Rheology-based modeling to identify the structure factor of polymeric materials

Abstract

In at least one example, a method for rheology-based modeling to identify a structure factor of polymeric materials includes generating a data set for a plurality of polymer ensembles, where each of the plurality of polymer ensembles comprises a corresponding plurality of polymers within a defined range of molecular weights, generating a respective rheology curve for each of the plurality of polymer ensembles, where the respective rheology curve comprises a plurality of input features for a corresponding polymer ensemble, rescaling a modulus value of the respective rheology curves for each of the plurality of input features to generate a plurality of output features, and training a machine learning model to determine a structure factor profile for polymer chains from a rheology measurement of an unknown polymer sample utilizing the plurality of output features with corresponding values from the data set.

Description

RHEOLOGY-BASED MODELING TO IDENTIFY THE STRUCTURE FACTOR OF POLYMERIC MATERIALSTechnical Field

[0001] The present disclosure relates to rheology-based modeling to identify the structure factor of polymeric materials. Such techniques can be particularly useful to predict when a polymer sample includes long chain branching (LCB) to manipulate a flow behavior of polymer formulations.Background

[0002] Polymer rheology is an important aspect of polymer solution design and processing control. Techniques to manipulate the flow behavior of polymer formulations can be exemplified by tuning molecular weight distribution (MWD), designing branching structures, adding flow modifiers, and / or adjusting processing conditions. The resulting rheology behaviors such as shear thinning and strain hardening determine the processability of the formulations and impact the properties of final products.

[0003] Polymer rheology has been used as a characterization method to probe molecular structure. Measuring such rheological properties can require a significantly larger number of samples than other characterization techniques such as gel permeation chromatography (GPC), light scattering, and / or membrane osmometry. The application of rheology to characterize polymer structure holds value for the conditions beyond the capability of other techniques, such as the MWD measurements of ultrahigh molecular weight polyethylene (UHMWPE), which has higher molecular weight chains than the upper limit of the capability of GPC.

[0004] Characterization of the molecular structure of polymeric materials relies on separation methods. The separation methods can be time consuming, sensitive, and / or incomplete. In instances where separation methods may not be available (e.g., plant laboratories, recycling facilities) the molecular structure characterization of plastics can be challenging.Linear rheology measurements on the other hand are robust enough to be implemented in plant environments, and experimental execution along with data analysis and interpretation can be sufficiently automated. A reliable method to study the structure-property-performancerelationships is lacking due to an increasing demand to recycle plastics for the manufacture of new products.Summary of the Disclosure

[0005] The present disclosure is directed to using improvements in machine learning technology to predict a property of a polymer sample. The prediction can be based on a data set that has been categorized based rheology properties of a plurality of polymer ensembles with a defined range of molecular weights. The data set can be generated and input to an artificial neural network (ANN) trained to predict the molecular weight distribution of an unknown polymer sample based on the rheology of the polymer sample. The trained neural network can be utilized to determine the structure factor for the polymer chains within the polymer sample and the structure factor can be utilized to determine the structure profile for the polymer chains with long chain branching (LCB). The trained neural network can be utilized to provide information to reverse engineer polymers with a particular rheological behavior, characterize post-consumer recycled polymers, and / or design new polymers or resins.

[0006] The above summary of the present disclosure is not intended to describe each disclosed embodiment or every implementation of the present disclosure. The description that follows more particularly exemplifies illustrative embodiments. In several places throughout the application, guidance is provided through lists of examples, which examples can be used in various combinations. In each instance, the recited list serves only as a representative group and should not be interpreted as an exclusive list.Brief Description of the Drawings

[0007] Figure 1 illustrates one example flow diagram of a method to generate a rheologybased model to identify the structure factor of polymeric materials.

[0008] Figure 2 is one example diagram illustrating an approach to generate a rheology curve for a plurality of polymer ensembles.

[0009] Figure 3 is one example diagram illustrating an approach to rescale a modulus value for a plurality of input features associated with rheology curves to generate a plurality of output features.

[0010] Figure 4 illustrates an example of a method for rheology -based modeling to identify the structure factor of polymeric materials.

[0011] Figure 5 illustrates an example of a method for rheology -based modeling.

[0012] Figure 6 illustrates an example of a machine-readable medium for rheology-based modeling.

[0013] Figure 7 illustrates an example of a device for rheology-based modeling.Detailed Description

[0014] The present disclosure relates to methods and devices for rheology -based modeling to identify the structure factor of polymeric materials, which may utilize machine learning models to predict when unknown polymer samples include long chain branching (LCB).

[0015] A machine learning model can be a function or equation for identifying patterns in data. A machine learning model can be part of a plurality of machine learning models utilized together to identify patterns in data. In a specific example, a machine learning model can be organized as a neural network. A neural network can include a set of instructions that can be executed to recognize patterns in data. Some neural networks can be used to recognize underlying relationships in a set of data in a manner that mimics the way that a human brain operates. A neural network can adapt to varying or changing inputs such that the neural network can generate a best possible result in the absence of redesigning the output criteria.

[0016] Artificial neural networks (ANNs) are networks that can process information by modeling a network of neurons, such as neurons in a human brain, to process information (e.g., stimuli) that has been sensed in a particular environment. Similar to a human brain, neural networks typically include a multiple neuron topology, which can be referred to as artificial neurons. An ANN operation refers to an operation that processes inputs using artificial neurons to perform a given task. The ANN operation may involve performing various machine learning algorithms to process the inputs. Example tasks that can be processed by performing ANN operations can include machine vision, speech recognition, machine translation, social network filtering, and medical diagnosis, among others. In a specific example, a neuron can receive Azinputs, with k corresponding to an index of inputs. For each input, the neuron can assign a weight vector, Wk, to the input. The weight vectors (e.g., weight value, etc.) can, in some embodiments, make the neurons in a neural network distinct from one or more different neurons in the network.In some neural networks, respective input vectors can be multiplied by respective weight vectors to yield a value, as shown by Equation 1, which shows an example of a linear combination of the input vectors and the weight vectors. (x1,2) = wxxx+ w2x2Equation 1

[0017] In some neural networks, a non-linear function (e.g., an activation function) can be applied to the value / (xi, x ) that results from Equation 1. An example of a non-linear function that can be applied to the value that results from Equation 1 is a rectified linear unit function (ReLU). An illustrated application of the ReLU function is shown by Equation 2. The ReLU function is used here merely as an illustrative example of an activation function and is not intended to be limiting. Other non-limiting examples of activation functions that can be applied in the context of neural networks can include sigmoid functions, binary step functions, linear activation functions, hyperbolic functions, leaky ReLU functions, parametric ReLU functions, softmax functions, and / or swish functions, among others.ReLU(x = max (x, 0)Equation 2

[0018] During a process of training a neural network, the weight vectors can be altered to “tune” the network. In at least one example, a neural network can be initialized with random weights. Over time, the weights can be adjusted to improve the accuracy of the neural network. This can, over time, yield a neural network with high accuracy. The present disclosure utilizes machine learning such as neural networks for predicting product properties through modeling of input data. In these embodiments, the weights can be tuned based on a number of factors. For example, the weights can be tuned utilizing a plurality of rheology curves for a plurality of known polymer ensembles with known molecular weight distributions. In this way, the plurality of rheology curves can be utilized as features for training the neural network such that the neural network is able to more accurately identify the structure factor of an unknown polymer sample based on a measured rheology of the unknown polymer sample.

[0019] Embodiments of the present disclosure include methods and devices for rheologybased modeling to identify the structure factor of polymeric materials. The rheology -based modeling (e.g., branch-on-branch (BoB) modeling, etc.) can include generating a data set for a plurality of polymer ensembles. In some embodiments, the rheology model can a modelingfunction that can be utilized to generate rheology curves for a plurality of different polymer ensembles that represent a relationship between a strain applied and a resulting stress of the polymer ensembles. In some embodiments, the rheology curves can include a plurality of features (e.g., input features for the machine learning model, etc.) for the corresponding polymer ensembles. In these embodiments, the plurality of features can include a modulus value and / or rescaled modulus value of the plurality of the polymer ensembles determined utilizing the rheology model.

[0020] In this way, the trained machine learning model can be utilized to identify the structure factor of polymeric materials utilizing the plurality of rheological features with corresponding molecular weight values from the data set. For example, the neural network can identify whether the polymer includes long chain branching or does not include long chain branching. When the neural network identifies that long chain branching exists, a structural property model can be generated for the polymer sample utilizing the structure factor and the molecular weight distribution.

[0021] As used herein, the singular forms “a”, “an”, and “the” include singular and plural referents unless the content clearly dictates otherwise. Furthermore, the word “may” is used throughout this application in a permissive sense (e.g., having the potential to, being able to), not in a mandatory sense (e.g., must). The term “include,” and derivations thereof, mean “including, but not limited to.”

[0022] As will be appreciated, elements shown in the various embodiments herein can be added, exchanged, and / or eliminated so as to provide a number of additional embodiments of the present disclosure. In addition, as will be appreciated, the proportion and the relative scale of the elements provided in the figures are intended to illustrate certain embodiments of the present invention and should not be taken in a limiting sense.

[0023] Figure 1 illustrates one example flow diagram of a method 100 to generate a rheology -based model to identify the structure factor of polymeric materials. The method 100 can be implemented to train one or more machine learning models of a machine learning module or ANN to predict the structure factor from a rheology measurement of an unknown polymer sample. In some examples, the method 100 can be executed by a computing device as described herein. The method 100 can be utilized to train a neural network or other type of machine learning model to determine the polymer structure factor of an unknown polymer sample basedon a rheology measurement of the unknown polymer sample. As used herein, the structure factor can be a numerical value that indicates whether a particular polymer sample includes long chain branching. In some embodiments, the trained neural network can be utilized to provide information to reverse engineer polymers with a particular rheological behavior, characterizing post-consumer recycled polymers, and / or designing new polymers or resins.

[0024] In some embodiments, the method 100 can analyze or simulate polymer ensembles to collect data to be utilized to train a machine learning model. As used herein, a polymer ensemble refers to a collection or group of polymer molecules that share certain characteristics or properties. For example, a polymer ensemble can refer to a collection of a particular type of polymer within a particular range of molecular weights. In some embodiments, the polymer ensembles can refer to pseudo polymer ensembles that can be theoretical representations that are generated based on theoretical ensembles of particular polymers. In this way, actual measurements may not need to be performed on a plurality of real polymer ensembles to obtain rheology information related to the plurality of polymer ensembles. For example, a rheology model can be utilized to generate rheology information for a plurality of selected pseudo polymer ensembles. Unless specified otherwise, “polymer ensembles”, as used herein includes “pseudo polymer ensembles”.

[0025] In some embodiments, at step 101 the method 100 can include data generation. In some embodiments, data generation includes generating a data set of information related to a plurality of polymer ensembles. As described further herein, the data set can include molecular weights and blending ratios for corresponding polymers of the plurality of polymer ensembles. In some embodiments, the data set can be utilized to generate rheology data for the plurality of polymer ensembles. In these embodiments, the rheology data can be utilized to generate rheology curves for each of the plurality of polymer ensembles. In some embodiments, the data generation can include utilizing small-amplitude oscillatory shear (SAGS) data to collect data from actual polymer ensemble samples. In other embodiments, the data set can be generated utilizing a pseudo polymer ensembles, actual polymer ensembles, and / or a combination thereof.

[0026] In some embodiments, the data generation can include generating pseudo polymer ensembles within a particular molecular weight range and generate rheology curves for the pseudo polymer ensembles based on a reaction model. A reaction model refers to a conceptual or mathematical representation of a chemical reaction. For example, a reaction model can describea transformation of reactants into products or a theoretical result of a particular test (e.g., rheology test, etc.). In some examples, the reaction model can include various steps and intermediates involved in the process. In some embodiments, the reaction model can be based in part on Tobita Monte Carlo Simulation. In a specific example, the pseudo polymer ensembles can be a generated model of a particular polymer ensemble with particular properties. In this way, the pseudo polymer ensemble can be utilized to generate rheology data and / or rheology curves based on the reaction model utilizing the branch-on-branch (BoB) modeling.

[0027] In some embodiments, the polymer ensembles can be generated based on a particular simulation equation. For example, the properties of the polymer ensembles can be generated utilizing Tobita Monte Carlo Simulation. The Tobita Monte Carlo Simulation utilizes the principles of Monte Carlo methods to generate polymer systems. Monte Carlo simulations, in general, involve the use of random sampling and statistical techniques to obtain numerical results for complex systems or problems that may be difficult to solve analytically. These simulations can include chain conformation simulations, thermodynamic simulations, molecular interaction simulations, among others. In some embodiments, a pseudo polymer ensemble can be simulated based on a chain segment that is chosen for a birth conversion rate. The birth conversion rate can refer to an extent a monomer are chemically linked to form larger polymer chains.

[0028] In these embodiments, the chain segment can be utilized to determine a development based on the probability determined by the dimensionless rates. In these embodiments, the rates can include, but are not limited by a termination rate, a combination rate, a branching rate, a scission rate, and / or other rates. In some embodiments, the rates can be utilized to determine a final conversion rate for the chain segments forming a plurality of polymer chains of each of the plurality of polymer ensembles. In this way, a plurality of pseudo polymer ensembles can be generated, and a rheological model can be utilized to generate rheology data for each of the plurality of pseudo polymer ensembles. As described herein, the rheology data can be utilized to generate a plurality of rheology curves corresponding to the plurality of pseudo polymer ensembles.

[0029] In some embodiments, at step 102 the method 100 can include data preprocessing. In some embodiments, data preprocessing can include selecting a portion of the generated rheology curves to be utilized for training the machine learning model. As described herein, the plurality of polymer ensembles can be pseudo polymer ensembles that are generated by areaction model or simulation. In a specific example, reaction model or simulation can generate more than 30,000 polymer ensembles that are each within a molecular weight range. In this example, a portion of the plurality of polymer ensembles can be selected to be utilized for training the machine learning model.

[0030] As described further in reference to Figure 2, the plurality of polymer ensembles can be utilized to generate a graphical representation of a molecular weight versus a blending ratio of a first polymer and a second polymer. For example, the blending ratio can be a mixture ratio of a quantity of linear low-density polyethylene (LLDPE) and low-density polyethylene (LDPE) within the polymer ensemble. Although LLDPE and LDPE are illustrated in this example, other types of polymers and blending ratios can be utilized in a similar way.

[0031] In some embodiments, step 102 can include rescaling a modulus value of the respective rheology curves for each of the plurality of input features to generate a plurality of output features. As described herein, the plurality of rheology curves can represent a relationship between a strain value and a stress value associated with a particular polymer ensemble. In these embodiments, the modulus value can be rescaled between a value of 0 and 1 to generate a plurality of rescaled rheology curves for the plurality of rheology curves. In some embodiments, the rescaled rheology curves can be utilized as input data for training the machine learning model.

[0032] In some embodiments, step 102 can include calculating a relationship between the rescaled modulus value and a composition identified within the data set. For example, a feature graphical representation can be generated that illustrates the rescaled modulus value versus a composition value. In these embodiments, the composition value can be a blending ratio of a first polymer and a second polymer. In some embodiments, the feature graphical representation or data utilized to generate the feature graphical representation can be utilized to train the machine learning model.

[0033] In some embodiments, the rescaled rheology curves and / or linear rheology curves from the plurality of polymer ensembles can be utilized with the corresponding molecular weight distributions to determine a plurality of structure factor curves. As described further with reference to Figure 3, the plurality of structure factor curves can include the structure factor value over a plurality of molecular weight values. In some embodiments, it can be difficult to utilize the structure factor as a descriptor for the neural network since the values of the structurefactor can be relatively close for polymers with long chain branching and polymers without long chain branching. For this reason, it can be beneficial to utilize a binary classification system to separate polymers with long chain branching and polymers without long chain branching before determining a structural profile.

[0034] In some embodiments, at step 103 the method 100 can include initial structure generation. The initial structure generation can include training a machine learning model such as a neural network utilizing the data processed at step 102. In some embodiments, a neural network can be trained by altering weighting vector values for the neural network based on the data processed at step 102. In this way, the neural network can be trained to identify patterns associated between the rheology of a polymer sample and a molecular weight distribution of the polymer sample. As described herein, the data processed at step 102 can include relationship data between the rheology and molecular weight distribution of pseudo polymer ensembles and / or real polymer ensembles.

[0035] In addition, the neural network can utilize the rheology and molecular weight distribution to determine a structural profile utilizing the structure factor. In some embodiments, the neural network can classify an unknown polymer sample utilizing a binary classification to determine if the unknown polymer sample includes long chain branching. In some embodiments, the neural network can determine the structure factor for the plurality of polymer ensembles to determine whether the plurality of polymer ensembles include long chain branching or do not include long chain branching. Structure factor g can be utilized as a descriptor to correlate linear rheology to polymer structure utilizing Equation 1. g= <R_ g branch)2> / <R_(g linear)2>Equation 1

[0036] The structure factor g can be a result of branch number, branch length and / or branch structure. In some embodiments, the structure factor can be utilized by the neural network to generate a structure profile for the plurality of polymer ensembles. For example, the neural network can utilize a binary classification system to identify a first class of polymer ensembles that include long chain branching and a second class of polymer ensembles that does not include long chain branching. In this example, the second class can utilize the structure factor of 1 to determine the structure profile and the first class can have the structure factor calculated utilizing the molecular weight distribution and linear rheology curve. In these examples, the structurefactor for polymer ensembles with no long chain branching is equal to 1 and the structure factor for polymer ensembles with long chain branching is less than 1 (e.g., 0.95, etc.).

[0037] In some embodiments, the processed data from step 102 can be utilized with a mean-squared-logarithm error (MSLE) or other loss type functions. As used herein, MSLE can be a variant of the mean squared error (MSE) that incorporates a logarithmic function (e.g., natural logarithm, base ten logarithm, etc.). The use of the logarithmic function can be relevant when utilizing values that can span several orders of magnitude. The logarithmic transformation helps to penalize underestimates and overestimates more evenly, making the metric sensitive to the relative differences between predicted and true values.

[0038] In some embodiments, at step 104 the method 100 can include neural network optimization. As used herein, optimizing the neural network can include executing an optimization model on the weight vector values to improve or increase an accuracy of outputs associated with the neural network. For example, a Bayesian optimization model can be utilized to determine optimal weight vector values for the neural network such that the weight vector values generate a weight distribution that is closer to a known weight distribution for a known input sample polymer ensemble. In addition, the optimization model can be utilized to more accurately determine when a particular polymer ensemble includes long chain branching.

[0039] In some embodiments, at step 105 the method 100 can include model evaluation. As used herein, the model evaluation can include comparing the determined classification of a polymer ensemble to a known classification of the polymer ensemble to increase the accuracy of determining whether the polymer ensemble includes long chain branching. Further, a model evaluation can include performing a plurality of iterations by providing rheology data and molecular weight distribution to the neural network to determine an output of the structure factor profile and comparing the output to a known polymer structure. In some embodiments, the model evaluation can include performing an evaluation of a portion of test datasets. That is, the rheology information and the molecular weight distribution associated with the portion of test datasets can be utilized as inputs and the generated structure factor profile outputs can be compared to known polymer structures for the corresponding inputs. In some embodiments, the evaluation can pass when the difference between the generated structure factor outputs and the known polymer structures are within a threshold difference.

[0040] Figure 2 is one example diagram 210 illustrating an approach to generate a rheology curve for a plurality of polymer ensembles. Diagram 210 illustrates a blending ratio graphical representation 211 and a rheology curve graphical representation 212. In some embodiments, the blending ratio graphical representation 211 can illustrate blending ratio 213 of a polymer compared to a molecular weight 214 of a polymer. The blending ratio graphical representation 211 can be a visual representation of data associated with a plurality of pseudo polymer ensembles that have a fixed molecular weight between the range identified by molecular weight 214 on the X-axis and a corresponding blending ratio blending ratio 213 on the Y-axis.

[0041] In some embodiments, the pseudo polymer ensembles can be representations of polymer ensembles that reflect expected properties of the plurality of polymer ensembles. In some embodiments, a particular range of molecular weight 214 and blending ratio 213 can be utilized based on a type of polymer ensemble to be detected. For example, the machine learning model can be trained for polymer types of LLDPE and LDPE with different ranges of the blending ratio 213. In these embodiments, the molecular weight 214 range can be based on a common range of molecular weights for LLDPE and / or LDPE molecules. In a specific example, the molecular weight 214 range can be 103grams per mole (g / mol) to 107g / mol. Although this specific range of molecular weight 214 is utilized in the blending ratio graphical representation 211 other ranges can be selected and utilized in a similar way.

[0042] In some embodiments, the blending ratio 213 can be a ratio between a first polymer and a second polymer. As described herein, the blending ratio 213 can be a ratio between LLDPE molecules, LDPE molecules and / or combinations thereof, however other polymer blending ratios can be utilized in a similar way. In some embodiments, the values of the blending ratio 213 can be expressed in a plurality of ways to define a percentage of the first polymer and a percentage of a second polymer within the sample of the polymer ensemble.

[0043] In some embodiments, the data associated with the blending ratio graphical representation 211 can be utilized to generate data for the rheology curve graphical representation 212. The data associated with the blending ratio graphical representation 211 can be utilized to determine the plurality of values utilized to generate the rheology curve graphical representation 212. For example, the molecular weight and corresponding blending ratio of a particular sample from the blending ratio graphical representation 211 can be utilized to generate a corresponding value of the rheology curve graphical representation 212. The plurality of valuesof the rheology curve graphical representation 212 can represent a rheology value that is predicted utilizing a BoB model with the corresponding blending ratio of the polymer ensemble. The rheology curve graphical representation 212 may also be referred to in the art as a flow curve. The rheology curve graphical representation 212 can be a graphical representation of a relationship between an angular frequency 216 and a modulus value 215 of a polymer ensemble. For example, the rheology curve graphical representation 212 can include a modulus value 215 on a first axis (e.g., y-axis) and an angular frequency 216 on a second axis (e.g., x-axis). In this example, the rheology curve graphical representation 212 can represent the modulus values 215 at corresponding angular frequency values 216.

[0044] In some embodiments, the rheology curve graphical representation 212 can represent the modulus value 215 ranging from 102Pascal (Pa) to 107Pa. Although this range is illustrated in the rheology curve graphical representation 212, other ranges are also possible. In these embodiments, rheology curve graphical representation 212 can represent the angular frequency 216 ranging from 10'8radians / second (rad / s) to 108rad / s. Although this range is illustrated in the rheology curve graphical representation 212, other ranges are also possible. In some embodiments, the rheology curve graphical representation 212 illustrates data from the data set in linear rheology regime to illustrate the modulus at varied the angular frequency 216 of the corresponding polymer ensemble.

[0045] Figure 3 is one example diagram 320 illustrating an approach to rescale a modulus value for a plurality of input features associated with rheology curves to generate a plurality of input features. The diagram 320 can illustrate a rescaled rheology curve graphical representation 321 converted to the structure factor representation 322.

[0046] As described herein, the modulus value can be a shear modulus value (G*). In these embodiments, the modulus value can be a predicted modulus value for each of the plurality of polymer ensembles as described in reference to Figure 2. In some embodiments, the rescaled modulus value can be rescaled from the modulus value 215 of rheology curve graphical representation 212 as illustrated in Figure 2 to a rescaled modulus 323 between 0 and 1 as illustrated in the rescaled rheology curve graphical representation 321. In some embodiments, the angular frequency values 216 from the rheology curve graphical representation 212 as illustrated in Figure 2 can remain within the same range.

[0047] In this way, the rescaled rheology curve graphical representation 321 can rescale the modulus value within a specific range and maintain the corresponding angular frequency. In some embodiments, a MinMaxScaler can be utilized to rescale the modulus values and / or predicted modulus values for the plurality of polymer ensembles within a specified range. As used herein, a MinMaxScaler can be a processing technique for transforming a particular feature or value within a specified range. In these embodiments, a maximum value and a minimum value can be selected from the data set. For example, the maximum modulus value and the minimum modulus value can be selected from the data associated with the rheology curve graphical representation 212 as illustrated in Figure 2. The other modulus values from the data set can be rescaled to fall between the maximum modulus value and the minimum modulus value.

[0048] In some embodiments, the rescaled modulus values 323 can be utilized as input values for generating corresponding composition values 326 and an output feature representation 322 can be generated based on the rescaled modulus values 323 and corresponding composition values 326. The corresponding composition values 326 can be a predicted blending ratio for each of the corresponding rescaled modulus values 323. In this way, the neural network can be trained for a plurality of rescaled modulus values 323 and corresponding composition 326 or blending ratios. In this way, the neural network can receive a modulus value associated with an unknown sample and convert the modulus value to a rescaled modulus value. The rescaled modulus value can be utilized to determine a corresponding composition as illustrated by the output feature representation 322.

[0049] In some embodiments, the linear rheology and corresponding molecular weight distribution for the plurality of polymer ensembles can be utilized to generate the structure factor representation 322. The structure factor representation 322 can include the structure factor 325 with a corresponding molecular weight 326 for the plurality of polymer ensembles. The structure factor representation 322 can be a visual representation of the relationship between a molecular weight 326 and structure factor 325 of the plurality of polymer ensembles. In this way, the neural network can be trained to identify when a polymer ensemble includes long chain branching based on a linear rheology and molecular weight. As described further herein, the neural network can be utilized to perform a binary classification where a first class includes long chain branches and a second class does not include long chain branches. In this example, the first class can havethe structure factor calculated to determine a structural profile while the second class can utilize a designated structure factor of 1.

[0050] Figure 4 illustrates an example of a method 440 for rheology-based modeling. The method 440 can be implemented to train one or more machine learning models of a machine learning module or ANN to predict the structure factor profile for polymer chains from a rheology measurement of an unknown polymer sample. In some examples, the method 440 can be executed by a computing device as described herein. The method 440 can be utilized to train a neural network or other type of machine learning model to determine the structure factor profile for polymer chains from a rheology measurement of an unknown polymer sample. In some embodiments, the trained neural network can be utilized to reverse engineer polymers with a particular rheological behavior, characterizing recycled polymers, and / or designing new polymers or resins.

[0051] At step 431, the method 440 can include determining the linear rheology and molecular weight distribution of a target sample. As described herein, the machine learning model (e.g., neural network, etc.) can be trained to determine a molecular weight distribution of a target sample (e.g., unknown sample, etc.). In some examples, the linear rheology of the target sample can be determined through testing and the molecular weight distribution can be determined based on the linear rheology. In some embodiments, the linear rheology and molecular weight distribution can be utilized to determine whether the target sample includes long chain branching.

[0052] At step 432, the method 440 can include executing a binary classification of the target sample. In some embodiments, the binary classification can be implemented since the difference between the structure factor of a polymer sample with long chain branching can be very similar to the structure factor of a polymer sample with no long chain branching. In this way, utilizing the structure factor as a descriptor within the neural network may not result in an accurate determination. For example, the structure factor for a polymer with no long chain branching can be a value of 1 and the structure factor for a polymer with long chain branching can be a value of 0.95. For this reason, the binary classification model can be utilized to classify the target sample into a first class (e.g., Class 0) that includes long chain branching or a second class (e.g., Class 1) that does not include long chain branching.

[0053] In some embodiments, polymer samples that have the structure factor of 1 are classified into the second class and polymer samples that have the structure factor of less than 1 are classified into the first class. That is, when the structure factor is less than 1, the neural network can classify the sample as including long chain branching.

[0054] At step 433, the method 440 identifies the target sample includes long chain branching. As described herein, the method 440 can identify the target sample of including or having long chain branching when the determined structure factor is less than 1.

[0055] At step 434, the method 440 identifies the target sample does not include long chain branching. As described herein, the method 440 can identify the target sample of not including or not having long chain branching when the structure factor is equal to 1.

[0056] At step 435, the method 440 performs a structural profile prediction. The structural profile prediction can be determined utilizing the structure factor values and corresponding molecular weight values and rheology curves. As described herein, the value of the structure factor can be less than 1, which will alter the structure factor profile differently compared to samples with no long chain branching. In some embodiments, the structural profile can be illustrated by a structural profile graphical representation 430 that represents the structure factor 437 and the molecular weight distribution 438. That is, the structure factor 437 will change between a value of 0 and 1 based on the changes of the molecular weight distribution 438. In this way, the structural profile 439 can represent the structure factor 437 of the target sample for each of the molecular weights of the molecular weight distribution 438.

[0057] At step 436, the method 440 utilizes the structure factor of 1 for the all polymer chains of the target sample. Since the structure factor equals 1 for all polymer chains of the target sample, it may not be necessary to generate a structural profile graphical representation 430 since it would be a straight line across the structure factor 437 at value 1.

[0058] Figure 5 illustrates an example of a method 540 for rheology-based modeling. The method 540 can be implemented to train one or more machine learning models of a machine learning module or ANN to predict the structure factor profile for polymer chains from a rheology measurement of an unknown polymer sample. In some examples, the method 540 can be executed by a computing device as described herein. The method 540 can be utilized to train a neural network or other type of machine learning model to determine the structure factor profile for polymer chains from a rheology measurement of an unknown polymer sample. Insome embodiments, the trained neural network can be utilized to reverse engineer polymers with a particular rheological behavior, characterizing recycled polymers, and / or designing new polymers or resins.

[0059] At step 541, the method 540 can include generating a data set for a plurality of polymer ensembles. In these embodiments, each of the plurality of polymer ensembles comprise a respective plurality of polymers within a defined range of molecular weights. As described herein, the data set can be generated through pseudo polymer ensembles that exhibit predicted properties. As described herein, the predicted properties can be determined based on modeling. For example, the BoB modeling can be utilized to predict the rheology properties of the plurality of polymer ensembles. In this way, a group of polymer ensembles can be selected and a data set can be generated utilizing the predicted properties of the selected polymer ensembles. In some embodiments, the polymer ensembles can be selected based on predicted properties of potential unknown polymer ensembles to be analyzed.

[0060] In some embodiments, a polymer ensemble refers to a collection or group of polymer molecules that share certain characteristics and / or properties. As used herein, polymers are relatively large molecules composed of repeating structural units called monomers. The polymer ensemble concept acknowledges an inherent variability that can exist within a group of polymer molecules, which may have differences in terms of chain lengths, molecular weights, conformations, and / or chemical compositions.

[0061] In some embodiments, the plurality of polymer ensembles are compositions of Linear Low-Density Polyethylene (LLDPE), Low-Density Polyethylene (LDPE), and combinations thereof. In these embodiments, the method 540 can include generating a rheology curve for one or more of the plurality of polymer ensembles based on a blending ratio of the LLDPE and LDPE. As described herein with reference to Figure 2, a blending ratio 213 with corresponding molecular weight 214 can be utilized to generate a predicted rheology curve graphical representation 212. In some embodiments, the method 540 includes generating a linear rheology curve for one or more of the plurality of polymer ensembles based on a blending ratio of the LLDPE and LDPE.

[0062] At step 542, the method 540 can include generating a respective rheology curve for each of the plurality of polymer ensembles. In some embodiments, the rheology curve is a representation of a loss modulus versus angular frequency of the plurality of polymer ensembles.In these embodiments, the respective rheology curve comprises a plurality of input features for a corresponding polymer ensemble. In these embodiments, the strain value can represent a pseudo strain to be applied to a particular polymer ensemble and the corresponding stress value can be a predicted stress value for the polymer ensemble based on a predictive model (e.g., BoB model, etc.). In some embodiments, the modulus value, strain value, stress value, and / or angular frequency value can be simulated values for the plurality of polymer ensembles. In some embodiments, the plurality of input features includes a first value to represent an angular frequency applied to a corresponding polymer ensemble and a second value to represent a modulus of the corresponding polymer ensemble at the first value. As described herein, the respective rheology curves are representations of a relationship between a modulus value and an angular frequency value of the plurality of polymer ensembles. As described herein, this can be a predicted relationship based on a predictive model utilized to analyze the selected polymer ensembles.

[0063] At step 543, the method 540 can include rescaling a modulus value of the respective rheology curves for each of the plurality of input features to generate a plurality of output features. As described herein, the rescaled modulus value can be utilized as an input for training the neural network and the output features can be composition features. The output features and / or input features can be utilized to train a neural network to alter the weighting vectors such that a rescaled modulus value of an unknown polymer ensemble can be utilized to accurately predict the composition and / or molecular weight distribution of the unknown polymer ensemble.

[0064] In some embodiments, the method 540 can include generating a rescaled rheology curve for one or more of the plurality of polymer ensembles based on the plurality of output features. As described herein, the rescaled rheology curve can be a representation of the rescaled modulus value versus the angular frequency value. In this way, the rescaled modulus value can be utilized to generate a composition value that can be utilized to train a machine learning model as described further herein.

[0065] At 544, the method 540 can include training a machine learning model to determine the structure factor profile for polymer chains from a rheology measurement of an unknown polymer sample utilizing the plurality of output features with corresponding values from the data set. In some embodiments, the machine learning model can be a neural networkthat can be trained utilizing the rescaled modulus values and corresponding composition values as described herein. In these embodiments, the determined composition values can be utilized to accurately determine a molecular weight distribution and / or other properties of the unknown polymer sample. As described herein, the molecular weight distribution and the linear rheology curve can be utilized to determine the structure factor associated with the polymer chains within a polymer ensemble.

[0066] In some embodiments, the method 540 includes generating a binary classification model for the unknown polymer sample that comprises a first class that includes polymer ensembles that include long-chain branching (LCB) and a second class that includes polymer ensembles that lack LCB. As described herein, a binary classification system can be utilized to increase an accuracy of identifying polymers with long chain branching and identifying polymers without long chain branching. In this way, the structure factor profile can be individually determined for the polymers with long chain branching, which can have a different structure factor for different molecular weights.

[0067] As described herein, the modulus value from a rheology measurement of an unknown polymer sample can be rescaled and utilized as an input value for the machine learning model to determine an output composition value. The output composition value can be a blend ratio of the unknown polymer sample. As described herein, a correlation can exist between the composition value and a molecular weight distribution. In this way, the machine learning model can utilize the composition value to determine the molecular weight distribution of the unknown polymer sample.

[0068] In some embodiments, the method 540 can include evaluating the machine learning model by providing a known rheology curve for a known polymer ensemble to the machine learning model to generate an output molecular weight distribution graph and comparing the output molecular weight distribution graph to a graphical representation of the unknown polymer sample. In some examples, evaluating the machine learning model can include performing a plurality of test data inputs to the machine learning model to determine when the outputs provided by the machine learning model are within a particular threshold or range output values. In this way, the machine learning model can be further tuned to increase accuracy of determining the molecular weight distribution of unknown polymer samples.

[0069] Figure 6 illustrates an example of a machine readable medium 650 for rheologybased modeling. The machine readable medium 650 can be communicatively connected to a processor resource 652 by a communication path 654. In some examples, a communication path 654 can include a wired or wireless connection that can allow communication between devices and / or components within a single device. As used herein, the processor resource 652 can include, but is not limited to: a central processing unit (CPU), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a metal-programmable cell array (MPCA), a semiconductor-based microprocessor, or other combination of circuitry and / or logic to orchestrate execution of instructions 656, 658, 660, 662. In a specific example, the processor resource 652 utilizes a non-transitory computer-readable medium storing instructions 656, 658, 660, 662, that, when executed, cause the processor resource 652 to perform corresponding functions.

[0070] The machine readable medium 650 may be electronic, magnetic, optical, or other physical storage device that stores executable instructions. Thus, a non-transitory machine- readable medium (MRM) (e.g., machine readable medium 650) may be, for example, a non- transitory MRM comprising Random-Access Memory (RAM), read-only memory (ROM), an Electrically Erasable Programmable ROM (EEPROM), a storage drive, an optical disc, and the like. The machine readable medium 650 may be disposed within a controller and / or computing device. In this example, the executable instructions 656, 658, 660, 662, can be “installed” on the device. Additionally, and / or alternatively, the machine readable medium 680 can be a portable, external, or remote storage medium, for example, which allows a computing system to download the instructions 656, 658, 660, 662, from the portable / external / remote storage medium. In this situation, the executable instructions may be part of an “installation package”.

[0071] The machine readable medium 650 includes instructions 656 to provide a data set for a plurality of polymer ensembles. In these embodiments, each of the plurality of polymer ensembles comprise a respective plurality of polymers within a defined range of molecular weights and a blending ratio of the respective plurality of polymers.

[0072] The machine readable medium 650 includes instructions 658 to generate a respective rheology curve for the plurality of polymer ensembles based on a predicted modulus value to the respective plurality of polymers and a predicted angular frequency value of the respective plurality of polymers for each of the plurality of polymer ensembles. In theseembodiments, the predicted modulus value and predicted angular frequency value can be for a particular strain that can be a simulated strain value. As described herein, the plurality of polymer ensembles can include pseudo polymer ensembles that can represent a polymer ensemble within a particular molecular weight range. In this way, the predicted modulus, predicted strain, and / or predicted stress of the plurality of polymer ensembles can be based on predictive modeling, such as, but not limited to BoB modeling.

[0073] In these embodiments, the rheology curve comprises a plurality of input features based on the predicted modulus and predicted angular frequency of the plurality of polymer ensembles. In some embodiments, the respective rheology curves are linear rheology curves. As used herein, a linear rheology curve can refer to a portion of rheological behavior of a material that exhibits a linear relationship between strain and stress. In rheology, stress is the force applied to a material per unit area, and strain is the resulting deformation.

[0074] In some embodiments, the machine readable medium 650 can include instructions to generate the respective linear rheology curve utilizing a correlation of features under different frequencies of rheology. For example, the different frequencies of rheology can refer to different conditions that are utilized during rheology measurements. For example, different frequencies can include, but are not limited to static frequency, low frequency (e.g., 0.1 Heartz (Hz) to 10 Hz), intermediate frequency (e.g., 10 Hz to 1000 Hz), and / or high frequency (e.g., above 1000 Hz, etc.). In these embodiments, the different frequencies of rheology can be utilized to determine relationships between the applied strain and resulting stress at different conditions.In some embodiments, the machine readable medium 650 can include instructions to generate the respective rheology curves utilizing a correlation of features under different frequencies of oscillation. In these embodiments, the features can be a modulus that can be based on the blending ratio and the different frequencies can be different levels of angular frequency. In this way, the respective rheology curve can be generated for each of the plurality of polymer ensembles that utilize different predicted modulus values and corresponding predicted angular frequency values.

[0075] In some embodiments, the machine readable medium 650 can include instructions to map nonlinear relationships between a molecular structure of the polymer ensembles and rheology behavior of the polymer ensembles. In some embodiments, the machine readable medium 680 can include instructions to train the machine learning model to identify nonlinearrelationships within the rheology measurement and compare the identified nonlinear relationships to the rheology curve for the plurality of polymer ensembles. As used herein, nonlinear relationships to the rheology curve refer to areas of a rheology curve that do not adhere to linear relationships. In rheology, a relatively high stress (e.g., high frequency, etc.) and / or a relatively high strain of the polymer material can result in nonlinear behavior. Nonlinear behavior in the rheology curve indicates that the response of the material has deviated from a simple, proportional relationship between stress and strain. Some types of nonlinear relationships observed in rheology include nonlinear elasticity, yield stress, thixotropy and rheopexy, strain hardening and strain softening, viscoelasticity, among other nonlinear relationships.

[0076] The machine readable medium 650 includes instructions 660 to rescale a modulus value (e.g., shear modulus value, etc.) for the plurality of input features of the respective rheology curves to generate a plurality of output features. In these examples, the modulus value is a numerical value representing the ratio of the predicted stress and predicted strain. Specifically, the shear modulus value represents a material property that characterizes a material's response to shear stress. Shear stress occurs when parallel forces act on different planes of a material in opposite directions, causing deformation by sliding layers of molecules over each other. Mathematically, the shear modulus is defined as the ratio of shear stress to shear strain. That is, the shear modulus represents the material's resistance to deformation under shear stress. A higher shear modulus indicates greater stiffness and resistance to shear deformation, while a lower shear modulus suggests a more compliant and deformable material.

[0077] The machine readable medium 650 includes instructions 662 to train a machine learning model to determine an unknown structure factor profile for an unknown polymer from a rheology measurement of the unknown polymer utilizing small-amplitude oscillatory shear (SAGS) data. As used herein, the SAGS data can be obtained by subjecting a material to a controlled oscillatory shear deformation with a small amplitude. For example, in some SAGS experiments, a sinusoidal shear stress or strain is applied to the material, and the resulting response (strain or stress) is measured. The amplitude of the applied shear is kept small enough to ensure that the material responds linearly to the deformation. This means that the material's response is directly proportional to the applied stress or strain, allowing for the characterization of its linear viscoelastic behavior. As described herein, the structure factor profile can be determined based on the structure factor associated with a molecular weight distribution of apolymer that has been classified as having long chain branching. As described herein, a binary classification system can be utilized to separate polymer ensembles that include long chain branching from polymer ensembles that do not include long chain branching.

[0078] In some embodiments, machine readable medium 650 includes instructions to determine a degree of polymerization of the unknown polymer based on the rheology measurement of the unknown polymer. The degree of polymerization of a polymer can include a measure of the number of monomer units (repeating structural units) in a polymer chain. For example, the degree of polymerization can quantify the extent to which monomer units are polymerized to form the polymer. In some embodiments, the molecular weight distribution that is determined by the neural network can be utilized with the molar mass of a monomer unit to determine the degree of polymerization. The degree of polymerization can correspond to a length of polymer chains, which can affect a polymer's mechanical strength, viscosity, and other physical and chemical characteristics of the polymer.

[0079] As described herein, the machine learning model can be a neural network that can be trained utilizing the input data and corresponding output data associated with the plurality of polymer ensembles. As described herein, this data can be generated by utilizing predictive modeling such as BoB or other types of predictive modeling associated with polymer structure. In this way, the quantity of the plurality of polymer ensembles and corresponding data can be relatively high compared to utilizing actual measured data.

[0080] In addition, the data can be more cohesive since the data was collected utilizing the same or similar predictive modeling techniques. In some embodiments, the machine learning model can be tuned based on the linear relationships and nonlinear relationships of the data set. The machine learning model can be utilized to predict a plurality of features of an unknown polymer sample including, but not limited to a molecular weight distribution and / or a blending ratio.

[0081] Figure 7 illustrates an example of a device 770 for rheology-based modeling. In some examples, the device 770 is a computing device that includes a processor resource 752 and a machine readable medium 750 to store instructions 771, 772, 773, 774, 775, 776 that are executed by the processor resource 752 to perform particular functions. Figure 7 illustrates how a computing device can execute instructions to perform functions described herein.

[0082] The device 701 includes instructions 771 stored by the machine readable medium 750 that is executed by the processor resource 752 to generate a data set utilizing a rheology model for a plurality of polymer ensembles. In these embodiments, the rheology model can be a predictive model such as a BoB model that can be utilized to predict rheology data based on the properties of the plurality of polymer ensembles. In these examples, the data set includes molecular weights and blending ratios for corresponding polymers of the plurality of polymer ensembles. As described herein, the data set can be generated using pseudo polymer ensembles that represent different blending ratios of polymers and / or different molecular weights. In this way, the data set can be generated without having to perform corresponding experiments on the polymer ensembles.

[0083] The device 770 includes instructions 772 stored by the machine readable medium 750 that is executed by the processor resource 752 to combine experimental data with the data set. In these examples, the experimental data includes rheology measurements of additional polymer ensembles. As described herein, the plurality of polymer ensembles can be pseudo polymer ensembles. In this way, a plurality of additional experimental data can be added to the data set. The additional experimental data can be data collected from experiments conducted on real polymer ensembles. In some embodiments, the experimental data can be utilized to improve the data set by adding real world data that is not based on a particular model. In some embodiments, the experimental data can help identify outliers of the particular model utilized to generate the data set.

[0084] The device 770 includes instructions 773 stored by the machine readable medium 750 that is executed by the processor resource 752 to generate a respective rheology curve for the plurality of polymer ensembles based on a modulus value from a predicted stress applied and a predicted resulting strain for corresponding polymers of each of the plurality of polymer ensembles. In these embodiments, the respective rheology curves each comprise a plurality of input features that include a modulus value and angular frequency value for the plurality of polymer ensembles.

[0085] In some embodiments, the device 701 includes instruction to generate a rheology curve for one or more of the plurality of polymer ensembles based on a blending ratio of LLDPE and LDPE of the polymer ensembles. The device 701 includes instructions 774 stored by the machine readable medium 750 that is executed by the processor resource 752 to rescale themodulus value for the plurality of input features of the respective rheology curves to a scale of a value of 0 to 1 to generate a plurality of output features.

[0086] The device 701 includes instructions 775 stored by the machine readable medium 750 that is executed by the processor resource 752 to generate a rescaled rheology curve for each of the respective rheology curves based on the plurality of output features. In some embodiments, the device 701 includes instructions to calculate a relationship between the rescaled modulus value and a composition identified within the data set. In these examples, the composition is a blending ratio between a first polymer and a second polymer of the plurality of polymer ensembles.

[0087] The device 701 includes instructions 776 stored by the machine readable medium 750 that is executed by the processor resource 752 to train a machine learning model to determine an unknown structure factor profile for an unknown polymer based on a rheology measurement of the unknown polymer utilizing the rescaled rheology curve with corresponding molecular weights and blending ratios for the plurality of polymer ensembles from the data set. As described herein, the unknown polymer includes no LCB when the structure factor is equal to 1 and includes LCB when the structure factor is less than 1. In this way, the plurality of polymer ensembles can be separated into a first class that includes LCB and a second class that does not include LCB. As described herein, the structure factor profile can be generated for the first class based on the linear rheology and molecular weight distribution.

[0088] In some embodiments, the device 701 includes instructions to calculate a composition of the plurality of polymer ensembles based on the rescaled rheology curve. As described herein, the composition of the plurality of polymer ensembles can be utilized to determine a molecular weight distribution and / or other properties associated with the unknown polymer sample.

[0089] In some embodiments, the device 701 includes instructions to map a relationship between the rheology measurement of the unknown polymer and a corresponding molecular weight distribution of the unknown polymer to calculate a ratio. In some embodiments, the device 701 includes instructions to identify the unknown polymer includes no long-chain branching (LCB) when the ratio is approximately 1 : 1 and identify the unknown polymer includes LCB when the ratio is not 1: 1.

[0090] As described herein, the device 701 includes instructions to calculate a relationship between the structure factor profile and molecular weight when the unknown polymer includes LCB. In these embodiments, the device 701 can include instructions to calculate the relationship for LDPE, LLDPE, and LDPE / LLDPE blends. In some embodiments, the relationship is based on a blending ratio of the unknown polymer.

[0091] Although specific embodiments have been described above, these embodiments are not intended to limit the scope of the present disclosure, even where only a single embodiment is described with respect to a particular feature. Examples of features provided in the disclosure are intended to be illustrative rather than restrictive unless stated otherwise. The above description is intended to cover such alternatives, modifications, and equivalents as would be apparent to a person skilled in the art having the benefit of this disclosure.

[0092] The scope of the present disclosure includes any feature or combination of features disclosed herein (either explicitly or implicitly), or any generalization thereof, whether or not it mitigates any or all of the problems addressed herein. Various advantages of the present disclosure have been described herein, but embodiments may provide some, all, or none of such advantages, or may provide other advantages.

[0093] In the foregoing Detailed Description, some features are grouped together in a single embodiment for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the disclosed embodiments of the present disclosure have to use more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive subject matter lies in less than all features of a single disclosed embodiment. Thus, the following claims are hereby incorporated into the Detailed Description, with each claim standing on its own as a separate embodiment.

Claims

ClaimsWhat is claimed is:

1. A method, comprising: generating a data set for a plurality of polymer ensembles, wherein each of the plurality of polymer ensembles comprises a corresponding plurality of polymers within a defined range of molecular weights; generating a respective rheology curve for each of the plurality of polymer ensembles, wherein the respective rheology curve comprises a plurality of input features for a corresponding polymer ensemble; rescaling a modulus value of the respective rheology curves for each of the plurality of input features to generate a plurality of output features; and training a machine learning model to determine a structure factor profile for polymer chains from a rheology measurement of an unknown polymer sample utilizing the plurality of output features with corresponding values from the data set.

2. The method of claim 1, further comprising generating a rescaled rheology curve based on the plurality of output features.

3. The method of claim 1, further comprising generating a binary classification model comprising for the unknown polymer sample that comprises a first class that includes polymer ensembles that include long-chain branching (LCB) and a second class that includes polymer ensembles that lack LCB.

4. The method of claim 1, wherein the rheology curve is a representation of a loss modulus versus angular frequency of the plurality of polymer ensembles.

5. The method of claim 1, wherein the plurality of polymer ensembles are compositions of linear low-density polyethylene (LLDPE), low-density polyethylene (LDPE), and combinations thereof.

6. The method of claim 5, further comprising generating a linear rheology curve for one or more of the plurality of polymer ensembles based on a blending ratio of the LLDPE and LDPE.

7. The method of claim 1, wherein the plurality of input features include a first value to represent a rate of oscillation of a corresponding polymer ensemble and a second value to represent a shear modulus of the corresponding polymer ensemble at the first value.

8. The method of claim 1, further comprising training the machine learning model to identify nonlinear relationships within the rheology measurement and compare the identified nonlinear relationships to the rheology curve for the plurality of polymer ensembles.

9. The method of claim 1, wherein the rheology measurement is a measured rheology of the unknown polymer utilizing oscillatory rheometer.

10. The method of claim 1, further comprising mapping nonlinear relationships between a linear rheology, molecular weight distribution, and a structure factor profile for the plurality of polymer ensembles.

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