Compared to uncross-linked products cross-linked products

1. Introduction. Hyaluronic acid (HA) is a kind of macromolecular anionic polymer existing in the biological body, which is widely used in medicine, the cosmetics …

Compared to uncross-linked products cross-linked products. The common feature of non-cross-linked hyaluronic acid nano-needles is that they penetrate the skin and dissolve rapidly, and the non-cross-linked hyaluronic acid will migrate under the skin, so it is difficult to maintain the long-term expansion effect in a fixed position. In order to achieve the relatively long-term antiwrinkle effect, a kind of cross-linked and non-cross-linked compound ...

The molecular weight of the uncross-linked polymer was 225,000, its density was 0.92 g/cm", and the average molecular weight of a repeat unit was 68. ... Use Equation 10.5.15 to estimate My for each of the following samples and compare the calculated value with that obtained from the known fraction of repeat units cross-linked: Fraction cross ...

Jan 1, 2003 · The TGA curves of uncross-linked blends, analyzed under nitrogen atmosphere, are shown in Fig. 3. The temperatures of 5 and 10% decomposition for both uncross-linked and cross-linked blends are summarized in Table 2. These temperatures decrease with increasing wax content for uncross-linked blends, being somewhere between those of pure wax and ... DOI: 10.1016/S0141-3910(00)00097-5 Corpus ID: 97889480; Thermal properties of uncross-linked and cross-linked LLDPE/wax blends @article{Krupa2000ThermalPO, title={Thermal properties of uncross-linked and cross-linked LLDPE/wax blends}, author={Igor Krupa and Adriaan Stephanus Luyt}, journal={Polymer Degradation and Stability}, year={2000}, volume={70}, pages={111-117}, url={https://api ... Feb 1, 2014 · Higher concentrations and longer cross-linking times did not result in a significant increase in the number of cross-linking products obtained. Therefore, a 5 s cross-linking time in 10% formaldehyde was chosen for the following experiments. However, most of the albumin molecules existed in an uncross-linked state. Identification of albumin ligands The SP 4 assay, together with the ICTP assay, which is specific for the trivalently cross-linked C-telopeptide, was used for the isolation of the differently cross-linked C-telopeptide structures ...The TGA curves of uncross-linked blends, analyzed under nitrogen atmosphere, are shown in Fig. 3. The temperatures of 5 and 10% decomposition for both uncross-linked and cross-linked blends are summarized in Table 2. These temperatures decrease with increasing wax content for uncross-linked blends, being somewhere between those of pure wax and ...The divergent nature of chemically and physically cross-linked products tailors them to specific applications. Chemically cross-linked foams feature fine-celled structures, epitomizing toughness and longevity, as seen in materials like cross-linked polyethylene foam and foam rubber. While their rough exterior may lack aesthetic …

Another effective approach toward continually reprocessable cross-linked polymers is to control the reversible transformation between a cross-linked and …Cross-linked thermoplastics represent an important class of materials for numerous applications such as heat-shrinkable tubing, rotational molded parts, and polyolefin foams. By cross-linking olefins, their mechanical performance can be significantly enhanced. This chapter covers the three main methods for the cross-linking of thermoplastics ...Purpose To evaluate the 36 months changes in posterior corneal surface parameters in keratoconic eyes after accelerated corneal cross-linking and to compare the data with uncross-linked progressive and non-progressive keratoconic eyes. Methods Thirty five cross-linked, 30 uncross-linked progressive, and 30 uncross-linked non-progressive keratoconic eyes were included. Maximum keratometry (Kmax ...These varieties of cross-linked EPDMs were then compared to an uncross-linked EPDM in terms of density, radius of gyration, free volume, mean square displacement, and uniaxial tensile stress-strain ... As a product of the cross-linking of atoms at various places, multiple EPDM macromolecular chains with various …Compared with cross-linked AEMs, uncross-linked membranes with similar ion exchange capacities showed a much higher water uptake and swelling degree. Cross-linked membranes showed vastly improved alkaline stability, oxidation stability and mechanical properties compared with uncross-linked membranes due to the effective …These varieties of cross-linked EPDMs were then compared to an uncross-linked EPDM in terms of density, radius of gyration, free volume, mean square displacement, and uniaxial tensile stress-strain ... As a product of the cross-linking of atoms at various places, multiple EPDM macromolecular chains with various …May 23, 2022 · The common feature of non-cross-linked hyaluronic acid nano-needles is that they penetrate the skin and dissolve rapidly, and the non-cross-linked hyaluronic acid will migrate under the skin, so it is difficult to maintain the long-term expansion effect in a fixed position. In order to achieve the relatively long-term antiwrinkle effect, a kind of cross-linked and non-cross-linked compound ... Sep 27, 2023 · In the realm of nail enhancements, the terms cross-linked and uncross-linked refer to the chemical structure of the enhancements. Specifically, cross-linking describes the process by which polymer chains (the basic building units of the nail enhancer) are linked together into a network, often through covalent bonds.

The DSC curves of all the systems, pure LLDPE, cross-linked LLDPE and uncross-linked and cross-linked blends, show beside the main exothermic peak another very small peak at about 70°C (Fig. 2, Fig. 4 — peak at about 70°C is obvious and reproducible in original curves, but is not so obvious in reproduction). The main peak is easy to explain.Here, we describe the isolation and characterisation of carboxy-terminal telopeptide structures of type I collagen from human mineralised bone. Analysis of the collagen cross-links within the purified structures indicated the presence of trivalent ICTP structures, divalently cross-linked peptides and uncross-linked telopeptide chains.In this paper, two novel different cross-linked structures and uncross-linked anion-exchange membranes (AEMs) based on chitosan (CS) were prepared and characterized. Cross-linked N-(1-methyl-1-chloropropyltriethoxysilane)piperidyl chitosan (CNSiPCS) and cross-linked N-(1-methyl-1-dibromohexane)piperidyl chitosan (CNHePCS) were synthesized by the reaction of 1-methyl-1 ...We would like to show you a description here but the site won’t allow us.The process of cross-linking makes the hyaluronic acid resistant to enzymatic breakdown and thereby it is able to remain in the body for months after filling. Longer-lasting effect. Cross-linked hyaluronic acid is longer-lasting and more stable compared to non-cross-linked or natural hyaluronic acid. So it is a better option for …A cross-linking reagent is required to improve mechanical strength and degradation properties of biopolymers for tissue engineering. To find the optimal preparative method, we prepared diverse genipin-cross-linked chitosan/collagen scaffolds using different genipin concentrations and various cross-linking temperatures and cross …

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When it comes to purchasing Fud chorizo, there are a few key factors to consider in order to get the best value for your money. From comparing prices at different stores to evaluat...The aim of this study was an investigation on the proliferation rate of normal human epidermal keratinocytes (NHEK) on the cross-linked and uncross-linked fibrinogen/polycaprolactone (Fbg/PCL) nanofibers to determine a suitable scaffold for skin tissue engineering. Nanofibrous scaffolds were prepared by electrospinning of different …Iodinated fiber mesh implanted in a rabbit model was significantly X-ray opaque compared to the uncross-linked fiber mesh and medical grade surgical swabs. Further, opacity of the iodinated mesh was evident even after 60 days, though the intensity was reduced, which indicates the biodegradable nature of the iodinated polymer.Sep 27, 2023 · In the realm of nail enhancements, the terms cross-linked and uncross-linked refer to the chemical structure of the enhancements. Specifically, cross-linking describes the process by which polymer chains (the basic building units of the nail enhancer) are linked together into a network, often through covalent bonds. These authors found that compared with uncross-linked 6FDA 0.5 /DABA 0.5-180 membrane, the pure CO 2 permeability of 6FDA 0.5 /DABA 0.5-400 membrane after decarboxylation-induced cross-linking increased by about 10-fold [25]. These results support our findings that tuning the DABA content in polymer backbone is an effective …Compared with cross-linked AEMs, uncross-linked membranes with similar ion exchange capacities showed a much higher water uptake and swelling degree. Cross-linked membranes showed vastly improved alkaline stability, oxidation stability and mechanical properties compared with uncross-linked membranes due to the effective …

The uncross-linked cellulose hydrogels had a swelling ratio of 325%, while the swelling ratio of the cross-linked hydrogels could achieve ~ 900%. With increasing …of cross-linking suggested that calmodulin was bound at the calmodulin binding domain of MLCK. Preparation of the 110-kDa Product-Separation of the products of the cross-linking reaction was attempted in order to isolate the 110-kDa product from uncross-linked MLCK FIG. 1. Cross-linking of calmodulin and MLCK with DCC.Before having surgery, tell your doctor or dentist about all the products you use (including prescription drugs, nonprescription drugs, and herbal products). During pregnancy, this medication should be used only when clearly needed. Discuss the risks and benefits with your doctor. It is unknown if this drug passes into breast milk.We would like to show you a description here but the site won’t allow us.In a multi-center, patient-blind, RCT of 660 patients with knee OA, 3 different viscosupplements were used: High molecular weight, chemically cross-linked, non-animal derived HA (hylan) High ...Are you in need of a Windows 10 product key to activate your operating system? Whether you’ve just built a new computer or are looking to upgrade from an older version of Windows, ...Increase in Young's modulus as well as the maximum stress is observed in the cross-linked system compared with the uncross-linked chitosan system and CS/HAP nanocomposites. The stress–strain behavior of chitosan system and a system with different percentages of HAP (10%, 20% & 30%) are shown in Fig. 2 (b).Apr 22nd, 2021. Jet injection of HA resulted in significant skin improvement with minimal downtime, pain and side effects. Researchers Diane MacGillis, MD, and Yuri Vinshtok, MD, investigated the clinical efficacy of non-crosslinked hyaluronic acid (NCL-HA) and crosslinked hyaluronic acid (CL-HA) for aesthetic skin concerns when delivered ...Nanoscale carriers that stably load drugs in blood circulation and release the payloads in desirable sites in response to a specific trigger are of great interest for smart drug delivery systems. For this purpose, a novel type of disulfide core cross-linked micelles, which are facilely fabricated by …Fig. 6 is obtained by determining the ratio of elastic deformation to plastic deformation for uncross-linked chitosan and cross-linked chitosan films. According to nanoindentation results, (h max − h f)/h f for uncross-linked and cross-linked chitosan films is around 2.1 and 1.3, respectively. As stated before, these fractions approximate the ...

Among them, xQPAF-C3-VB with 17.4% degree of cross-linking showed glass transition at 75 °C compared to 62 °C for the uncross-linked membrane. A selected cross-linked membrane with 17.4% degree of cross-linking and IEC = 1.16 meq g −1 exhibited high performance in alkaline water electrolysis cell (1.67 V at 1.0 A cm −2).

The amounts of these uncross-linked products were affected by temperature; elution at 65°C yielded more Pre and Rz from XL-B and XL-A, respectively, …Question: An important application of Equation 10.5.15 is the evaluation of Mx; P.J. Flory, N. Rabjohn, and M.C. Shaffer measured the tensile force required for 100% elongation of synthetic rubber with variable cross-linking at 25∘C† The molecular weight of the uncross-linked polymer was 225,000 , its density was 0.92 g/cm3, and the average …In a multi-center, patient-blind, RCT of 660 patients with knee OA, 3 different viscosupplements were used: High molecular weight, chemically cross-linked, non-animal derived HA (hylan) High ... Chemistry. Chemistry questions and answers. An important application of Equation 10.5.15 is the evaluation of M.; P.J. Flory, N. Rabjohn, and M.C. Shaffer measured the tensile force required for 100% elongation of synthetic rubber with variable cross-linking at 25°C. The molecular weight of the uncross-linked polymer was 225,000, its density ... FRAM does offer an oil filter cross reference chart, which can be found via its search engine on its website, as of 2015. The chart showcases competitors, such as Motorcraft, with ...Jun 10, 2019 · In a multi-center, patient-blind, RCT of 660 patients with knee OA, 3 different viscosupplements were used: High molecular weight, chemically cross-linked, non-animal derived HA (hylan) High ... Further, the dimers and trimers of ferulic acid are cross linked with AXs and form feruloylated AXs, which have a significant role in the synthesis of cross-linked AXs (hydrogels). [ 4 ] Hydrogels are colorless product derived from the modification of complex carbohydrates polymers with high hydration capacity and viscosity. [ 5 ]

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Fumes: are the same thing as vapors. are the liquid form of a solid. are a blend of sootlike particles and vapors. usually result from freezing a liquid. are a blend of sootlike particles and vapors. The (___) the nail plate, the better the foundation will be for nail enhancements. thicker. more porous. thinner. older.The uncross-linked cellulose hydrogels (B0) contained water of 90.8%, while with the incorporation of borax, the water content contained in the cross-linked B1 hydrogels increased to 92.6%.In today’s digital age, where technology plays a vital role in our daily lives, the need for seamless integration between devices has become increasingly important. One such integr...an adhesive. a nail polish base coat is a type of. primer. which of the following is not a basic type of primer? dual acid. a substance that can cause visible and possibly permanent skin or eye damage is. a corrosive. a corrosive acid-based primer can cause painful burns and _____________ to soft tissue and eyes. scars.Increase in Young's modulus as well as the maximum stress is observed in the cross-linked system compared with the uncross-linked chitosan system and CS/HAP nanocomposites. The stress–strain behavior of chitosan system and a system with different percentages of HAP (10%, 20% & 30%) are shown in Fig. 2 (b).Fig. 6 is obtained by determining the ratio of elastic deformation to plastic deformation for uncross-linked chitosan and cross-linked chitosan films. According to nanoindentation results, (h max − h f)/h f for uncross-linked and cross-linked chitosan films is around 2.1 and 1.3, respectively. As stated before, these fractions approximate the ...Study with Quizlet and memorize flashcards containing terms like When should you remove an artificial nail?, Methyl methacrylate monomer (MMA):, Compared to uncross-linked products, cross-linked products: and more.Biodegradable blends of potato starch and polyvinyl alcohol were prepared by solution casting method. Citric acid was employed to introduce the plasticizing effect into the starch materials. Glutaraldehyde as cross-linker was used to enhance the properties of the blend films. Cross-linking is a common method to improve the strength and stability of starch products. The effects of citric acid ...Mar 30, 2012 · Rationale: Chemical cross-linking in combination with a mass spectrometric analysis of the created cross-linked products is an area of growing interest for deriving low-resolution structural information of proteins and protein complexes. One of the greatest challenges is the complexity of the created cross-linking mixtures, which can be met by ... We would like to show you a description here but the site won’t allow us.The cross-linked chitosan coating increased both the tensile strength and the elastic modulus, and reduced the elongation at break of the sheets when compared with the control sheet. With the cross-linking of the coating, the macromolecules are covalently linked, forming a three-dimensional network and reducing the mobility of the chains, … ….

Aug 1, 1995 · @article{AlAssaf1995TheES, title={The enhanced stability of the cross-linked hylan structure to hydroxyl (OH) radicals compared with the uncross-linked hyaluronan}, author={Saphwan Al-Assaf and Glyn O. Phillips and David J. Deeble and Barry J. Parsons and H James Starnes and Clemens von Sonntag}, journal={Radiation Physics and Chemistry}, year ... Comparative study of cross- and uncross-linked arabinoxylans extracted from maize bran with special reference to their structural and antioxidant potential November 2022 International Journal of ...Premium: Combine different sources to define the main & linked products; Distinguish between Related Products, Upsells & Cross-sells. Related products are displayed on the single product page where, in most cases, written “Related products” to promote products that share the same tags or categories with the main item that is being viewed.The amounts of these uncross-linked products were affected by temperature; elution at 65°C yielded more Pre and Rz from XL-B and XL-A, respectively, …The rooftop symbols were a bit too prominent for comfort China’s Zhejiang province has a large Christian population, but that will become quite a bit less apparent if authorities h...With the assumptions that the cross-linked products had a spherical shape and the R g values approximated the molecular radii, the polymer volumes after 95% cross-linking were calculated to be between just 33% and 39% of the original dendrimer volume. Given a less than 10% mass reduction in the RCM reaction, this size reduction indicates a ...When the cross-linking was complete, the thickness and grammage of the coatings were increased when compared with their non-cross-linked counterparts. The weight gain observed after the cross-linking is due to the accumulation of the CA attached by esterification into the hydroxyl groups in the nanocellulose fibers (De Cuadro et al. …The SP 4 assay, together with the ICTP assay, which is specific for the trivalently cross-linked C-telopeptide, was used for the isolation of the differently cross-linked C-telopeptide structures ... Compared to uncross-linked products cross-linked products, Fig. 6 is obtained by determining the ratio of elastic deformation to plastic deformation for uncross-linked chitosan and cross-linked chitosan films. According to nanoindentation results, (h max − h f)/h f for uncross-linked and cross-linked chitosan films is around 2.1 and 1.3, respectively. As stated before, these fractions approximate the ... , Jun 10, 2019 · In a multi-center, patient-blind, RCT of 660 patients with knee OA, 3 different viscosupplements were used: High molecular weight, chemically cross-linked, non-animal derived HA (hylan) High ... , Premium: Combine different sources to define the main & linked products; Distinguish between Related Products, Upsells & Cross-sells. Related products are displayed on the single product page where, in most cases, written “Related products” to promote products that share the same tags or categories with the main item that is being viewed., Oct 3, 2017 · The synthesis of GDMA-PMMA resin is carried out by the cross-linking process of GDMA with methyl methacrylate (MMA) through free radical polymerization, in which the GDMA-cross-linked PMMA polymer is acquainted with being an effectual sustenance for solid phase peptide production as illustrated in Figure 1. , In today’s fast-paced world, effective communication is key to success. Whether you’re a student, professional, or simply someone who wants to improve their productivity, the abili..., a subunit in the cross-linked product. Cross-linked Go can be ADP-ribosylated by pertussis toxin. This ADP- ribosylation is inhibited by GTPrS with a concentra- tion dependence that is indistinguishable from that of the control, uncross-linked Go. These two kinds of ex- periments indicate that a, is able to change its confor- mation even though ..., Cajot et al. reported disulfide-cross-linked micelles which displayed a slow drug release profile under physiological conditions but rapidly released the drug in a reductive environment, mimicking that of the cytoplasm and cell nucleus. 50 Jing 51 and other groups 52, 53 have demonstrated the improved stability and therapeutic effects of …, The aim of this study was an investigation on the proliferation rate of normal human epidermal keratinocytes (NHEK) on the cross-linked and uncross-linked fibrinogen/polycaprolactone (Fbg/PCL) nanofibers to determine a suitable scaffold for skin tissue engineering. Nanofibrous scaffolds were prepared by electrospinning of different …, The common feature of non-cross-linked hyaluronic acid nano-needles is that they penetrate the skin and dissolve rapidly, and the non-cross-linked hyaluronic acid will migrate under the skin, so it is difficult to maintain the long-term expansion effect ..., When it comes to productivity software, two names often come to mind: WPS Office and Microsoft Office. Both programs offer a wide range of features and tools to enhance your work e..., Increase in Young's modulus as well as the maximum stress is observed in the cross-linked system compared with the uncross-linked chitosan system and CS/HAP nanocomposites. The stress–strain behavior of chitosan system and a system with different percentages of HAP (10%, 20% & 30%) are shown in Fig. 2 (b)., The results were compared with calculated values obtained previously4 on the basis of the theory. ... the uncross-linked polymer, Tg is cross-linked polymer and n, Iodinated fiber mesh implanted in a rabbit model was significantly X-ray opaque compared to the uncross-linked fiber mesh and medical grade surgical swabs. Further, opacity of the iodinated mesh was evident even after 60 days, though the intensity was reduced, which indicates the biodegradable nature of the iodinated polymer., About 0.5 g un-cross-linked and cross-linked films, which were cured at 140, 150, and 165 °C for 0, 3, 5, 10, and 15 min were put into 100 mL of distilled water. After 10 h, the films were removed and the filtrate with unreacted oxidized sucrose were collected. Aldehyde concentrations in the filtrate were quantified using iodometric titration., FRAM does offer an oil filter cross reference chart, which can be found via its search engine on its website, as of 2015. The chart showcases competitors, such as Motorcraft, with ..., The divergent nature of chemically and physically cross-linked products tailors them to specific applications. Chemically cross-linked foams feature fine-celled structures, epitomizing toughness and longevity, as seen in materials like cross-linked polyethylene foam and foam rubber. While their rough exterior may lack aesthetic …, SEM microphotographs of the chitosan microspheres cross-linked with d,l-glyceraldehyde and glutaraldehyde are compared in Figure 6. No visible changes in the morphological aspect of the spray-dried chitosan microspheres due to the chemical cross-linking were observed, compared to the uncross-linked microspheres already shown …, The aim of this study was an investigation on the proliferation rate of normal human epidermal keratinocytes (NHEK) on the cross-linked and uncross-linked fibrinogen/polycaprolactone (Fbg/PCL) nanofibers to determine a suitable scaffold for skin tissue engineering. Nanofibrous scaffolds were prepared by electrospinning of different …, Are you in need of a Windows 10 product key to activate your operating system? Whether you’ve just built a new computer or are looking to upgrade from an older version of Windows, ..., A, B: cross-section and surface of 3.3 mg/ml collagen sponges cross-linked by 100mM EDC for 24 h, respectively. C, D: cross-section and surface of 10.0 mg/ml collagen sponges cross-linked by 100mM ..., DOI: 10.1016/j.jmbbm.2011.08.006 Corpus ID: 42702849; Nano and micro mechanical properties of uncross-linked and cross-linked chitosan films. @article{Aryaei2012NanoAM, title={Nano and micro mechanical properties of uncross-linked and cross-linked chitosan films.}, author={Ashkan Aryaei and Ahalapitiya H. Jayatissa and Ambalangodage C. Jayasuriya}, journal={Journal of the mechanical behavior ..., The yuan now accounts for 48% of China's cross-border transactions versus 47% for the US dollar. Jump to For the first time ever, the yuan has eclipsed the US dollar as the most us..., Cross-linking. FeCl 3 (6.7 g, 41.3 mmol) was dissolved into 11.0 ml of DMM to prepare cross-linking solution with the DMM/FeCl 3 molar ratios of 3:1. Reaction solutions with different ratios of DMM/FeCl 3 were prepared similarly by changing the amount of FeCl 3.Then, the membrane was immersed into a closed bottle (50 ml) …, Flow rates of uncross-linked blends are also discussed. The conservation of good mechanical properties of polyethylene and an improvement in the flow rate of the melt was the aim of this work. The ..., Thermal properties of cross-linked and uncross-linked low-density polyethylene (LDPE)/Fischer–Tropsch wax blends were investigated in this paper. For cross-linked blends, the gel content was determined. It was observed that the gel content increases with an increase in DCP concentration. The degree of crystallinity decreased with an increase ..., As expected, the surface morphology and fiber diameter were observed to remain relatively unchanged when compared to uncross-linked electrospun gelatin scaffolds. The SEM image of the uncross-linked and DHT cross-linked gelatin scaffolds are depicted in Figure 1. The gelatin nanofibers presented randomly oriented morphology and smooth surfaces., Abstract. Thermal properties of cross-linked and uncross-linked LLDPE/wax blends were investigated. The blends were prepared through thorough mixing of the powdery ingredients, followed by 10 min ..., The SEM image of the uncross-linked and DHT cross-linked gelatin scaffolds are depicted in Figure 1. The gelatin nanofibers presented randomly oriented morphology and smooth surfaces. The distributions of the fiber diameter for uncross-linked gelatin scaffolds are observed to be on average 675±30 nm, and the DHT cross-linked gelatin scaffolds ..., The STPP cross-linked coacervates were used as wall materials for Sichuan pepper essential oil (SPEO) encapsulation with encapsulation efficiency of 87.25 %. Compared with uncross-linked microcapsules, cross-linked microcapsules showed higher SPEO retention at high temperature, different pH, and high ionic concentration., PRC and final D worsened in the cross-linked and progressive uncross-linked groups, and did not change in the non-progressive group. Conclusion: Despite a decreased K max , the posterior corneal surface parameters, posterior elevation values were determined to have significantly worsened in the cross-linked group and this increase was higher ..., Oct 22, 2014 · Iodinated fiber mesh implanted in a rabbit model was significantly X-ray opaque compared to the uncross-linked fiber mesh and medical grade surgical swabs. Further, opacity of the iodinated mesh was evident even after 60 days, though the intensity was reduced, which indicates the biodegradable nature of the iodinated polymer. , GLI release showed controlled behavior compared to commercial anti-diabetic drugs. ... which approved by U.S. Food and Drug Administration (FDA), and has been used in cosmetics, pharmaceutical products, and foods for many ... For this purpose, 10 mg of cross-linked GNPs or uncross-linked gelatin (G) were heated with 3 ml of 0.5 …, The molecular weight of the uncross-linked polymer was 225,000, its density was 0.92 g/cm", and the average molecular weight of a repeat unit was 68. ... Use Equation 10.5.15 to estimate My for each of the following samples and compare the calculated value with that obtained from the known fraction of repeat units cross-linked: Fraction cross ...