Stress optical measurement of the third normal stress difference in polymer melts under oscillatory shear

Kornfield, Julia A.; Fuller, Gerald G.; Pearson, Dale S.

doi:10.1007/bf01332377

Cited by 20 publications

(8 citation statements)

References 29 publications

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“…where c°= (1 -«,;)Cj. Note that in the limit of all« = 0 these equations reduce to (18) and (19). Once the stressoptic coefficients are determined from optical and mechanical experiments on the pure components and the coupling coefficients are assessed, eqs 2, 28, and 29 form a new system of three equations in two unknowns, which can be used to determine GA* and Gb* in a miscible polymer blend.…”

Section: Constitutive Relationship Between Shear Andmentioning

confidence: 99%

Measuring Component Contributions to the Dynamic Modulus in Miscible Polymer Blends

Zawada¹,

Fuller²,

Colby³

et al. 1994

Macromolecules

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A novel approach to investigating the rheology of miscible polymer blends is described based on complementary infrared polarimetry and mechanical rheometry measurements. The method provides a means by which the blend dynamic modulus G*(m) may be separated into the individiual contributions due to each of the blend components. This separation is made possible by converting the observables of dynamic infrared 1,3-dichroism and birefringence experiments to those of dynamic shear stress experiments through the use of constitutive relations and the application of the stress-optic rule. The approach is extended to cover blend systems which exhibit orientational coupling, an effect which influences the optical anisotropies but does not contribute to the state of stress. Validity of the analysis technique is demonstrated by studying highly entangled miscible blends of 1,4-polyisoprene, PI (Mw = 75 000), and 1,2-polybutadiene, 1,2-PB (Mw = 204 000), containing a fraction of deuterium-labeled PI chains (Mv = 90 000). Orientational coupling in this blend is observed and is found to be characterized by a coupling coefficient e = 0.35 ± 0.05.

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Section: Constitutive Relationship Between Shear Andmentioning

confidence: 99%

Measuring Component Contributions to the Dynamic Modulus in Miscible Polymer Blends

Zawada¹,

Fuller²,

Colby³

et al. 1994

Macromolecules

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“…See Table 1 of [28] for a summary of the literature on measurements of first, second, or third normal stress differences in LAOS flow (the third normal stress difference is the sum of the first and second (see Fig. 4.7 of [7,[29][30][31][32][33])). In the present paper, Table 1 summarizes the literature on analytical solutions for molecular models for the normal stress differences arising in large-amplitude oscillatory shear flow, which each arise as Fourier series of even-valued harmonics (see Section II.P of [13]).…”

Section: Introductionmentioning

confidence: 99%

Normal stress differences in large-amplitude oscillatory shear flow for dilute rigid dumbbell suspensions

Schmalzer

Bird

Giacomin

2015

Journal of Non-Newtonian Fluid Mechanics

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Walters leads through his research publications (including his seminal contribution on the complicating role of instrument compliance in large-amplitude oscillatory shear flow measurement [27]), his excellent books on rheology [26,58,59], his educational videography [60-64], his conference organization, his book editorship [65-67], his founding editorships (Journal of Non-Newtonian Fluid Mechanics and Rheology Reviews) and his interesting work on the history and personalities of rheology [61,68]. a b s t r a c tWe examine the simplest relevant molecular model for large-amplitude oscillatory shear (LAOS) flow of a polymeric liquid: the suspension of rigid dumbbells in a Newtonian solvent. We find explicit analytical expressions for the shear rate amplitude and frequency dependences of the zeroth, second and fourth harmonics of the first and second normal stress difference responses. We include a detailed comparison of these predictions with the corresponding results for the simplest relevant continuum model: the corotational Maxwell model. We find that the responses of both models are qualitatively alike. The rigid dumbbell model relies entirely on the dumbbell orientation to explain the viscoelastic response of the polymeric liquid, including the higher harmonics in large-amplitude oscillatory shear flow. Our analysis employs the general method of Bird and Armstrong (1972) for analyzing the behavior of the rigid dumbbell model in any unsteady shear flow.We derive the first three terms of the deviation of the orientational distribution function from the equilibrium state. Then, after getting the ''paren functions,'' we use these for evaluating the normal stress differences for large amplitude oscillatory shear flow. We find the shapes of the first normal stress difference versus shear rate loops predicted to be reasonable [see Fig. 1(a)]. We find that the second normal stress difference is not proportional to the first, and that its shape differs markedly from that of the first [cf. Fig. 1(a) and (b)]. We discover the same remarkable qualitative similarity between the predictions of the rigid dumbbell model and the corotational Maxwell model for the first normal stress difference. We find no qualitative similarities between the dumbbell and the continuum models for any of the predicted coefficients of the second normal stress differences in large-amplitude oscillatory shear flow.

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“…Parallel motion of the flow cell plates is provided by a translation stage, where the flow cell windows are mounted onto the stage by securing them in aluminum holders that are bolted into the stage. Further details regarding the flow cell can be found in another publication [33], and complete information about its design and operation can be found elsewhere [34]. The transmitted beam leaving the flow cell is first intercepted by a beam splitter (oriented at less than 5 ° with respect to the optical axis, so the polarization of neither beam is significantly changed), then it is observed by two separate detectors: the dichroism detector which receives the transmitted beam, and the birefringence detector which receives the reflected beam through a second polarizer oriented at -45 o.…”

Section: Experimental Methodsmentioning

confidence: 99%

Relaxation dynamics of selected polymer chain segments and comparison with theoretical models

et al. 1990

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Abstract." Simultaneous measurement of infrared dichroism and birefringence is used to study selected polymer segment dynamics in isotopically labeled block copolymers. Two different polymers were studied: polybutadiene and poly (ethylene propylene). The first type consisted of a triblock with a short middle block labeled and a diblock with a short end block labeled, while the second type consisted of a triblock with three equal blocks and the end blocks labeled. Results of step strain experiments at -10 °C for polybutadiene and at room temperature for poly(ethylene propylene) indicated that segments located at chain ends relax faster than segments located at chain centers. These experimental data were compared to the predictions of two molecular models: the bead-spring model of Rouse and the tube model of Doi and Edwards, and it was found that both models correctly predict the qualitative features of segmental relaxation. However, the tube-model predictions were closer to the experimental results. In addition, when the effects of ofientational coupling interactions between segments in the melt were incorporated into this model, its predictions quantitatively agreed with the experimental results. The orientational coupling coefficient for poly(ethylene propylene) was 0.45 as measured from previous work, and for polybutadiene it was found to be 0.4.

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Stress optical measurement of the third normal stress difference in polymer melts under oscillatory shear

Cited by 20 publications

References 29 publications

Measuring Component Contributions to the Dynamic Modulus in Miscible Polymer Blends

Measuring Component Contributions to the Dynamic Modulus in Miscible Polymer Blends

Normal stress differences in large-amplitude oscillatory shear flow for dilute rigid dumbbell suspensions

Relaxation dynamics of selected polymer chain segments and comparison with theoretical models

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