Determination of Percent Crystallinity of Side-Chain Crystallized Alkylated-Dextran Derivatives with Raman Spectroscopy and Multivariate Curve Resolution

Abstract

We demonstrate a methodology to estimate the percent crystallinity of polymers directly with Raman spectroscopy and multivariate curve resolution (MCR) by alternating least-squares (ALS). In this methodology, the Raman spectrum of semicrystalline polymer is separated into two constituent components (crystalline and molten) and their corresponding concentrations. The percent crystallinity can be estimated as the change in area intensity of the molten spectral-component when polymer cools from a temperature above melting point to room temperature. The number of carbons in the crystalline lattice has also been estimated from the position of longitudinal acoustic (LA) Raman bands with the correlation established by Mizushima and Simanouti [ Mizushima, S.; Simanouti, T. J. Am. Chem. Soc. 1949 , 71 , 1320 ]. The new method allows direct Raman estimation of absolute percent crystallinity of polymers. Until now, Raman spectroscopic estimation of percent crystallinity was possible only in conjunction with other techniques or by using internal standards.

A General Approach for Estimating Lamella‐Thickness Distribution in Polymers with Low‐Frequency Raman Spectroscopy: Application to Lamella Formation in Crystallizing Polyethylene

“…in which is the length of one C−C bond, E is the elastic modulus of the C−C chain, and is the density ( =972 kg m −3 , =3.05×10 11 kg m −1 ⋅s −2 , and C−C bond length=1.28×10 −10 m) …”

“…Similar to the case of alkanes, the longitudinal acoustic mode (LAM) in the Raman spectrum of PE is sensitive to the length of all‐ trans C−C chains in its crystalline lamella . We have recently shown that the hydrocarbon length of the pendent alkyl‐chains in dextran derivatives can be obtained to an accuracy of one carbon atom using Raman spectroscopy . However, contrary to alkanes, polymers show a distribution of lamella of different thicknesses in the solid state, thus preventing a direct estimation of LTD from the Raman spectrum .…”

“…However, contrary to alkanes, polymers show a distribution of lamella of different thicknesses in the solid state, thus preventing a direct estimation of LTD from the Raman spectrum . Furthermore, owing to the inverse relation between the chain length and LAM frequency, the individual LAM bands for each lamella cannot be spectrally resolved in the case of PE with all‐ trans C−C segment lengths in lamellae that approach 200 carbon atoms . It is also important to note that the intensities at different wavenumbers within this band will be altered due to the dependence on frequency and temperature (i.e., the Boltzmann factor) .…”

“…[2] We have recently shown that the hydrocarbon length of the pendent alkyl-chains in dextran derivatives can be obtained to an accuracy of one carbon atom using Raman spectroscopy. [3] However,c ontrary to alkanes, polymers show adistribution of lamella of different thicknesses in the solid state, thus preventing ad irect estimation of LTD from the Raman spectrum. [4,5] Furthermore, owing to the inverse relation between the chain lengtha nd LAM frequency, the individual LAM bandsf or each lamellac annot be spectrally resolved in the case of PE with all-trans CÀCs egment lengths in lamellae that approach 200 carbon atoms.…”

“…[4,5] Furthermore, owing to the inverse relation between the chain lengtha nd LAM frequency, the individual LAM bandsf or each lamellac annot be spectrally resolved in the case of PE with all-trans CÀCs egment lengths in lamellae that approach 200 carbon atoms. [2,3] It is also important to note that the intensities at different wavenumbers within this band will be altered due to the dependence on frequencya nd temperature (i.e.,t he Boltzmann factor). [6] Hence, directly relating the LAM peak position in the Raman spectrum of PE to its lamellar thickness is inappropriate.…”