressure of species i Q N2 nitrogen supply r rate of reaction r A chemical reaction rate r i reaction rate of species i R pellet radius (modeled as a sphere); radius of the sphere of end-group movement R average radius at the initial stage of SSP R 0 radius of the sphere of end-group movement when L>2R 0 R j reaction rate of reaction j R r average radius after a long SSP time s displacement of polymer chain in its tube S length of side of cube occupied by an end group S/V surface-to-volume ratio t time; reaction time T temperature; reaction temperature T g glass-transition temperature T m melting point T p (P ) polymerization temperature under high pressure u velocity v overlapping volume between two spheres; molar volume v N2 gas flow rate V volume that an end group occupies in an amorphous region W water x ratio of n 1 in n (n 1 /n); distance from the center of a polymer particle x ratio of n 1 in n (n 1 /n ) x c mole fraction of crystalline domains

7 ABBREVIATIONS AND SYMBOLS 287 x i X n y i z mole fraction in the polymer phase number-average degree of polymerization mole fraction in the gas phase axial position in a solid state polymerization reactor Greek Letters β γ P,i δ ε κ λ μ μ 0 μ tube ρ φ c φ v φ w H j (IV) S j ( W ) r activity coefficient of species i in the polymer phase tube diameter void fraction of a bed thermal conductivity viscosity mobility mass density; density of PET degree of crystallinity volume fraction crystallinity weight fraction crystallinity heat of reaction for reaction j difference between the intrinsic viscosity before and after a solid-phase polymerization reaction entropy of reaction for reaction j reduced weight loss